Citation
Rigorous compilation of the Northern International Reference Stars

Material Information

Title:
Rigorous compilation of the Northern International Reference Stars
Creator:
Cole, Carl Stephen, 1954-
Publication Date:
Language:
English
Physical Description:
xi, 133 leaves : ; 28 cm.

Subjects

Subjects / Keywords:
Astronomical catalogs ( jstor )
Correctional system ( jstor )
Declination ( jstor )
Estimation methods ( jstor )
Least squares ( jstor )
Parametric models ( jstor )
Proper motions ( jstor )
Radiocarbon ( jstor )
Reference stars ( jstor )
Right ascension ( jstor )
Astronomy thesis Ph.D
Dissertations, Academic -- Astronomy -- UF
Stars -- Catalogs ( lcsh )
Stars -- Proper motion ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph.D.)--University of Florida, 1986.
Bibliography:
Bibliography: leaves 131-132.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
Carl Stephen Cole.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000940976 ( ALEPH )
16656153 ( OCLC )
AEQ2510 ( NOTIS )
AA00004855_00001 ( sobekcm )

Downloads

This item has the following downloads:


Full Text












RIGOROUS COMPILATION OF THE
NORTHERN INTERNATIONAL REFERENCE STARS






BY


CARL STEPHEN COLE


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1986




RIGOROUS COMPILATION OF THE
NORTHERN INTERNATIONAL REFERENCE STARS
BY
CARL STEPHEN COLE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA


ACKNOWLEDGEMENTS
I would like to thank Drs. T. Corbin, J. Hughes and C.
Smith of the Astrometry Division of the U.S. Naval
Observatory and Dr. W. Warren the Astronomical Data Center
at the NASA Goddard Space Flight Center for providing those
data required to carry out this research. I would also like
to acknowledge the support which I received from the
Division of Sponsored Research at the University of Florida
in the form of a graduate research assistanceship.
Dr. Heinrich Eichhorn suggested the topic of this
research and has guided me through its execution. He has
also introduced me to the international community of
astrometrists and has gained their co-operation on my
behalf. I am very grateful for Dr. Eichhorn's advice and
for the knowledge which he has imparted to me.
Finally I owe many thanks to Leslie Gilbert for her
patience and the emotional support which she has given me
throughout my tenure as a graduate student.
11


TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS ii
LIST OF TABLES v
LIST OF FIGURES ix
ABSTRACT x
CHAPTER
I. INTRODUCTION 1
The Establishment of an Inertial Reference
Frame 1
The International Reference Star Program ... 4
II. CATALOGUE COMPILATION 7
The Estimation of Systematic Differences ... 7
Critique and Analysis of the Tabular
Procedure 10
Description of Simultaneous Reduction .... 16
III. REDUCTION PROCEDURES 20
Precession 20
Model Parameter Estimation 22
Star Parameter Estimation 25
Sequence of Iterations 27
IV. RESULTS 110
Residuals Between the Two Versions of the
NIRS 110
Internal Errors 118
Perth 70 Residuals 122
V. CONCLUSIONS 129
iii


REFERENCES 131
BIOGRAPHICAL SKETCH 133
iv


LIST OF TABLES
TABLE PAGE
1. Succesive Corrections Computed with Biased
Estimates 15
2. Smoothing Coefficients 25
3. Iteration Sequence 30
4. Independent Catalogues Used in the Compilation
of the NIRS 32
5. Corrections Applied to the AGK3R 39
6. Corrections Applied to the AGK2A 41
7. Corrections Applied to the W20 43
8. Corrections Applied to the Albany 10 45
9. Corrections Applied to the Bonn 00 47
10. Corrections Applied to the Bord 50 49
11. Corrections Applied to the Sch 50
12. Corrections Applied to the Bonn 25 52
13. Corrections Applied to the W2-50 53
14. Corrections Applied to the W3-50 55
15. Corrections Applied to the GCH 1-50 57
16. Corrections Applied to the Cape02 00 58
17. Corrections Applied to the Nice 10 59
18. Corrections Applied to the Nice 25 60
19. Corrections Applied to the GCH Z 10 60
20. Corrections Applied to the Paris 90 61
v


21. Corrections Applied to the Paris 00 62
22. Corrections Applied to the GCH 2-25 63
23. Corrections Applied to the Berl 20 64
24. Corrections Applied to the GCH 00 64
25. Corrections Applied to the Toul3 00 65
26. Corrections Applied to the Cape 2-25 66
27. Corrections Applied to the Cape 3-25 67
28. Corrections Applied to the W 40 68
29. Corrections Applied to the W 00 69
30. Corrections Applied to the W ZOD 25 70
31. Corrections Applied to the Cape 1-50 71
32. Corrections Applied to the Bord 00 72
33. Corrections Applied to the ALB99 00 72
34. Corrections Applied to the Mun97 OOi 73
35. Corrections Applied to the Mun97 OOii 74
36. Corrections Applied to the Kon 00 74
37. Corrections Applied to the Pulk99 00 75
38. Corrections Applied to the Madn 10 76
39. Corrections Applied to the Berg 1-25 77
40. Corrections Applied to the ABB-6 00 79
41. Corrections Applied to the Buch 50 79
42. Corrections Applied to the Bonn09 00 80
43. Corrections Applied to the ABB+20 00 80
44. Corrections Applied to the ABB0 00 81
45. Corrections Applied to the Lund44 50 82
46. Corrections Applied to the Stras 30 83
47. Corrections Applied to the Cin 00 85
vi


48. Corrections Applied to the PFKSZ 87
49. Corrections Applied to the Lund42 50 89
50. Corrections Applied to the Cin 25 91
51. Corrections Applied to the Moscow40 50 93
52. Corrections Applied to the Tri 25 95
53. Corrections Applied to the Bruss 25 96
54. Corrections Applied to the Leid21 25 98
55. Corrections Applied to the Leid24 25 99
56. Corrections Applied to the Lund 25 100
57. Corrections Applied to the Leid27 25 100
58. Corrections Applied to the Berl Z 10 101
59. Corrections Applied to the Konl9 25 101
60. Corrections Applied to the Toul3 00-II 102
61. Corrections Applied to the Pulk 10 102
62. Corrections Applied to the Lick 17 103
63. Corrections Applied to the Lick 28 103
64. Corrections Applied to the Turin 10 104
65. Corrections Applied to the Bord 00-11 104
66. Corrections Applied to the 0ttw28 25 105
67. Corrections Applied to the Ottw42 50 107
68. Corrections Applied to the Konl7 25 109
69. Mean Right Ascension Residuals, Corbin minus
Cole 114
70. Mean Declination Residuals, Corbin minus Cole . 115
71. Mean Proper Motion in Right Ascension Residuals,
Corbin minus Cole 116
72. Mean Proper Motion in Declination Residuals,
Corbin minus Cole 117
vii


73. Mean RMS errors 119
74. Position Residuals, Perth 70 minus NIRS 123
75. Mean Right Ascension Residuals, Perth 70 minus
NIRS 127
76. Mean Declination Residuals, Perth 70 minus NIRS 128
viii


LIST OF FIGURES
FIGURE PAGE
1. Distribution of Right Ascension Residuals,
Corbin minus Cole Ill
2. Distribution of Declination Residuals, Corbin
minus Cole Ill
3. Distribution of Proper Motion in Right Ascension
Residuals, Corbin minus Cole 112
4. Distribution of Proper Motion in Declination
Residuals, Corbin minus Cole 112
5. Distribution of Right Ascension RMS Errors .... 120
6. Distribution of Declination RMS Errors 120
7. Distribution of Proper Motion in Right Ascension
RMS Errors 121
8. Distribution of Proper Motion in Declination RMS
Errors 121
9. Distribution of Right Ascension Residuals, Perth
70 minus NIRS 125
10. Distribution of Declination Residuals, Perth 70
minus NIRS 125
ix


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
RIGOROUS COMPILATION OF THE
NORTHERN INTERNATIONAL REFERENCE STARS
By
Carl Stephen Cole
December 1986
Chairman: Heinrich Eichhorn
Major Department: Astronomy
The tabular method of determining the systematic
differences between two star catalogues is discussed. It is
noted that the tabular method is subjective in nature and
that the estimation of the model parameters does not use all
available model constraints. Furthermore, these estimates
are not least squares estimates nor are they unbiased.
The simultaneous estimation of both target parameters and
model parameters is applied to the compilation of a complete
star catalogue. By simultaneously using all available
constraints on all available data, more precise estimates
for the target parameters are obtained. The input material
x


of the Northern International Reference Stars (NIRS) is used
and the resulting catalogue is compared to the NIRS
catalogue compiled by Corbin using standard techniques. It
is shown that the new estimates of the star parameters have
smaller formal errors than estimates derived from the same
material but using conventional procedures. Both versions
of the NIRS are used to predict the star positions of the
later observed Perth 70: A Catalogue of Positions of 24900
Stars and these predicted positions are compared to the
actual observed positions. It is found that a simultaneous
reduction results in a slight but significant improvement in
the predicted positions.
xi


CHAPTER I
INTRODUCTION
The Establishment of an Inertial Reference Frame
One of the goals of kinematic astronomy is the empirical
establishment of a frame of reference in which Newton's
first and third postulates of motion are valid. To those
involved in this endeavor, two important facts become
readily apparent. First, in all areas of science which
involve dynamics, such as lunar and planetary theory,
galactic dynamics, astronautics, among others, the
determination of an inertial reference frame to some
required accuracy is essential. Second, the complexities of
the determination of this inertial reference frame are often
completely ignored. The fact that the determination of an
inertial reference frame has been taken for granted is a
tribute to all the astronomers who have, over the centuries,
performed this indispensable service for their fellow
scientists. This work, however, is never finished. As
science progresses so does the precision of measurements
increase which in turn requires an increased accuracy of the
standard.
Due to the rotational and revolutionary motion of the
Earth, it has long been realized that stars can be used to
1


2
define, in practice, an inertial reference frame. The
sighting of stars has been used by sailors for centuries to
determine their latitude and longitude on the rotating Earth
and, more recently, star positions are being used to
navigate the Voyager spacecraft past Jupiter, Saturn, Uranus
and Neptune. In kinematic astronomy, the most frequently
used coordinates are not cartesian coordinates but spherical
polar coordinates. This is so because the position of an
object, which is defined by two angular coordinates (e.g.
right ascension and declination), can be accurately
determined to a fraction of a microradian while the radial
distance is known only to one or two significant figures if
at all. The position of a star, defined by these two
angular coordinates, fixes its place on the imaginary
"celestial sphere." Conversely, any two non-diametrically
opposed stars whose position and proper motion estimates
are given in a star catalogue, uniquely define the
coordinate system of that catalogue and provide the basis
for the establishment of an inertial reference frame.
A coordinate system (or simply a "system") in connection
with a star catalogue, is not necessarily inertial; rather,
estimates for the parameters needed to transform the system
to an inertial reference frame are assumed known. If
estimates for the distances and radial velocities of some of
the stars in a catalogue are known, this information can be
combined with the positions and proper motions in order to


3
estimate Oort's constants of galactic shear and galactic
rotation as well as the solar motion. Thus the kinematics
of our Milky Way galaxy are described and an inertial
reference frame is established.
A fundamental star catalogue contains the positions and
proper motions of at least several hundred stars and
therefore overdetermines, in a sense, the system which is
defined. In light of this, certain concepts related to a
catalogue's system need further clarification. Eichhorn
(1982) has given concise definitions to these concepts.
First, it must be borne in mind that the "star positions"
which are listed in a star catalogue are only estimates. If
the errors in these estimates are purely random, the system
is defined by any randomly selected subset of star positions
to the precision of the individual positions. However, if
there are systematic errors of star positions dependent on
which part of the sky is under consideration, or other
parameters charcterizing the stars such as brightness or
color, the system will be dependent on which subset of star
positions is used to define it.
It is often found that there exist differences in the
systems of catalogues which are functions of the sections of
the sky under consideration. In order to combine
independent star catalogues into a compilation catalogue,
these systematic differences must be modeled and the
parameters of these models must be estimated. In this way


4
it is possible to correct the systematic trends of each
independent catalogue in order to bring them all onto a
common "system."
This research investigates the techniques used to model
the systematic differences between the systems of star
catalogues, as well as the procedures used to estimate the
parameters of these models.
The International Reference Star Program
The International Reference Star program (IRS) is a
multinational effort whose execution has required more than
a quarter of a century. Its aim is to provide more than
40,000 accurate and precise star positions and proper
motions over the entire sky (Scott 1967, Scott and Schombert
1970, Smith 1979, Corbin 1985). Transit circle catalogues
from around the globe are being compiled into compilation
catalogues with a density of about one star per square
degree. With these catalogues, the fundamental system of
the Fourth Fundamental Catalogue (FK4) (Fricke and Kopff
1963) can be extended to fainter magnitudes such that over
300,000 star positions of all stars to the 9th magnitude can
be tightly related to the fundamental system.
The northern half of this program (NIRS) can be traced
back to the Catalog of Reference Stars for the Dri tter
Katalog der Astronomischen GeselIschaft (AGK3R). One of the
aims of the NIRS was to provide proper motions for the AGK3R


5
stars. Unavoidably (and fortunately), this also led to
improved positions. The NIRS was compiled from observed
positions in 64 independent meridian catalogues whose mean
epochs date back as far as 1889.
The catalogue of Northern International Reference Stars
(NIRS) (Corbin 1974, 1977, 1982) contains positions and
proper motions of 20194 stars in the declination zone -5 to
+90 degrees of apparent visual magnitude 6.5 to 9.5. NIRS
was compiled from independent catalogues (ICs) which only
contain star positions measured at a given epoch. Corbin
constructed this catalogue in a two-step process. First,
the systematic differences between the star positions in
each of the ICs and the reference star positions of the FK4,
which is the target system, were calculated. Systematic
corrections were computed from these differences and applied
to all star positions in the ICs in order to bring them onto
the system of the FK4. Second, from the thus corrected and
weighted IC positions, a complete catalogue of appropriate
stars was constructed.
It must be noted that Corbin used no intercomparisons of
ICs to calculate systematic corrections. That is, when
estimating the parameters of the models of systematic
differences, the only constraints which were used were those
which minimized the systematic differences in star positions
between ICs and and the reference catalogue. The
constraints which require that the systematic differences in


6
star positions between independent catalogues also be
minimized were not used. In light of this fact, it is
apparent that better estimates of the parameters are
available with procedures which use all available
constraints on all available data (cf. Eichhorn and Cole
1985).


CHAPTER II
CATALOGUE COMPILATION
The Estimation of Systematic Differences
The difference between the position estimate of a star in
two catalogues originates from the random errors of the
observations from which the positions in each of the
catalogues were computed and the inconsistencies of the
systems defined by the star positions of the catalogues. In
computing corrections to bring a catalogue onto a system,
one seeks to minimize the differences between the defining
systems without changing the accidental errors in the
individual position estimates. In correcting for systematic
errors, the usual procedure is to model the source of the
error, guided by the geometry and, when indicated, the
physics of the actual measuring situation. In the case of
star catalogues this technique is impossible, in practice,
because there are too many small sources of systematic
errors which occur at different stages of the data reduction
process. Often, their presence is either unsuspected or
reasonably accurate models for them are difficult to
establish. Systematic errors can, for example, be
introduced by an inaccurate refraction correction. Likewise
it is difficult to determine the optical characteristics of
7


8
an instrument which was destroyed in the Second World War.
It is thus easier to lump errors from all sources together
and model them by some empirical interpolary function.
We see that the systems defined by star catalogues, since
they are only estimates, can only approximate the
unobtainable ideal target inertial reference frames.
Therefore the actual, true systematic errors of a catalogue
can never be rigorously and unambiguously found or even
defined. What can be defined and estimated are model
dependent systematic differences between the systems defined
by any two catalogues. Once systematic differences^ are
found, they can be applied to the positions in one catalogue
as systematic corrections in order to bring the two
catalogues ideally onto the same system. Regardless of the
functional form of the model for the systematic differences
between two catalogues, when two or more catalogues are
being combined, there are, in principle, two distinct
methods to compute these systematic differences.
The traditional methods utilize the comparisons of the
positions of only those stars common to each IC and the
reference system (the FK4 in this case) for the derivation
of the systematic corrections for that IC. Systematic
corrections are then determined from these individual
comparisons only. Since the star density in a typical IC is
1
For the purposes of this research, the term "systematic
error" will be used to denote the systematic difference
between an IC and the FK4.


9
much higher than that of the reference system, systematic
properties of an IC have often been estimated from as few as
5 percent of the star positions in that IC.
Traditionally, position differences averaged over blocks
of the sky and smoothed with adjacent blocks are applied as
systematic corrections. It appears that several problems
arise with this traditional tabular method. First, the
smoothing coefficients are chosen on a subjective basis.
Second, not all of the available model constraints are used
in estimating the model parameters. This means that the
procedure which estimates the model parameters does not
constrain these model parameters to minimize some measure of
the systematic differences between all ICs but rather the
model parameters are constrained only to minimize a measure
of the systematic differences between each IC and the
fundamental system. Finally when estimating the parameters
in the tabular model, the estimates obtained are not least
squares estimates but estimates used only because, from a
computational standpoint, they are easily accessible. While
this results in an acceptable star catalogue, the process
involves a high level of subjective judgement which is
undesirable and uncommon in most scientific investigations.
More sophisticated models (Bien et al. 1978) define as the
measure for the systematic differences the sum of orthogonal
functions (Brosche 1966, Schwan 1977, 1985) and then use
individual positions in a least squares algorithm to
determine the parameters of these functions.


10
On the other hand, a simultaneous reduction sets up all
condition equations in closed form and solves for target
parameters (star positions and proper motions) and model
parameters (systematic errors) at the same time. The
advantage here is that all available constraints on all
available data are used to estimate both sets of parameters
and that all estimates are least squares estimates.
Critique and Analysis of the Tabular Procedure
In spite of the fact that the tabular method has been
producing very good results for over a century, it is poorly
defined and the underlying assumptions have never been
explictly stated. That is, the tabular method, with
smoothing included, has never been defined in terms of a
model, but only as a "cookbook recipe" as it were. Without
the benefit of a model and specifically, without the benefit
of the assumptions concerning the joint probability
distribution of the random quantities, it is impossible to
assign a meaning to terms such as the bias and variance of
the estimated parameters. One cannot speak of the bias of
an estimate unless one knows the expected value of that
estimate. One cannot know the expected value of an estimate
unless one knows the probability distribution of that
estimate. One cannot know the probability distribution of
an estimate unless there exists a model which specifies the
dependence of the estimate on the random quantities.


11
In the simplest case of a tabular method without
smoothing, the systematic error of an IC is considered a
fixed constant in each subjectively delineated domain. The
model for the observed error of the position of star y in
domain v, a /is
MV
A =p +e y=l,2...n v=l,2...m (1)
yv Mv yv v
where p is the fixed but unknown systematic error in domain
v
number v and is an independent and normally distributed
random error with mean zero and constant variance a^ for all
yv Under these assumptions one invokes the principle of
least squares and minimizes the sum of all In this way
one obtains estimates p for p as the mean of all A :
V V MV
n a
v A
A
p = E -
v -in
1=1 v
IV
(2)
n of course, being the number of differences formed in the
2 2
vth domain. An unbiased estimate, s for a is
n
v
2 JlAiv-nvPv .
- TvT
(3)
So far this is statistically sound, because the estimates of
the systematic errors are uncorrelated under the given
assumptions. The estimate of their (diagonal) covariance
matrix is
S2 = diag(S^/n,, S2/n_...S2/n)
11 2 2 mm
(4)


12
where m is the number of domains involved in the process.
Unfortunately, the model in (1) proves inadequate.
Experience has shown that the domains cannot at the same
time be chosen small enough to model with sufficient
accuracy the structure of the systematic differences and yet
large enough not to mask the random errors of the
observations. The accepted solution to this problem calls
for choosing smaller domains and then "smoothing" each
A
estimate, p^, with its immediate neighbors. It is during
this process of smoothing that the reference to a model and
its underlying assumptions is lost. However, this procedure
will still produce some kind of a numerical result.
If smoothing is involved, one can only infer a model
working backwards from the "recipe." It is implied that the
model for the observed error of the position of star ^ in
domain v is
m m
A
tv
. a.p,+e ,
j=l uv'
. .a .=1
1 = 1 3
(5)
where the p.s are again fixed constants, r is again an
3 UV
independent and normally distributed random error and the
a_.s are subjectively chosen smoothing constants with
smoothing occurring over domains in the neighborhood of v .
A
The method of least squares would yield the estimates, p ,
by minimizing the quantity
m
n .
3
m
n
m
Z Z e. = Z Z (Aii- Z a p ) .
i = l i= 1 i = l i=l ^ k=l
(6)


13
In practice this is, however, not done; rather the pv s are
obtained from equation (2)!
The assumptions of the model function and those of the
procedure for estimation of the model parameters thus
contradict each other. The model function (5) is predicated
on the assumption that the p s are correlated, thus giving
v
justification for the smoothing process, while the
estimation of the model parameters from (2) is based on the
assumption that the p_s are independent.
Assuming the model (5), the estimates of the model
parameters from (2) are therefore biased. The bias of an
estimate is the expected value of the estimate minus the
true value of the parameter or
m
Z
j = l
a .p .
3 J
(7)
which is, in general, not equal to zero. One result of
these estimates being biased is that once systematic
differences are calculated, smoothed and applied as
systematic corrections, if systematic differences were again
calculated and smoothed using the same coefficients, the
resulting corrections would not be zero. That is, after a
catalogue is "corrected" using these biased estimates, if
systematic corrections were again calculated in the same
manner, the second set of corrections would be different
from zero.


TABLE 1
Succesive Corrections Computed with Biased Estimates
Corrections computed for the Bord 50 declinations:
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
30
2
7
10
13
13
9
12
16
18
17
13
9
8
6
5
2
1
1
-1
0
-1
-3
-4
-1
25
6
8
12
13
17
15
17
19
18
17
13
9
8
7
7
7
5
5
4
4
3
2
2
4
20
4
2
3
5
7
9
12
15
14
12
10
7
6
5
4
5
3
0
-2
-4
-3
0
1
3
15
-1
-5
-5
-3
-2
2
2
3
4
6
8
5
2
1
2
4
2
-2
-6
-8
-6
-5
-1
-2
10
-4
-7
-7
-7
-5
-3
-3
-5
-2
-1
1
0
-2
-1
0
1
-1
-4
-5
-5
-3
-2
-1
-3
5
-8-
10-
12-
-13-
-11
-9
-8-
10
-9-
10
-9
-8
-7
-6
-5
-5
-5
-5
-7
-7
-6
-3
-3
-4
0
13-
14-
17-
-19-
-18-
17-
17-
15-
-12-
-12-
11-
10-
10-
11-
10-
11
-8
-8-
10-
12-
13
-8
-8
-8
Corrections
computed
f or
"corrected1
1 Bord
50
declinations
30
-2
0
1
2
0
-4
-3
0
1
1
0
0
0
0
-1
-2
-3
-2
-2
-1
-1
-3
-4
-3
25
1
2
3
2
4
2
2
3
2
2
0
-1
0
1
2
2
1
2
2
3
2
1
1
1
20
1
-1
-2
-1
0
1
2
4
2
0
0
-1
0
0
0
1
0
-1
-1
-1
-1
0
0
1
15
0
-2
-3
-2
-3
0
-1
-1
-1
1
3
1
-1
-1
0
1
1
-1
-2
-3
-2
-1
0
-1
10
1
0
0
1
1
2
1
-2
0
1
3
2
0
1
2
2
1
0
0
0
1
1
2
0
5
0
0
-2
-2
0
0
0
-2
-1
-2
-1
-1
-1
0
0
0
0
0
-1
-1
0
1
1
1
0
-3
-2
-4
-4
-3
-4
-4
-4
-1
-2
-2
-2
-2
-3
-3
-4
-1
0
-2
-4
-5
-1
-1
0


16
calculators. Often, the necessary computing effort was the
deciding factor as to whether a project was feasible or not.
With the advent of computers, it is now practical to
undertake enormous data reduction problems which require the
simultaneous estimation of tens of thousands of parameters
without taking any computational shortcuts which degrade,
even if ever so slightly, the results. It is now possible
to reduce the avoidable subjectiveness of a scientific
investigation so that its results can be judged on an
objective basis.
It must also be noted that there are many vital interests
in the results of astrometrists. For example, the time
standard provided by astrometrists is relied on to
syncronize global satellite communications and calibrate
radio navigation. Thus astrometrists must be absolutely
certain of their results. With this in mind one might argue
that caution should be exercised in the acceptance of any
new procedure. While this is a legitimate concern, because
of the importance of this work, catalogue astrometry does
deserve the full analytical treatment which is now
available. There is no excuse for not using a rigorous
reduction in the compilation of a complete star catalogue.
Description of Simultaneous Reduction
As mentioned above in regard to estimating the systematic
errors of a catalogue, there are two distinct methods to


17
compute these estimates. In the tabular procedure, one
estimates the systematic characteristics of a catalogue and
adjusts the catalogue in order to correct these systematic
trends. Once all the catalogues are on the same system,
estimates for the individual positions and proper motions
are calculated.
In a simultaneous reduction, systematic corrections
(model parameters) and positions and proper motions (target
parameters) are estimated simultaneously. In this way not
only are the systematic differences between the independent
source catalogues and the fundamental system of the FK4
minimized, but the systematic differences between all
catalogues are minimized as well. The incorporation of all
available information for the derivation of systematic
corrections yields a result more precise and accurate than
that achieved by traditional methods. The idea that all
parameters, used in the construction of a complete
catalogue, should be solved for in a single adjustment was
first suggested by Eichhorn (1974) and later described by
him in more detail (Eichhorn 1980).
Within the framework of this research I have employed
this principle to estimate simultaneously systematic
corrections for all ICs used to construct the NIRS on the
basis of exactly the same model and from exactly the same
raw material as those used by Corbin. Corbin's model
computes differences on a grid at each hour of right


18
ascension and each five degrees of declination and then uses
two-way linear interpolation to compute corrections to
individual IC positions. The smoothing coefficients and the
weights of the individual catalogues were also the same as
in the model used by Corbin. The only difference between
the the reductions was the method of computing systematic
differences.
Consider the linear matrix equation
Y = xe + ZP + e (8)
where Y is a vector of observations, j3 and P are the target
and model parameters respectively, X and Z are their
respective coefficient matricies and £ is a vector of errors
with covariance matrix Z This equation could be
alternately and more compactly written
Y = [XZ][|] +e= A£ + e.
(9)
A simultaneous reduction estimating both model and target
parameters would yield least squares estimates
6
[-] = $ = [AX'_ZA] -1ATZY.
P
If model parameters are estimated first and target
parameters second, the least squares estimates are
P= (ZTZZ)_1ZTZ(Y-X6)
(io:
and
(ID


19
- T _1 T ~
1 = (X IX) X I(Y-ZP)
where g' are preliminary estimates for g. In trying to
perform a simultaneous reduction of the NIRS using the same
model as Corbin, I had to decide how to handle two problems.
First there was the computational difficulty of inverting
the A £A matrix in (10). Since I have approximately 40,000
star parameters and 20,000 model parameters, this means that
a 60,000 by 60,000 element matrix must be inverted.
Although there exist procedures (cf. Lawson and Hanson 1974)
which render a solution without the direct inversion of this
matrix, a problem of this size requires more virtual address
space than the Fortran application, which was at my
disposal, had available. This work was performed on a VAX
11/750. The second problem was that the model parameter
estimates that Corbin used were not least squares estimates
but the estimates described above. The obvious solution to
both of these problems was to iterate on a solution. An
iterative process converges toward the same solution as the
closed form (cf. Faddeeva 1959) but with less computational
difficulty and also allows for the use of traditional
tabular method of estimating model parameters.


CHAPTER III
REDUCTION PROCEDURES
In the previous chapter, I have criticized the tabular
procedure on three grounds: 1) the process is subjective in
nature, 2) not all available model constraints are used and
3) the estimates for the model parameters are biased. The
premise of this research is that by using all available
model constraints, a more precise and accurate result is
produced. Therefore, I have used the same subjective model
and the same biased parameter estimates as Corbin used for
my compilation of the NIRS. The differences in the two
versions of the NIRS are thus due only to the fact that I
have constrained the model parameters to minimize the
systematic differences in star positions between independent
catalogues as well as the systematic differences between
independent catalogues and the FK4. The aim of this
research was not to produce the best possible catalogue but
rather to show that a simultaneous reduction produces
superior results to those of the classical method.
Precession
The first step taken to recompile the NIRS was to precess
all of the independent catalogue positions to the coordinate
20


21
system orientation of the FK4. The catalogues used in the
recompilation of the NIRS are given in table 4 at the end of
this chapter. The precession was carried out using Newcombs
constants of precession. Three angles, £ z and 0, were
computed for each catalogue epoch, these are (cf Eichhorn,
1974)
£ = [(23402.253 + 139.75^ + 0.061t?)tf
+ <30-23 + 18.0t3J
z = c + [(79.27 + 0.66ti)tJ + 0.32t2] 64g0Q0 (12)

i i f
- (42.67 + 0.37tilt2 41.8t3l
where t. is the initial epoch of orientation relative to
i
1900.0 and t^ is the difference, final minus initial epoch
of orientation. Both t and t are reckoned in Bessel
i f
millennia. The constant tt/648,000 is necessary to convert
from arcseconds to radians. Next, the IC positions are
precessed to 1950.0 with the above angles and the following
formulae
X = cos cos (a + £ -j)
Y = cos sin(a + £ j) cos9 + sin<5 sin0
Z = -cos sin(a + £ ) sin0 + sin cos0
a5Q = arctan (Y/X) + z + j
(13)


22
6_q = arctan (z/^x^ + y^)
where X, Y, and Z are temporary cartesian coordinates, and
a, 6 and a <5 are the right ascension and declination at
50 50
the initial and final epoch respectively. A vector
resolution arc-tangent function was used to insure the
proper quadrant for a
Model Parameter Estimation
After all IC positions had been precessed, the next step
was to compute systematic corrections. Right ascensions are
used in the following discussion but an analogous procedure
was applied to declinations. It must also be noted that
right ascensions were first multiplied by the cosine of the
reference declination before differences were calculated.
First differences in positions were computed for each star
in each IC using the reference position and proper motion.
These differences were summed over blocks of one hour by one
degree centered on the hour and the degree. That is a block
that covered 13^ would extend from 12^ 30m to 13^ 30m.
These sums are
Aa (a, 6) = L
a+0^5 6+0.5 cos6 ^
Zo -V^taref pa(1950.0-Ta)-a] (14)
a-075 6-0.5 br
where a(a 6 ) is the systematic difference, is the
estimated variance of the reference star position at the
epoch of the IC position, a
ref
ref
and 6
are the reference


23
right ascension and declination, ya is the reference proper
motion and a is the IC position observed at epoch Ta. The
estimated variance of an FK4 position was calculated using
the errors and central epoch given in the FK4 and the epoch
of the IC position. The variance for an NIRS position was
calculated in a like manner except that an additional
variance term was included to represent the error of the
system of the NIRS. That is, the reference system of the
FK4 is defined only in terms of the set of FK4 stars. If
that set of stars is altered, then the ideal reference
system, which the altered set approximates, is no longer
exactly that of the FK4. Even though the system of the NIRS
is an approximation to that of the FK4, they are not
identical. Therefore, the variance of an NIRS position
consists of two parts. The first is due to the error of the
star position within the system of the NIRS and the second
is due to the error of the system of the NIRS itself.
In order to estimate the variance due to the error of the
system of the NIRS, the Perth 70 and Corbin's version of the
NIRS were used. After matching 3324 stars between the Perth
70 and the NIRS, the one sigma dispersion of Perth 70
positions and the NIRS predictions of the Perth 70 were
found to be 0.22 arcseconds in right ascension and 0.30
arcseconds in declination. This dispersion is due to the
position errors within the catalogues as well as the errors
of the systems of the catalogues. Since the mean error of a


24
position is published in each catalogue, the errors of the
the systems of the catalogues can be estimated.
2 2 2 2 2
£NIRS + £P70 + £SNIRS £SP70
(15)
The square of the dispersion, is the sum of the squares
of the mean errors of a catalogue position, and e'
:2 and e2
NIRS P70
plus the squares of the estimated errors in the catalogue
2 2
systems, e and e The residual variance could be
SNIRS SP70
split equally between the systems of the two catalogues, but
I chose to have the ratio of system errors equal the ratio
of the mean position errors. The system error used for an
NIRS position was .064 arcsecond in right ascension and .070
arcsecond in declination.
Once tables of differences for each IC were calculated,
these differences were smoothed with adjacent differences
according to the following scheme:
h 0
+3n +6
A a (a, ) =
Z Z A.B.Aa(a + i, 6 + j)
,h 1 3
i=-3 i=-6
(16)
h
+3n +6
Z Z A.B. n(a + i,6 + j)
l j J'
i=-3 j=-6
where A. and B. are the smoothing coefficients in table 2
i 3
and n(a, 6) is the sum of the reciprocal variances for the
appropriate IC, hour and degree. The smoothing coefficients
used (regular or light) for each catalogue are listed in
table 4. After differences have been summed and smoothed,
they are then averaged over zones of five degrees:


o
25
A ' a(a )
y 0 D A'a(a 6 + j)
j=-2 J 1
+ 2
where D is the denominator in
3
associated A'a (a/ 6)-
equation
(16)
(17)
of the
TABLE 2
Smoothing Coefficients
i
Regular
A.
l
1
B .
J
i
Light
A .
l
j
Bj
Oh
4
O
0o
10
0h
8
0
10
lh
2
1
8
lh
3
1
8
2 h
1
2 o
8
2h
0
2
5
3
5
3
2
4
5
4
0
5
2
5
0
6
2
6
0
Once tables of systematic differences are computed for
each catalogue, they were applied to the IC positions as
systematic corrections using two-way linear interpolation.
Right ascensions were first multiplied by the cosine of the
declination, corrected and then divided by the cosine of the
declination.
Star Parameter Estimation
After correcting the systematic errors of the ICs, the
position and proper motion were calculated for each star


26
using a weighted least squares algorithm. Corbin (1982)
calculated weights for each IC used in the construction of
the NIRS using three different methods. Method A was based
on the deviations of an IC from the final NIRS compiled with
each catalogue receiving equal weight. Method B was
similarly based on deviations from a mean NIRS but this time
the mean NIRS was compiled without the particular IC whose
weight was being determined. Method C was based on the
deviations of an IC from the reference system which was used
to calculate its systematic corrections. Corbin then used
the arithmetic mean of these three methods in the final
compilation of the NIRS. I have used these same weights,
listed in table 4, in my compilation of the NIRS.^
The following algorithm was used to calculate star
parameters. First the central epoch, T, and position, P,
were calculated:
P =
l
.w.P.
1=1 i i
Z w.
i=l 1
T =
l
L w.T.
i=l 1 1
iiwi
(18)
1
For a discussion of selecting weights used in catalogue
compilation, see Khrutskaya 1980.


27
where T\ is epoch and P^ is the position of the star in
catalogue i and is product of the the weight associated
with catalogue i and the number of observations for that IC
position divided by the mean number of observations per IC
position for that IC. Next the T. were referenced to the
central epoch:
ip I = iji rp
i i
(19)
and the proper motion was calculated:
4 =
Z w T P .
i=l 1 1 1
l
Z w T
i=l 1 1
,2
(20)
Finally, estimates for the variance of the position and
proper motion, V and V^, were calculated:
l
ili wi(P- p yT ')
v = =^-=-
l
(1-2) Z w.
i=l 1
m2
Vu =
i=l wi(pi p ~ yTi')
i \ 2
(1-2) Z w.T.
,2
i=l
i i
(21)
Sequence of Iterations
Now that the basic mechanics of the reduction have been
described, a discussion of the iteration sequence is in
order. Within an iteration the first step was to eliminate


28
outliers (IC positions with large residuals), the second was
to determine and apply systematic corrections and the third
was to compile a new version of the NIRS.
Corbin used several criteria for selection of AGK3R stars
to use in the NIRS. Among these was the requirement that a
star with only two observations must have those two
observations separated by a minimum of 28 years. Because of
the convolution of these criteria with the selection of
outliers, I chose those stars which appeared in Corbin's
final NIRS catalogue to use in the compilation of my version
of the NIRS. This, however, did not eliminate the problem
of identifing the outliers.
In duplicating the model and method used by Corbin, I
chose the same criterion for rejecting outliers. Corbin
rejected an IC position if the absolute value of its
residual was 3.5 times the mean absolute residual for
positions in that catalogue. Corbin established residual
limits for each IC and I have used these same pre-set limits
in my compilation of the NIRS. Residual limits for each IC
are listed in table 4.
The problem here is that one must compute systematic
corrections before residuals can be analyzed. In using an
IC position with a large residual to calculate corrections,
the corrected system of a catalogue can be distorted such
that other positions, which would not normally be excluded,
now exceed the residual limit. I decided to take an


29
iterative approach to this problem. The largest outliers
were removed first such that the systems of the catalogues
were not influenced by them in the next iteration. Then the
residual limit was lowered and the next largest outliers
were removed. This process was repeated until the residual
limit was lowered to that of the individual catalogues. In
iterations one and two, no IC positions were removed. In
iteration three, only IC positions whose residual absolute
values were greater than five arcseconds were removed. The
iteration residual limit was lowered in succesive iterations
as given in table 3 until the residual limit for an IC was
the individual limit given in table 4.
For the first iteration, the only reference system was
the FK4. Only catalogues 1 through 10 had FK4 observations,
thus only these first ten catalogues were corrected. For
the second iteration, the reference system included the FK4
as well as 6317 NIRS positions and proper motions computed
in the first iteration, thus allowing all ICs to be
corrected. For the third and subsequent iterations, the
reference system included the FK4 and 20194 NIRS positions
and proper motions.
Only the first ten ICs were corrected in the first
iteration; thus for the first computation of the NIRS, only
positions from the first ten ICs were used. In addition,
only those stars with three or more IC positions were
compiled into the first version of 6317 NIRS positions and


30
TABLE 3
Iteration Sequence
Iteration
Residual3
Limit
Number of Stars
Compiled into NIRS
1
none
6317
2
none
20194
3
5.0"
20194
4
2.0"
20194
5
1.8"
20194
6
1.6"
20194
7
1.4"
20194
8
1.2"
20194
9
1.0"
20194
10
0.8"
20194
11
0.6"
20194
12
0.4"
20194
13-25
b
20194
a. The residual must be greater in absolute value than
both the iteration residual limit and the individual
catalogue limit in table 4 in order for an IC position
to be rejected.
b. For the 13th through 25th iterations the individual
catalogue limits in table 4 were used.
proper motions. For the second and subsequent iterations,
all IC positions were used to calculate 20194 NIRS positions
and proper motions.
Tables 5 through 68 at the end of this chapter give the
corrections applied to the independent cataolgues for my
compilation of the NIRS. Each IC position was corrected
with values from this table using two-way linear
interpolation. The units are hundredths of arcseconds and
the right ascensions corrections have been multiplied by the
cosine of the declination. Furthermore, corrections whose


31
absolute values exceeded 99 hundredths of an arcsecond were
replaced by 99 hundredths with the appropriate sign.


TABLE 4
Independent Catalogues Used in the Compilation of the NIRS
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
1
AGK3R
Catalog of Reference stars for the
Dritter Katalog der Astronomischen
Gesellschaft
1.00
1.00
0.46
0.45
regular
2
AGK2A
Katalog der Anhaltsterne fr das
Zonenunternehmen der Astronomischen
Gesellschaft
0.52
0.36
0.53
0.68
regular
3
W20
Catalogue of 9989 Standard and
Intermediary Stars
0.26
0.46
0.71
0.62
regular
4
Albany 10
Albany Catalog of 20811 Stars for
the Epoch 1910
0.21
0.32
0.83
0.71
regular
5
Bonn 00
Katalog von 10633 Sternen
0.25
0.46
0.73
0.59
regular
6
Bord 50
Catalogue Mridien de 2024 Etoiles
Rephres de la Zone +11 a +18
0.70
0.64
0.41
0.50
regular
7
Sch
Katalog von 3356 schwachen Sternen
1.00
0.88
0.36
0.45
regular
8
Bonn 25
Katalog der Intermediaren Sterne
von +50Declination bis zum Nordpol
0.23
0.31
0.68
0.71
regular
9
W2-50
Catalog of 5216 Stars for 1950.0
1.05
0.69
0.42
0.59
regular
10
W3-50
Catalog of 5965 Stars for 1950.0
1.09
0.88
0.42
0.50
regular
11
GCH 1-50
First Greenwich Catalogue of
Stars for 1950.0
0.42
0.45
0.62
0.62
light


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
12
Cape02 00
Cape General Catalogue of
Stars for 1900.0
0.22
0.32
0.71
0.68
regular
13
Nice 10
Catalogue Deduit des Positions
Observes a 1'aide du Cercle
Mridien de 1'Observatoire de
Nice de 1912 a 1914
0.30
0.29
0.56
0.68
light
14
Nice 25
Catalogue De 1020 toiles
Intermediaires
0.59
0.34
0.45
0.62
light
15
GCH Z 10
Greenwich Catalogue of Stars for
1910.0
0.13
0.22
0.86
0.77
light
16
Paris 90
Catalogue de 11Observatoire
de Paris, Seconde Partie
0.04
0.07
1.50
1.20
light
17
Paris 00
Paris Catalogue de 10656 toiles
de Repre de la Carte du Ciel
0.07
0.19
1.13
0.89
regular
18
GCH 2-25
Second Greenwich Catalogue of
Stars for 1925.0
0.35
0.41
0.59
0.65
light
19
Berl 20
Berlin-Babelsberg Katalog von
8803 Sternen zwischen 31 und
40 Nordlicher Deklination
0.28
0.19
0.65
0.89
light
20
GCH 00
Greenwich Second Nine-year catalogue
of Stars for the Epoch 1900.0
0.25
0.34
0.68
0.59
light
21
Toul3 00
Troisme Catalogue de Toulouse
0.30
0.47
0.65
0.56
light
CO
CO


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
22
Cape 2-25
Second Cape Catalogue of Stars
for the Equinox 1925.0
0.30
0.39
0.65
0.62
light
23
Cape 3-25
Third Cape Catalogue of Stars
for the Equinox 1925.0
0.38
0.51
0.56
0.53
regular
24
W 40
Washington Results of Observations
made with the nine-inch
0.77
0.78
0.50
0.41
regular
Transit Circle
25
W 00
Washington-Results of Observations
with the Nine-inch Transit
Circle 1903-1911
0.28
0.41
0.65
0.53
regular
26
W ZOD 25
Washington-Catalog of 3520 zodiacal
Stars based on Observations with
the Six-inch Transit Circle
1928-1930
0.35
0.37
0.63
0.68
regular
27
Cape 1-50
First Cape Catalogue of Stars
for the Equinox 1950.0
0.88
1.31
0.50
0.35
light
28
Bord 00
Second Catalogue de L'Observatoire
de Bordeaux
0.07
0.13
1.24
0.92
regular
29
ALB99 00
Albany Zone Catalogues for the
Epoch 1900 Catalogue of 2800
stars between 2 of South and 1 of
North Declination
0.11
0.20
0.83
0.68
regular
30
Mun97 00ib
Mnchen Sternwarte Katalog
1.13
1.29
0.39
0.35
light
von 1867 Sternen (+375 to +47?5)


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
31
Mun97 OOil3
Mnchen Sternwarte Katalog
von 1867 Sternen (+55 to +60)
1.14
0.83
0.35
0.40
regular
32
Kon 00C
Konigsberg Rektaszensions -
Beobachtungen von 4066 Sternen
0.45
0.00
0.56
0.00
regular
33
Pulk99 00
Pulkovo A Catalogue of 8820
0.07
0.19
1.20
0.80
regular
Stars between 5 South and 15
North Declination
34
Madn 10
Madison Catalogue of 2786
Stars for the Epoch 1910
0.17
0.17
0.85
0.80
light
35
Berg 1-25
Erstes Bergedorfer
Sternverzeichnis 1925.0
0.33
0.20
0.53
0.80
regular
36
ABB-6 00
Abbadia Catalogue de 7443 Etoiles
0.13
0.17
0.71
0.71
light
37
Buch 50
Bucharest KSZ Catalogue of
Faint Stars for 1950.0
0.49
0.34
0.62
0.80
light
38
Bonn09 00
Bonn Katalog von 2199 Sternen
fr 1900.0
0.17
0.51
0.71
0.56
regular
39
ABB+20 00
Abbadia Catalogue de 14263
Etoiles
0.17
0.28
0.86
0.62
light
40
ABB0 00
Abbadia Catalogue de 13532
toiles
0.14
0.17
0.86
0.80
light
41
Lund44 50
Meridian Observations of Faint
AG Stars
0.12
0.13
1.00
1.05
light
oo
cn


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
42
Stras 30
Strasbourg Catalogue de 2251
Etoiles Faibles
0.39
0.21
0.60
0.80
light
43
Cin 00
Cincinnati Catalog of 4683
Stars for the Epoch 1900
0.12
0.10
1.00
1.10
regular
44
PFKSZ
Preliminary General Catalogue
of Fundamental Faint Stars
1.87
1.46
0.40
0.40
regular
45
Lund42
50
Meridian Observations of
Miscellaneous Stars
0.16
0.08
0.75
1.40
regular
46
Cin 25
Cincinnati Catalog of 2300
Stars for the Equinox 1925.0
0.11
0.12
0.92
0.90
regular
47
Moscow
50
Catalog of Faint Stars
0.26
0.32
0.80
0.80
regular
48
Tri 25
Catalogo di 2390 Stelle Osservate
al Cerchio Meridiano
0.09
0.07
1.10
1.20
light
49
Bruss .
25
Brussels Catalogue de 1339
toiles Fondamentales
0.40
0.32
0.55
0.66
regular
52a
Leid21
25
Leiden A Catalogue of the
Positions and Proper Motions
of 1533 Red Stars
0.29
0.26
0.55
0.60
light
53
Leid24
,25
Leiden General Catalogue
of Positions and Proper Motions
0.76
0.82
0.40
0.40
regular
of 1190 Standard Stars


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
54
Lund 25
Katalog von 11800 Sternen der
Zone +35 bis +40 AG Lund
0.11
0.16
1.05
1.00
light
55
Leid27 25
A Catalog of 1073 Stars in the Zone
of North Declination 55 to 60
0.34
0.20
0.50
0.67
regular
56
Berl Z 10
Katalog von 1886 Sternen
zwischen +79 und +90
0.35
0.17
0.59
0.80
regular
57
Konl9 25
Konigsberg-Katalog von 2043 Sternen
0.38
0.47
0.70
0.55
light
58
Toul3 00-I
Appendice II du Troisime
Catalogue de Toulouse
0.11
0.15
0.89
0.80
regular
59
Pulk 10
Katalog von 3396 Sternen zwischen
39 und 46 nrdlicher Deklination
0.30
0.44
0.59
0.56
light
60
Lick 17
Publications of the Lick
Observatory, Vol. XV
0.67
0.73
0.35
0.41
regular
61
Lick 28
Meridian circle Observations
of 1188 Stars between 20
and 30 North Declination
0.47
0.35
0.56
0.62
regular
62
Turin 10c
Catalogo d'Ascensioni Rette
di 697 Stelle fisse
0.11
0.00
0.90
0.00
regular
63
Bord 00-11
Nouvelles Observations Des toiles
contenues dans le Second Catalogue
0.10
0.14
0.89
0.86
light
de 1'Observatoire de Bordeaux


TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
64
0ttw28
25
Results of Observations
the Reversible Meridian
1923-1935, Catalogue of
made with
Circle
1589 Stars
0.54
0.34
0.53
0.60
regular
65
Ottw42
50
Results of Observations
the Reversible Meridian
1935-1950, Catalogue of
made with
Circle
1525 Stars
0.54
0.32
0.53
0.62
regular
66
Konl7
25
Katalog von 546 Sternen
0.43
0.38
0.50
0.60
light
(A) Catalogue reference number as provided by Corbin
(B) Catalogue abbreviation as given by Corbin
(C) Right ascension weight
(D) Declination weight
(E) Right ascension residual limit in arc-seconds
(F) Declination residual limit in arc-seconds
(G) Smoothing coefficients used
a. Reference numbers 50 and 51 have no catalogue associated with them.
b. The Mun97 00 was observed in two seperate zones and is treated as two seperate
catalogues.
c. The Kon 00 and the Turin 10 are transit instrument observations of right
ascensions only.
to
oo


TABLE 5
Corrections Applied to the AGK3R
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
1
0
0
0
-1
-5
-1
3
-2
0
85
0
0
0
0
-1
-1
0
1
-1
0
80
-1
-3
0
0
1
2
1
-1
0
0
75
-1
-2
-2
-2
1
2
0
-1
-2
0
70
-2
1
-2
0
3
11
5
3
2
3
65
-4
-7
-9
-4
-2
3
2
7
5
6
60
1
-1
-1
4
1
3
-1
5
-2
1
55
1
1
1
2
-4
4
0
0
-4
-2
50
1
2
0
-1
-8
-4
-1
0
-3
3
45
3
1
4
-1
4
1
6
4
5
3
40
5
0
4
-1
2
-7
-1
0
2
-3
35
5
4
-3
-5
-4
-5
-2
-5
1
-1
30
5
8
0
0
-1
-1
-1
-2
0
0
25
2
1
-2
-2
-1
-2
-1
-1
1
2
20
0
0
0
-1
2
-2
-1
-3
1
2
15
1
2
1
6
2
-5
0
1
4
7
10
2
3
4
2
1
-2
4
2
7
4
5
-6
-3
-2
-2
-3
-6
4
0
3
4
0
-1
-2
-3
-4
-6
-4
-5
-2
-1
2
-5
2
6
3
0
-3
1
-2
0
0
0
-10
-8
1
3
3
0
0
6
4
10
10
11
12
13
14
15
16
17
18
19
20
21
22
23
1
2
0
4
7
6
2
1
-1
4
5
11
5
-3
-1
0
1
3
2
0
0
-5
0
0
1
-1
-5
-2
-5
0
1
1
0
0
2
2
4
2
-1
1
3
2
1
0
0
-4
-2
-2
3
4
2
-5
3
1
1
0
-4
-1
-3
-3
-1
5
7
2
0
2
-5
-5
-1
-1
4
3
-2
-2
1
4
3
0
6
1
0
-6
-2
-2
0
-1
0
4
2
2
1
1
0
2
-3
-1
-1
1
1
3
6
1
-1
0
3
1
3
2
2
1
6
0
2
-6
0
-5
2
2
5
3
1
2
-1
5
2
8
3
7
1
4
-5
-4
-2
-5
5
0
5
2
5
2
0
-5
1
-1
-1
-2
-7
-3
-7
-7
-4
-5
-2
-3
0
2
1
2
1
-1
0
2
4
14
6
5
-6
-1
1
1
0
0
0
1
3
4
11
6
3
-3
-1
1
-2
-2
-8
0
1
2
1
-2
0
0
-1
-1
-2
2
0
-3
0
2
5
1
0
0
6
2
1
1
-4
-1
0
6
3
3
1
0
-6
0
0
4
1
5
0
1
2
2
3
1
1
0
0
1
2
-1
5
0
4
4
6
-1
-1
1
5
0
0
0
1
-1
-1
1
-4
-2
-6
-4
-1
1
0
-4
-5
0
-1
-2
6-
12
4
-4
2
6
6
9
6
-4
-2
10
-4
0
0
0
1
2
0
1
2
1
-2
2
2
2
1
2
2
2
0
-3
-7
CJ


TABLE 5 CONTINUED
Declination
dec\ra
0 1
2
3
4
5
6
7
8
9
90
0-15
-1
-3
-2-
46
-4
-4
17
7
85
26 0-
10
3
7-
15
11
-2
10
-1
80
-26 1
-8
4
4
0
1
-5
7
8
75
-33-11
-5
1
-2
-7-
10
-8
1
-7-
70
6 2
10
-1
-2
-7
-3
0
6
4
65
4 4
8
3
2
7
4
0
8
10
60
-7 -2
-5
-5
2
8
1
-6
0
4
55
-3 -2
-2
-3
-2
1
-1
0
1
2
50
-7 -2
-1
2
-2
2
3
7
0
-9
45
-2 -3
0
3
0
1
3
9
3
-1
40
0 -2
-1
-2
-3
-2
0
3
8
6
35
3 2
3
2
1
1
0
-5
-1
-1
30
-1 2
8
3
-2-
10
-8
-8
0
-4
25
2 2
3
3
6
0
0
5
2
6
20
0 1
1
3
2
0
-1
0
-1
-8
15
-5 -8
-6
-2
-1
-2
-4
0
3
1
10
0 -7
-3
-1
6
5
6
0
6
9
5
0 -6
6
0
3
-5
0
-6
-1
-5
0
2 -2
7
5
1
0
-3
0
1
3
-5
1-12
-2
-1
1
2
5
5
-2
0
-10
15-22
2
-3
1
-1
0
-7-
12
3
11
12
13
14
15
16
17
18
19 20 21 22 23
-26
14
18
8
8
8
4
1-
11-20-25-22 -4
-6
12
-1-
15
-1
12
12
7-
15-11 -5 -3 19
5
7
-3-
10
-9
-9
-8
-9
-9 -7 8 -9 -7
-6
-1
2
2
-1
-6
-3
3
2-1-1 2 -6
0
1
1
0
5
-1
3
9
6 5 0 11 7
-3
-4
0
0
-4
-4
0
2
2-3 1-2 -1
-3
3
11
5
-2
-1
6
3
3-2 3-6 -2
-2
-1
2
2
-5
0
1
8
5 -3 -4 -8 -3
-6
0
3
7
3
2
6
5
7 -3 -8 -5 -6
-1
0
0
5
0
-3
4
-4
5514-1
-2
0
-1
-1
-1
0
7
-3
-8-2 0 2 -1
-3
1
0
3
-1
-3
2
1
-1 -1 -5 -3 -3
-3
-2
-3
-2
0
3
6
9
-4 0 -2 -4 -4
5
-1
-2
-2
-1
2
3
6
1 2 4 0 2
-8
-3
-2
1
0
-1
-1
1
2 -1 -1 -2 -1
0
-1
-7
-7
-4
-1
-1
-3
-2 -7 -6 -3 -6
9
4
5
1
7
7
4
3
2 7-2 0-3
3
2
1
-2
0
6
1
-5
0-3-2 1 -5
2
0
-2
-8
-9
-1
1
4
10 8 11 12 4
2
4
7
8
-2
1
1
11
11 2 -1 6 2
9
3
-5
6
-7
-9-
10
-5
2-10 -4 -1 -6
10
-7
14
17
11
6
9
6
2
-9
-3
3
4
1
3
-8
2
7
-2
0
2
8
-p>
o


TABLE 6
Corrections Applied to the AGK2A
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
13
9
6
3
11 64
26
-5
-2
29
85
-1
-2-
-15-
20-
17 29
12
-3
1
4
80
17
5
6
3
0
7
5
12
21
13-
75
28
4
18
24
16 17
12
19
18
32
70
14
8
14
18
14 12
10
15
22
22
65
11
13
21
21
14 10
10
14
23
12
60
4
7
11
14
9
7
11
12
23
11
55
4
11
7
5
8
7
3
14
18
22
50
5
4
6
0
4
0
4
8
15
11
45
5
1
-3
-8
-6 -6
-3
-4
2
5
40
4
2
-6
-8
-8
4
5
5
-5
11
35
-6
-5
2-
11
-7 -4
-3
1-
14
-7
30
-6
6
5
-5
-2 -6
4
4
0
1
25
-2
2
-1
4
-1 -6
-6
1
-3
6
20
1
4
7
6
4 -2
-1
-1
1
5
15
-5
-4
8
-2
-3 -8
-3
-4
-3
-4
10
5
0
1
0
-1 -6
-9-
10
-2
-2
5
4
1
3
-4
1 -4
-6
-5
5
4
0
-5
1
7
0
1 -1
2
-2
1
1
-5
-2
6
6
4
0 -3
5
6
10
2
-10
2
-4
4
-5
-3 -9
-6
-3
4
-5
11
12
13
14
15
16
17
18
19
20
21
22
23
53
44
15
-8-
31
16
10
15
4-
35-
51-
48
9
8
13
23
25
24
39
9
0-
17-
39
1
-5
12
11
7
22
6
5
2
7
_4_
15
4
5
9
6
23
9
8
6
1
-3
5
-1
-1
6-
17
2
3
11
7
0
8
3
-1
-5
-3
-4
-3-
13
1
1
14
14
6
5
3
0-
10
-5
10
-2
-2
-9
9
16
18
1
1
1
1
-3-
13
-6-
12
-1
-3
7
11
10
-3
0
-1
2
-4
-4.
13
-6
-5
-2
4
15
2
2
-6
-5-
13-
10
-4
-3
4-
10
-8
-4
2-
11
-5
-6
-1
-6
-3
-2
-1
-7-
13-
11
-5
8
-2
-2-
11
-6
-4
-6
2
-5
-8
-6
-7
-7
3
5
-4
-4-
10
-5-
13
-5
-3
-1
-8-
18-
17
8
4
-9
2
-4
2
-4
6
-2
7
-2
-4-
12
6
3
-5
-5
-4-
10
-9
3
9
7
3
2
-3
4
4-
11
-8
-5
-9
-7
-6
12
4
-5
-3
5
5
-4
-8
-4
0
-7
-5
-5
2
-4
2
-1
-2
2
-7
-2
7
-1-
13-
11
-6
8
-1
5
1
-5
8
-4
0
2
-3-
11-
11
1
3
10
6
3
-1
9
0
0
-6
-3
-6
-6
-7
-2
6
14
3
1
15
5
5
1
1
-3
-2
-2
5
-3
10
5
9
-2
5
3
15
8
6
5
1
3
-4
2
0-
11
10
62
-7
12
15
22
26
19
13
7
0
6
7
13
5
14
1
-3
11
8
6
-3


TABLE 6 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-13-
12
1
28
0
15
0-
10-
16
4
25
39-
52-
-32
-2
-1
4
-4
-5
8
31
24
-5-
39
85
14
5
5
30
-3
12
19
13
5
5
-4
18-
26
13
45
-4
6
-6
-3
5
20
-1
20
2
80
-3
1
-6
-3
7
8
11
6
9
15
-4
9
-9
14
16
-4
0
0
-5-
-13-
-11-
17
2
-7
75
-16
1
-6-
12
1
12
-3
-8-
11
9
6
17
9
7
-2
3
-3
1
-8
-7
-9
1-
11
-6
70
10
12
2
7
10
3-
11
4
27
10
2
0
5
-2
-7-
10
-5
-4
-1
0
-8
-2
-1
9
65
-2-
16
-8-
16
15
-9
-9-
10
15
5
3
-2
-3
7
8
3
6
-4
2
-9
-2-
10
3
-7
60
-1
0
4-
13
10
0
17
-3
-3
-4
-4
5
5
2
7
5
5
-7
1
-1
3
-3
-2-
10
55
1
0
3
1
7
4
6
5
-4
2
-8
1
-5
-9
-2
7
6
-6
5
6
9
0
4
4
50
2
-1
-1
-1
0
-6
7
-6
-1
14
-4
1
-3
4
-6
-4
-9
-6
-8-
11
4
-1
6
18
45
0
6
4
1
0
-4
3
-9
3
5
2
-6
-6
4
5
1
6
-2
4
0
-1
0
-2
-3
40
-5
-2
-2
3
3
2
-1
-1
5
4
10
-8
1
-7
-6
0
7-
12
6
6
6
-6
-7
-4
35
-10
2
-2
-4
0
2-
15
-5
-3
-3
2
-3
2
-8-
19
-2
7-
14
-6
-7
-3
-9-
11
-6
30
-2
9
8
-2
0
-2
-8
-6
3-
10-
12-
18
4
21
2
5
9
6
0
4
0
1
-7
-7
25
-6
3
7
7
3
5
9
6
2
0
8-
15-
14-
12
-9
3
2
11-
13
9
-4
0
-1
6
20
4
-6
3
-8
-5
-9
2
-3
11
-2
0
-4
-2-
10
-5
9
-3
6-
10
10
-3
0
-4
-4
15
12
4
16
0
4
-3
8
6
25
11
8
2
5
14
13
13
4
2
6
6
-1
-5-
12-
19
10
13
-5
-5
-1
2
6
-6
4
-6
3
1
-1
-3
-1
17
14
15
-1
0-
11
-3-
12
-1
-7
5
3
-1
-1
-6
-5
4
1
17
9
8
-6-
18
-4
-4
9
9
6-
12
1-
10
-2-
-14-
15-
14
0
-3
-6
-3-
12
-7-
11
-2
2
-3
6
-6
-9
4
-6
1
7
8-
14
-3-
15
2
-9
2
-7
-5
-20
-7
-4-
15
-8
-5
-5
-6-
10
0
-9-
23-
16
-7-
12
6
5
2
5
-1
1
-7-
17-
13
-10
-15-
11
7
-6
8
2
0
-1
3
14
7
-2
-3
30
-7
3
-9
4
8
16
7
13
5
11
ro


TABLE 7
Corrections Applied to the W20
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-10-
-14-
-14-
-12
-5
6
-5
-3
3
7
-6-
-11-
-36-
-14
-8-
-19
-7
-1
4
-6-
-20-
-49-
-35-
-17
85
32
8
4
-7
-1
-1
-5
0
10
19
3
-4
-9
11
20-
-15-
-27-
-27
-2
12
-3-
-11
-4
15
80
-2
-6-
-14-
-42-
-23-
-33-
-17-
-29-
-26-
-24
-6-
-18
15-
-16-
-14-
-28-
-12
11
27
22-
-30-
-13-
14
-1
75
-37-
-39-
-40-
-35-
-32-
-39-
-27-
-54-
-41-
-54-
-15-
-45
-8-
-71-
-34-
-62-
-57-
-37-
-49-
-36-
-50
-5-
-14-
11
70
-19-
-32-
-36-
-24-
-29
-9-
-36-
-44-
-33-
-38-
-37-
-45-
-34-
-34
-4-
-18-
-53-
-29-
47
-5-
-23-
-24-
-38-
-26
65
-34-
-45-
-42-
-21-
-48-
-14-
-41-
-67-
-63-
-75-
-66-
-41-
-29-
-38-
-21-
-36-
-62-
-27-
-63-
-16-
-20-
-59-
-44-
-31
60
-38-
-32-
-13
46-
-13-
-16-
-35-
-63-
-42-
-43
-9-
-27-
-43-
-75-
-40-
22
-3-
-52-
-59-
-75-
-26-
-57-
-26-
-11
55
-19-
-38-
-43-
-27-
-39-
-32-
-41-
-27-
-22-
-61-
-28-
-70-
-29-
-46-
-48-
-44-
-42-
-29-
-56-
-27-
-17-
-64-
-39-
30
50
-61-
-19-
-29-
-15-
-43-
-49-
-30-
-32-
-12-
-50-
-41-
-55-
-36-
-17-
-28-
-17-
-41
-5-
-48
1
-9-
-41-
-58-
-53
45
-53
-9-
-54-
-38-
-55-
-40-
-41-
-45
-8-
-25-
-59-
-33-
-65-
-52-
-39-
-27-
-33-
-41-
-15-
-39-
-26-
-22
-9-
-16
40
-39-
-43-
-84-
-40-
-26-
-14-
-36-
-42
_4.
-20-
-45-
-26-
-29-
-22-
-11-
-21-
-20
-4
11-
-15-
-24-
-40-
-12-
-24
35
-12
8-
-19
5-
-13
7
-9-
-21-
-40-
-15-
-19-
-10-
-16
12
29-
-35
-1-
-45-
-26-
-15-
-10-
-17
-7-
-31
30
-42-
-33-
-42-
-26-
-40-
-25
-7-
-32-
-17-
-19-
-23-
-46-
-51-
-39
2-
-35-
-26-
-45-
-40-
-39-
-31-
-32-
-20-
43
25
-25-
-54-
-39-
-38-
-30-
-48-
-26-
-47-
-23-
-32-
-28-
-42-
-28-
-19
11-
-20-
-63-
-44-
-33-
21-
-19-
-43-
-64-
-32
20
-44-
-64-
-50-
-35-
-43-
-40-
-33-
-44-
-41-
-62-
-78-
-42-
-36-
-42-
-35-
-46-
-38-
-35-
-33-
-40-
-41-
-37-
-47-
-17
15
-49-
-66-
-67-
-39-
-40-
-35-
-46-
-54-
66-
-61-
-82-
-41-
-39-
-37-
-33-
-31-
-43-
-27-
-36-
-46-
-62-
-73-
-46-
-41
10
-49-
-60-
-56-
-50-
-50-
-32-
-56-
-57-
-68-
-37-
-52-
-53-
-40-
-60-
-49-
-66-
-48-
-55-
-50-
-57-
-51-
-58-
-38-
-47
5
-56-
-57-
52-
-60-
-67-
-43-
-55-
-58-
-71-
-42-
-69-
-63-
-55-
-62-
-62-
-57-
-45-
-52-
-55-
-42-
-43-
-54-
-51-
-51
0
-55-
-47-
-49-
-51-
-70-
-74-
-58-
-86-
-76-
-54-
-87-
-54-
-63-
.44.
-32-
-52-
-70-
-78-
-81-
-86-
-58-
-65-
-61-
-57
-5
-64-
-48-
-52-
-53-
-64-
-62-
-46-
-54-
-60-
-73-
-90-
-66-
-71-
-63-
-32-
-60-
-42-
-42-
-41-
-70-
-51-
-64-
-58-
-55
-10
-77-
-60-
-65-
-62-
-40-
-64-
-54-
-81-
-45-
-78-
-16-
-30-
-19-
-75-
-50-
-62-
-36-
-39-
-57-
-41-
-46-
-55-
-62-
-50
-p
CO


TABLE 7 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-3
7-
-17-
10
-2
36
9
-8
-6
-3
85
2
9-
-13
-5
-5
23
8
9
14
14
80
33
0
-1
8
-3
-9
1
-7
14
14
75
41
4
5
-2
13-
-10
28-
26
-4
19
70
17
11
20
32
35
3
23
-8
-8-
21
65
16-
-11-
-25
2
10
-4
-7-
26-
-28-
-17
60
7
19
-7-
20
2
11
31
-8
-6
-2
55
-7
-3
12
4
-1
-7
5-
26
-3-
-12
50
34-
-34
2-
17
-1
10-
-15
-2-
18
17
45
10
-5
12
5-
16
9-
-19
7
-4
12
40
3-
-12
-4
12-
11
37
7
7
-9-
-12
35
-1
10
-7
6-
28-
-39-
-41
-4
12
-5
30
-6
22
15
-9
-2
1
-9
0-
13-
-11
25
-8
11
-5-
13
5
4-
-17
2-
10
18
20
-2
1
-5
-4
-2
-4
-6
-5
-7-
-21
15
2-
-20
0
-7
-1-
22
-7
-8
2-
-20
10
-8
-4-
12
-3-
13
3
10
-2
5
-5
5
6
28
-7
-1-
17
10
-2
-7
-5-
-25
0
-8
12-
17
5-
39-
-16-
-13
-5
2-
10
-5
30-
-14-
13
-1
-5
-6
26
-5
10
-5
-10
1
32
-5
6
2
13
22-
14
-3-
13
11 12 13 14 15 16 17 18 19 20 21 22 23
17-29-20-16-17-17-11 3 -5 27 11 2-27
11 -6 22 39 22 -9 1 1-14 15 18 0-31
-24 12 10 0 -4-13 13 5 30-33 11-13 -4
-24 2 -2-19-20 12 14 -2 36-15 12-11 1
-21 7-14 -9 -8 35 -5 -8-26 5 28 26 19
0 26-25-18-13 8-26 2 -4 -2 23 17-14
-25 14-27-20-34 18 16 -3 10-11 20 2 14
-27-23 27 -3-15 -8 3-19-13 -5 15 -5 38
-22 3 13-11-30-27 -1 -4 3 13 2 9-33
-17 21 1-15 -7-13 15-11-10-16 -8 15 2
-20 -3-22 -1 16-12-20 -4-14 -5 -5 -4 8
-16 18-14 -9-23-27-10 -3-22 -1 3-17 1
-41 -7-13 23 -9 1 -5-11-22-11 3-45
8-20 -7 10 -7 3-13-15 392-70
4-20-13 -8-13 -5 0-16 -3-14-12-26 1
-8-13-11 6-22 3 -7 -5-12-13-19 1 5
3 3 2 21 -1 27-13 1-8 2-9 2-5
-6 -4-18-28 -5 15 1-11 0-13 1-82
4 2 0 21 -3 -4 -3-15 4 8 10 14 9
-12 -3-11 23 -8 -1 4 -4 16-11 676
3 37-33 10-11 586 49-10 8-12 7
10
0
10
-4
-1
-1
1
-6
10
12
21
1
15
24
0
18
6
4
12
4
13
15


TABLE 8
Corrections Applied to the Albany 10
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-3
8-
-10
6-
-19
6
-7
3-
-20
3
85
-25-
-10-
-32
5-
-26
-6-
-26
-2-
-29
-2-
80
-39-
-48-
-60-
-29-
39-
-30-
-41-
-27-
-29-
-19-
75
-42-
-28-
-53-
-31-
-40-
-39-
-59-
-35-
-56-
-39-
70
-34-
-15-
-43-
-17-
-28-
-31-
-66-
-15-
-70-
-18-
65
-36-
-48-
-33-
-18
1-
-32-
-44-
-51-
-59-
-38-
60
-30-
-47-
-30-
-24-
-18-
-39-
-34-
-60-
-17-
-36-
55
-27-
-36-
-29-
-27
-5-
-36-
-24-
-31-
-10-
-18-
50
-31-
-22-
-29-
-35-
-28-
-13-
-17-
-22-
-33-
-29-
45
-43
7-
-26-
-31-
-35-
-34-
-50-
-25-
-38-
-51-
40
-44-
-48-
-54-
-60-
-38-
-52-
-73-
-39-
-39-
-41-
35
-65-
-66-
-60-
-45-
-73-
-74-
-96-
-75-
-77-
-51-
30
-73-
61-
-56-
-40-
-62-
-51-
-53-
-64-
-65-
-74-
25
-72-
-71-
-76-
-59-
-51-
-65-
-70-
-85-
-55-
-75-
20
-73-
-64-
-63-
-66-
-72-
-70-
-76-
-80-
-66-
-77-
15
-76-
-71-
-53-
-60-
-60-
-62-
-64-
-65-
-73-
-68-
10
-71-
-77-
-85-
-69-
-89-
-66-
-53-
-55-
-59-
-62-
5
-74-
-65-
-70-
-59-
-66-
-62-
-66-
-69-
-65-
-76-
0
-64-
-82-
-74-
-68-
-58-
-75-
-83-
-94-
-56-
-54-
-5
-52-
-70-
-67-
-71-
-47-
-71-
-49-
-71-
-60-
-83-
-10
-70-
73-
-73-
-66-
-56-
-86-
-55-
-65-
-53-
-64-
11 12 13 14 15 16 17 18 19 20 21 22 23
99 46 47-38 -6 -1 -4 -8-12-24-13 4 21
35-31 16-38 -9 -4 1 5-16-32-25-11 5
-25-18-25-37-32-31-32-46-40-43-37-40-45
-21-25-40-30-49-36-38-29-24-30-46-39-51
-18-44-75-42-54-31-28-21-31-40-62-28-31
-4-27-46-38-33-28-31-46-37-52-36-35-25
-19-27-26-34-40-49-41-30-22-44-27-33-20
-20-39 12-15-31-42-32 13-24-25-27-17-13
-14-46-28-45-36-55-56-34-39-30-38-26-14
-30-18-51-57-36-40-38-58-39-66-55-62-33
-44-30-31-42-55-52-51-66-59-68-45-52-41
-72-55-44-53-93-71-65-61-53-55-66-50-61
-26-26-72-66-70-57-66-74-67-84-85-53-70
-48-38-36-56-65-63-58-50-54-76-72-75-74
-58-67-53-65-81-72-76-58-91-68-65-82-95
-36-50-59-62-63-51-56-46-80-72-70-77-89
-42-47-64-77-71-77-65-60-64-60-80-75-65
-51-54-69-62-63-67-67-73-66-57-78-85-79
-59-57-76-65-87-75-78-90-95-94-94-75-75
-63-51-50-54-81-83-76-79-82-90-99-77-79
-29-65-54-67-79-70-65-74-60-70-73-71-81
10
3
66
53
61
33
25
24
21
27
34
36
58
29
55
72
56
54
79
50
41
25
<_n


TABLE 8 CONTINUED
Declination
dec\ra 0123456789
90 1 -6 -5 20 1 60 17 2 11 23-
85 -22-15-20 20-22 36 16 8 0-17-
80 2 5-27-25-39-11 17 23 1 2
75 23 15-27 1 16 21 29 32 15 16
70 -8 17 2 42 34 33 0 -4 -9-12-
65 11 26 12 -2 13 4 31 31 37 29
60 -4 6 -6-10 23 0 10 6 6 15
55 -6 -5 -6 -3 22 30 12-21-20-25
50 -19-12 -8 -5-10 12 -7 9 15 2
45 -14-12 82-3 4-19-14-16 5
40 8 13 8 -1 -2 -3-11-13-26 -4
35 -21 -4-36 -7-33-12-53 -8-14 -7-
30 -15 7 -8 17 -8 14-42-15-21 5
25 -32 -9 -9-15 1-29-27-26-22-15
20 -21 -4-15-43-13-32-27-33-25-33-
15 -23 -5-20-14-12 -9-42-28-24-11
10 -24-24-44-29-47-25-53-40-36-36-
5 -19-14-27-28-36-13-22-22-13-32-
0 -31-31 -1-15 -7 -2-40-36-29-14
-5 -29-22-30-25-44-28-41-24-47-29-
-10 -36 -5-31 -4-24-31-28 -5-28-26-
11
12
13
14
15
16
17
18
19
20
21
22
23
-28
41
40
46
45
45
32
27
11
-4-
-31
26
-7
-45
0
0-
-20
-3
-1
-3
12
-6
4
5
11-
-23
12-
-10
-9-
-20
-6
0
-5
7-
15
29
8-
-27-
-26
7
-1
29
3
9
22
25
26
32
55
42
18
8
-22-
-21
-6-
-15
14
11
22
12
16
16
12
11
-8
3
-4
7
10
26
-4
9
6
3
30
25
31
9
-10-
-28
8
7
3
16
3
12
-4
14
-2-
12
-3
13
0
-3
1
12
33
17
31
11
25
17
1
6
-1
-2-
-30
-5
8
13
21
6
11
17
34
15
-6
-22-
-19-
22
1
9
-5
17
4
2
-9
0
-2-
-12
12
14
9
5
17
3
20
15
14
4
16
18
13
0-
-13-
-12
6
-2
-6
4
-4
10
0
3
-8
-9
4
3-
-17
24
-6
6
9
4
11
2
-3
-9-
-18
-23
7
2
8
-6
4
13
-7
5-
-19-
-32-
-13-
-11
-33-
-14
-5
_4.
16
-7
-7-
-21
-8-
-15-
-22-
20
-5
-14-
-11-
-14
-9
-3
-6-
-15
-8
3
-3-
-15-
-15
-8
-32-
-27-
-34-
-43-
17
26-
-10-
-20-
-14-
-13-
-36
-9-
-32
-17-
-10-
-25-
-37-
16
8-
-19
-4
-9
3-
16
-9-
-12
-25-
-45-
-34-
-31
9-
-41-
-43-
-10
7
1
-2
-9-
-14
-41-
-55-
-39-
28
0-
13
5-
-14-
-14-
-33-
-30-
-20-
28
-30
-2-
-19-
-23-
-35-
13
8
8-
-28-
-20-
-10-
-13-
30
10
11
40
14
14
10
14
-7
-5
3
-9
0
13
-1
-6
22
5
31
11
-6
41
45
-P*
cr>


TABLE 9
Corrections Applied to the Bonn 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
65
-99-
99-
-99
99
99
99
99
99
0-
78-
-99-
-99-
-99-
-99-
-99
0
-7
-7
-7-
-14-
-80-
-51-
-99-
60
-72
42-
-85-
-99-
-99
15
20
47-
-45-
-64
1-
-50-
-70-
-26-
-50
6
8-
-34-
-19-
-34-
-70-
-56-
-99
55
-82-
-36-
-64-
-99-
-57-
-18-
-53-
-21-
-83-
-58-
-26-
-44-
-75-
-41-
-99-
-97-
-71-
-99
-4-
-24-
-30-
-59-
-99-
50
-58-
59-
-31-
-35-
-41-
-39-
-48-
-57-
-63-
-72-
-43-
-58-
-83-
-48-
-42-
-38-
-77-
-99-
-25-
-33-
-53-
-58-
-58-
45
-78-
-34-
-65-
-64-
-79-
-67-
-75-
-79-
-48-
-88-
-63-
-71-
-75-
-64-
-45-
-40-
-71-
-90-
-60-
-43-
-60-
-60-
-87-
40
-96-
-65-
-77-
-53-
-47-
-55-
-62-
-81-
-54-
-78-
-73-
-63-
-53-
-60-
-53-
-72-
-56-
-72-
-50-
-73-
-36-
-48-
-70-
35
-76-
-81-
-45-
-51-
-60-
-58-
-72-
-79-
-72-
-79-
-70-
-75-
-56-
-69-
-48-
-80-
-57-
-82-
-57-
-60-
-32-
-60-
-64-
30
-77-
-80-
-54-
64-
-48-
-50-
-83-
-89-
-97-
-89-
-97-
-72-
-79-
-53-
-81-
-84-
-82-
-80-
-38-
-42-
-62-
-78-
-69-
25
-50-
-43-
-45-
-54-
-75-
-98-
-99-
-80-
-82-
-52-
-87-
-75-
-99-
-47-
-72-
-69-
-99-
-69-
-30-
-27-
-74-
-84-
-67-
20
-54-
-52-
-57-
-21-
-67-
-57-
-97-
-73-
-99-
-66-
-71-
-70-
-89-
-55-
-66-
-64-
-73-
-60-
-41-
-56-
-46-
-75-
-53-
15
-43-
-47-
-41
-9-
-48
-8-
-94-
-56-
-95-
-94-
-51-
-46-
-59-
-38-
-58-
-50-
-43-
-49-
-58-
-47-
-38-
-80-
-63-
10
-20-
-44-
-14-
-10-
-44-
-48-
-89-
-70-
-92-
-94-
-61-
-52-
-60-
-59-
-69-
-58-
-37-
-41-
-34-
-29-
-16-
-70-
-41-
5
-36-
-34-
-24-
-22-
-73-
-44-
-30-
-44-
-53-
-56-
-52-
-42-
-42-
-31-
-67-
-67-
-56-
-36-
-37-
-29-
-13-
-12
-9-
0
-43
-7
8-
-21-
-46-
-45-
-17-
-82-
-57-
-60-
-45-
-81-
-53-
-29-
-34-
-26-
-28-
-12-
-19-
-33-
-32
-2-
-18-
-5
-42-
-21-
-61-
-89-
-88-
-47-
-30-
-40-
-58-
-45-
-31-
-93-
-62-
-29
-5
-1-
-24-
-23-
-16-
-15
-3
25-
-45-
-10
41
56
20
17
19
29-
-16-
-32-
-65-
-28-
-11-
-10-
-15-
-18
-2
-4-
-23-
-25
7
-6-
-27-
-41-
-90-
23
52
2
35
52
70
72
88
84
64
63
52
36
19
18
47
53


TABLE 9 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
65
44
54-
-99-
-99-
-99-
-99-
-99-
-99
0-
-58
16
16
98
98
99
0-
-99-
-99-
-99-
-99-
-99
35
60
99
60
42
38
5-
-12-
-38-
-67-
-38-
-23-
-95-
-99-
-97-
20
48-
29
-4-
48
47
11
2
-5-
-14
37
63
99
55
8
20
1
64
45
38
1
26
10
77
8
34
91
32
67
17
43
9
38
37
37
37
44
75
50
21
38-
-17
20
14
24
9
24
7
41
5
-2
36
17
45
-4
40
19
8
27
31
49
31
44
45
40
51
26
24
36
34
45
26
12
1
28
26
34
38
57
51
50
63
30
28
25
67
70
66
40
11
-2
-7
9
16
19
1
-6
-2-
-11
8
6
5
19
32
18-
-20
-5
-4
22
-1
32
27
41
35
0-
-10
-7
10
0
2-
-37-
-39-
-29
-4-
-23
9-
-20-
-21-
-33-
-24
18
-1
39
21
23
0
10
14
30
1
9
2
17
39
31
35
-3
-4-
.19-
-31
11
13
35
5
21
50
18
30-
-19
14
27
42
28
25
2
15
-3-
-13
17
17
0
2-
-14-
-20
-1-
-14
9
18
5
2
8
-1
27
-6
17
15
23
20
20
2
-8
16
-6
28
-4-
-23-
-14-
20
-4
14
-3
11
6
11
6
7
1
29
-7
4
1
24
21
15
34
3
32
11
41
-5
25
12
7
5
3
-5
8
24
37
52
47
26
9
28
-4
47
44
43
10
22
12
25
27
12
26
14
29
-2
16
8
13
21
14
13
11
9
18
11
27-
-19
23
26
9
5
25
22
22
17
29
48
14
21
-7
14
21
17
58
30
51
27
22
18
10
6
26
19
34
2
0
11
10
44-
-12
32
29
84
18
15-
-16
2
-3
16
19
22
58
34
51
25
6
49
66
87
22
-5
3
30
53
56
66
31
78
41
22-
-12-
-38-
-40-
-46
25
8
49
-1
34
50
62
38
93
38
89
-10
25
80
17
16
11
4
1
-2
-3
0
-6
13
44
76
30
49-
-25
15
50
81
0
24-
-58
86
-p.
oo


TABLE 10
Corrections Applied to the Bord 50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35
-25
24
4
10-
31-21-
16
-3-
13-
21-
54-
31
0
3
0-
13-
22-
22-29-
34-
33
-9-
12
30
3
18
3
12
1 1
7
12
8
6
8
13
13
9
1
-6
-9
8 27
18
7
5
7
25
15
10
8
1
0 0
-6
7
4
4
21
-1
-5
8
-4
-3-
10
1 0
14
13
12
11
20
1-
12
6
-5
2-12-
15
4
-5
0
16
0-
14
-8-
12
-9
-2
-2 -9
11
16
5
4
15
9
7
15
12
3 -2
2
13
12
15
22
10
12
4
4
6
18
16 18
22
26
21
18
10
3
1
-5
-2-
16 -8-
11
-2
11
6
0-
18
4
-2
4
-2
11
6 12
9
14
16
12
5
2
-2
-6
-8
2 -1
-4
-8
-2
6
-2
-1
4
2
-5
-1
-3
4 9
12
11
8
7
0
14
6
16
-8
22-12
16
-7
0
24
28
27
11
5
-8
8
8
24 19
15
5
12
21
-5
38
10
14
-2
40-1
38
17
71
74
32
1
-6
1
7
22
21
34 20
1-
13
33
51
Declination
dec\ra
0
1
2
3
4 5
6
7
8
9
10
11
12
13
14
15
16
17 18
19
20
21
22
35
-8
29
24
50
-8-31-
25
17
45
46
7
7
21
0-
25-
43-
47-
38-17
3
0-
48-
51
30
-15
9
6
15
4-11
3
17
16
18
9
12
1
9
0-
11-
21-
10-16
-6
-6-
13-
14
25
10
19
21
20
36 12
19
28
25
29
18
3
3
8
15
20
3
19 14
24
12
10
4
20
8
0
-3
1
-4 11
11
32
25
0
13
-1
11
9
-1
4
-5
-6 -4
-2
-7
-1
0
15
4
-5
-5
-3-
13 9
-2
3
-4
-3
13
-1
-7
1
1
4
3
-4-13
-9
-6-
10
2
10
0
-3
-7
-4
0 4
4
-9
9
9
11
2
-6
5
4
2
-6
-2 -3
-2
4
-4
7
5
-11
-3-
15-
20
-6-13
-5-
27
-9-
23-
15-
12
-5
-6
0
-6
-2
3-12
-5-
13
-2
0
0
-40
-8-
19-
25-
22-24-
30-
19
-4
-7
-3
-8-
14-
32-
18-
26
-1
11-16
-2-
35
-5-
15
-5
-90-
73-
97-
97-
80-71-
87-
50-
26
28
10
3-
14-
20-
25-
35-
43-
38-49-
33-
82-
67-
75
23
20
2
6
-8
12
8
-4
10
59
23
22
-6
11
-3
10
-9
9
2
65
-P*
to


TABLE 11
Corrections Applied to the Sch
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
5
8
-2-
18
3
19
15
26
20
23
13
9
14
8
9-
10
-9
-8
-1
-6
-3
-4
-1
3
85
-6
-8-
17-
28
-3
5
2
10
9
14
7
0
0-
15
-5-
10-
15-
18
-6-
19
-9
-6
1
0
80
-2-
-10
4
23
27
20
4
4
5
13
18
8
6-
12
-2
-5
3
-9
6
-5
3
9
19
16
75
18
15
17
16
16
22
17
21
17
24
33
45
33
11
5
-5
7
-3
1
3
4
1
9
15
70
13
15
26
25
24
23
19
22
24
33
21
31
12
16
8
-3
1
-6
-8
3
3
8
5
2
65
6
5
14
14
16
20
24
25
34
39
24
19
-1
4
5
-6
-2
-2
-1
2
-7
12
4
3
60
21
23
19
21
7
16
18
22
18
20
23
17
20
2
6
-2-
12
-5-
-13-
12
-6
3
4
6
55
13
11
9
12
1
16
9
23
11
20
17
9
11
-9
4
-4
-8-
12-
11
-5
1
-3
-3
-6
50
12
9
12
-5
-8
1
2
12
3
24
15
6
4
-6
2
1
1-
18
5
4-
10
-7
-8
-3
45
10
8
7-
-12-
12
-5
1
18
21
19
6
10
11
7
-3
0
-6
-4
10
20
3
-4
-4
-4
40
8
16
4
-3
-7
-9
-6
1
30
8
6
-1
0
1
-5
-8-
12
-6
-2
-5
-7
-8
-6
-1
35
5
3
-6
-2
-1
2
15
5
28
2
14
3
6
-4
0-
11
-5
-9
8
-4
-1
-7
-4
2
30
8
7
-3
-4-
14
-2
4
-9
9
9
12
0
10
-1
9
-4
-1
4
13
2
7
1
0
5
25
4
-1
0
5
0
1
-2
5
14
14
3
9
2
0
0
4
-4
6
10
8
11
5
7
0
20
9
3
3
1
-5
3
3
7
12
8
5
17
-5
-2
-9
3
1
7
7
15
16
7
6
-8
15
7
9
13
6
-8
-4
1
5
9
6
18
8
2
0
-2
10
5
6
2
19
14
15
3
3
10
-3
1
-6
7
-4
-6
2
11
3
0
3
-3
6
0
2
-1
-5
7
-4
6
2
18
-3
7
5
7
0
0
-8
-6-
18
1
-1
7
4
0
4
2
6
4
8
1
4
6
7
5
7
-4
1
0
5
-2
2
-7
-9-
12
-5
-6
14
5
-1
-3
-8
-1
-3
14
1
6
10
7
15
3
-2
3
-5
-1
5-
14
-2-
12
-4
-7
-6
0
6
1
-2
-3
2
-6
2-
14
5
5
4
4
-1
4
9
-10
-1
13-
12-
-12-
15
-4-
21-
-10
-5
17
5
5
5
13-
15
5
3
21
12
10
7
12
13
11


TABLE 11 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-22-
-39-
38-
-28-
23-
-44
-1
19
14
-7
85
8
-6
19
4
7-
23
2
1
-8-
18
80
-26-
-21
11
4
8
-4
4
-1
15
-6
75
-21
13
22
24
-6-
18
-9
7
11-
35
70
2-
-15
7
-7
5
-5
-8
-2
8
16
65
1-
-13
22
-6
10
1
0
-1
8
21
60
-1
-3
9
5
-2
6
-2
3
8
9
55
9
14
9
10
18
21
7
-1
11
9
50
-14
-4
-8
3
-1
3
11
4
9
-3
45
-12
10-
14
-1-
14
-6
11
10
8
16
40
-1
2
-4
3
4
7
14
-3
6
5
35
8
-7
-4-
17
9
15
26
-5
18
7
30
-6
-7
7
2
12-
18
-5-
21
-6
4
25
3
13
10
8
4-
10
4
0
9
18
20
-5
-3
1
-6
1
7
15
3
-2
0
15
0
-9
16
10
5
15
16
6
3
6
10
7
7
-2
11
1
3
7
-3-
11
3
5
1
-3
-9
-1
1-
-13
5
-9
-5
4
0
-5-
18
15
-7
-5-
28
8
7
4
0
-5
0-
34
-6-
32
-2-
26
1-
10
-8
3
-10
-22-
52
0
-9
34-
16
6
-7
0
0
11 12 13 14 15 16 17 18 19 20 21 22 23
29 45 23 -8 1 11 10 7 1 9-36-56-12
11 17-20-37 -6 27 40 19-44-25-36-12 15
-14 -1 -4 25 9 10 -7-11 -6 -5 6 47 6
9 17 9 30 -6 -7-42-17 42-1 9-24
33 -8 2 3-10-12 -7 17-14-16-20 -7 1
-5-28-10 12-14 -4 -9 10-13-19 -787
3 2 25 21 11 -1 1 11 6 2 -3 -3 -2
-2-15 8-6 9-7 0 5 10 8 -8-16 0
0 11 5 12-12 -6-17 12 7-1 0 10 6
1-11 -2 15 5 2-17 22-5 4 3 25 12
7 1 4-2 3 5-6 1-4-5 8 4 7
-6 13 10 12-6-3 5 3 9 -6 -6 1-11
13 -4-14 35-448903 7-22
6 2 6-10 4-818 8-12 -8 -2 -2
-14 8936-5 6-11 19 -3 7-10 -7
7 2-12 -4 -4 10 4-14 -2 -7 14 5-13
1-5 5 13 5-6 8 6-2 5-7 2 0
-4-16 5 5 11 -6 -8 -3-11 1-17 -6-18
-5-3 2 3 -8 -3-8 8 5 23 -6 7-26
27-3 10-11-14-30 15 -6 14-17 9 -6
15 17 13 21 20 0-22 5-18 -2 -7 -4-14
10
20
9
15
-4
15
9
22
6
-1
11
-3
-6
4
17
8
12
-2
4
-1
-3
14


TABLE 12
Corrections Applied to the Bonn 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-15
3
8
11
17
7
-4-
24
3
25
35
99
63
54-
24-
-45
4
-2
0
0-
34-
-74-
-99-
31
85
-6
6
17
27
27
17
15-
10
13
-4
-9
16
8
-9-
-26-
10
19
1-
-15-
-24-
49-
-45-
90
8
80
11-
41-
15-
22
-1
-8-
-13-
20
-5
-1
0
0
-5
-7-
-18-
52-
-73-
-49-
-56-
-75-
48-
-53-
40
-7
75
-2-
47
12
-9
-1-
-33-
-47-
-25-
31-
-13-
16
8-
11-
-22-
-20-
-37-
-64-
31
21-
-16-
-15-
-51-
-29-
46
70
-44-
31-
29-
34-
14-
37-
-46-
-46-
31-
-33-
-29-
-41-
34-
-43-
-26-
25
-8-
-35-
-38-
-53-
-58-
-79-
-30-
47
65
-46-
45
-6-
33-
30-
-47-
-45-
69-
50-
-51-
-34-
-40-
34-
-34-
-46-
-61-
-39-
60-
-65-
-26-
-48-
-42-
-46-
55
60
-37-
42-
-13-
57-
27-
73-
45-
-80-
-59-
-65-
-81-
-28-
-57-
-49-
-65-
-65-
19-
57-
-73-
-82-
-72-
-61-
88-
-57
55
-67-
35-
-52-
64-
48-
-99-
-55-
-99-
-25-
-72-
-83-
-62-
47-
-33-
-53-
-56-
-52-
-86-
-93-
-99-
-75-
-77-
-88-
47
50
-90-
-75-
-57-
60-
-72-
80-
-88-
-87-
-72-
-84-
-86-
-99-
-42-
-56-
-71-
-71-
-86-
-98-
-50-
-84-
-44-
-78-
-78-
-87
45
-99-
-99-
-99-
-99-
-97-
20-
-86-
-96-
-99-
-99-
-94-
-88-
-13-
-40-
-43-
-61-
-99-
99-
-90-
-89-
-35-
-85-
-99-
99
40
-99-
-99-
-99-
46
29
99
99
81
-1-
-59-
-74-
-94-
-59-
-87-
-63-
-92-
-99-
-99-
-99-
-99-
-71-
-89-
-83-
-98
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-9
6-
26
8-
-45
18
20
24-
-16-
-26-
-18
11
41
32
37-
-11
-6-
-18-
-21
2
11
35-
62
0
85
60
47
1
33-
-41
9
3
-1-
-38-
-25-
-35-
-10
11
38
53
14
13
-7
3
32
14-
-26-
-42
29
80
22
16-
-16-
-30-
-38-
-21-
-10-
-26-
-17-
-13-
-32-
-38-
-69-
-20
-8
-1-
-46-
-21
-9
24-
-33-
-34-
-33
15
75
-30
-5
7
6
15
-2
17
26
12
20
32
-3-
-31
5-
-27
27
-8
17
-3
27
-9
20
-8
13
70
32
9
-8
0
4
-6
-4
20-
-19-
-21
11
-9
5-
-12-
-50-
-18-
-42-
-27-
-21
-9
-2
15
8
51
65
15
12
1
6
23
3
11
14
15
18
17
-8
12
-7
13
12
7
15
16
39
22
41
5
14
60
-9
27
8
17
19
6
8-
-10
-2
3-
-14
-2
28
12
10
-6
-7
5
23
22-
-14
11-
-23-
-21
55
10
28-
-14
60
45
10
10
7
13
21
-9
-4
16
-5
11-
-11
17-
-12
42
28
-7
40
38
53
50
51
67-
-29
38
41
42
31
24
13
37
26
41
-1
15
35
34
39
31
51
57
22
76
18
74
45
69
78-
-22-
-32
-9
9
38
48
61
10
28
52
19
60
57
53
47
65
33
69
26
99
-7
77
40
99
99
95
61
51
28
99
99
99
99
99
96
70
99
63
73
73
80
46
99
99
99
99
99
CJ1
ro


TABLE 13
Corrections Applied to the W2-50
Right Ascension
dec\ra 0123456789
90 11 -1-11 1 4 23 6 22 7-10-
85 11 12 19 15 11 16 -8 4-5 5
80 -9-11 -2-15 -8 -3-17-14-32-20
75 -15-13-24-10-11-13 -9 -7-23-15-
70 -2 6-16 2236 -2-16 -3-
65 -3-15-30-25-13 2 -4 -2-11 -1-
60 -6-16-19 -5 -7 -9 -6-12-18-13-
55 -18-18-17-20-21-27-17-25-32-28-
50 -4-14-14-36-25-29 -5-10-21-29-
45 -1-19 -5-24-12-14 -6-23-18-36-
40 -18-25-25-30-21-24-34-42-28-29-
35 -17-26-33-42-34-35-46-43-18-25-
30 -11-34-36-47-18-23-12-21-19-19-
25 -15-18-27-46-19-32-19-28-28-28-
20 -30-33-33-41-28-28-22-28-26-25-
15 -37-37-30-15-26-27-29-32-34-38-
10 -19-35-40-42-41-52-33-39-31-33-
5 -40-52-50-44-43-52-37-37-40-32-
0 -46-52-61-66-64-46-44-46-69-46-
-5 -38-27-27-52-48-51-41-47-47-46-
-10 -64-46-45-47-44-56-44-51-24-36-
11 12 13 14 15 16 17 18 19 20 21 22 23
-55 -4 5 20 0 1 6 2 2 12 30 58 26
-13 10 10 9 4 5 1 2 15 22 15 30 4
-26 2 -5 -9 -6 -3 -7-7-2 5 8 1 -9
-18 -3-12-21-13-19-12-12-16 -3 21 7 0
8 -6 -9-12 -2-6 2-7 4 5 23 8 5
-8 -8-18 -2-13 -7 -8-23-14 -4 5 16 3
-10 -2-21-14-25 -4 -2 -9 -8 -1 -4 9 10
-4 -1-16-17-23-16-15-13-12 -5 -3 -1 -7
-18-19-14-15-22-13-12 -8-18-31 -5-12-14
0 -6 -9 -7 -9-17 -1-14 7-21 5-43-25
-22-23-32-14-11-29-11-29-17-21-27-42-19
-31-41-33-42-43-35-15-18-27-15-22-23 -3
11-15-14-37-17-16-13-24-19 -8-22-22-18
-19-38-45-37-14-13-12-25-18-23-18-24-18
-29-14-47-14-19-25-26-35-31-29-22-35-30
-47-29-53-22-27-15-21-29-34-22-28-38-36
-37-34-34-31-31-12-31-31-39-35-31-38-34
-36-48-42-40-44-26-43-25-43-41-32-33-45
-36-40-41-28-27-32-33-35-39-53-53-43-45
-62-46-50-52-40-37-37-53-42-39-48-46-42
-51-45-28-47-37-31-29-29-42-45-64-54-51
10
34
5
-6
10
15
31
26
28
31
16
28
53
17
27
33
62
44
47
55
53
45


TABLE 13 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-27-
-25-
-23-
14
-8-
-47
-4-
10-
-19-
-51-
85
33
-6-
-10
-6
8-
-20
10
0
-5-
-16-
80
-42-
-41-
-21
-1
-2
-3
-2
4-
-11
-6
75
-38-
18
-5
-2-
-26-
-26-
-21
12
7
-2-
70
-13
5
-2
-8
-8
-5
-3-
12-
-17
-2-
65
-20
1-
-17-
21
-1
-2
16
6
-3
14
60
-20
1-
-11
-9
0-
-22-
23
-7
1
1
55
-43-
-19-
-17
-2-
-13-
-15-
-11-
21
-8-
-17-
50
-12
-4-
-13
6-
33
-1
8-
11
-7-
-23-
45
-32-
-22-
-30
11-
-13-
-21
13-
15
-3
-1-
40
7
5
-4
1
5-
22
25-
10
28
4
35
-10-
-10-
-20
0-
-12
-3
33
-8
35
11
30
9
7
0
29
11
9-
17-
10
14
59-
25
33
19
22
24
25
37
28
6
25
26
20
14
5
9
14
14
5
22
2
3
-2
15
8
-6-
-14
8
19
-7
-6
2
7
46
10
19-
11
0
14
11
37
16
17
25
33
5
15
-5
21
7
21
44
22
0
7
5
0
-7
6
4
9
-7-
-27-
-11
5
30
23
-5
8
11-
-10
15
21
40
23
2
17
28
-10
20
32
14
7
15
19
9-
24-
-17
3
11
12
13
14
15
16
17
18
19
20
21
22
23
-13
8
-7
13-
-15
-9
-2
-1
0
-8-
-28-
-54-
28
12
19
16
20
4
3
8
3
-3
8
10
0
20
19
22
7
23
6
-3
8
6
-6
27
-4
5-
-10
-22-
-11
-8
38
-4
3
0
8
4
11-
-17
2
1
-10-
-12
14
33
10
-5
11
1
8
-3
7
2
5
4
-6
10
12
7
7
21
0
-6-
-12
20
1
9
-5
-5
15
4
-8
12
2
2
5
-3
11-
-14-
-11
-6
-7
20
-1
-8
8-
-13
4-
-17-
-19-
-21-
-31-
-42
7
1
4-
-10
6
13
4
36
-3
13
11
7-
-11
20
-2
9
13
19
SO
-25
27
-5
40
14
-7-
-17
16
-1
16
7
25
SO
18
23
6
7
4-
-21
4
10
22
14
5
-6
12
31
13
14
-6
_4_
-11-
-11
6
12
6
35
20
31
41
9
6
24
15
31
-1
17
29
22
37
24
48
44
27
22
5
22
11
13
25
4
27
32
40
50
31
37-
13
2
12
16
10
28
11
35
29
20
3
15
34
4
16
-6
11
2
16
19
51
32
39
38
39
14
11
24
2
22
-9
21
18
15
5
29
31
35
8
20
1
-8
14
4
5
27
17
12
28
7
18
31
25
3
-2
13
21
-24
29
19
17
25
12
16
14-
13
6
-1
15-
-12
-22
23
11
16
26
1
13
-1
31
51
41
34
2
10
34
12
18
22
26
12
-9
22
12
29
15
18
19
7
20
24
4
23
16
11
15
cn
-P^


TABLE 14
Corrections Applied to the W3-50
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
6
8
0
13
6
12
4
18
1
6
85
1
15
27
26
14
12
1
15
-8
3
80
-19
-9
14
6
9
10
2
-2-
20
-3
75
-18-
10
14
-5
14
-4
-2-
31-
33-
16
70
15
26
29
-2
5
1
22
11
13
20
65
0
1-
27
-9-
-25-
-14
-4-
10-
11-
34
60
6-
24
-4
22
42
13
6
-8
-7-
38
55
18
0
6
-2
4
14
-4
-1
-5
4
50
10
1
3
2
-3
13
4
-5
-7
1
45
17
8
12
6
13
16
16
5
7
-4
40
12
9
9
1
10
-6
4
3
9
-5
35
11
4
0-
10
3
-7
4-
13
5
-6
30
18
5
1
5
19
10
17-
17
10
-7
25
29
24
7
15
14
13
18
7
15
10
20
5
24
5
6
15
10
12
11
18
9
15
4
17-
12
22
17
0
7
5
7
8
10
12
17
-3
5
-1
6
9
-7
9
7
5
-1-
14
-3
-5-
10-
14
6-
23
-4
0
0
5-
18
7
3-
-15-
32
4-
14-
12
-3
-5
-17
9-
18
-4-
-12-
17
2
-9
-7
-6
-10
-21
15-
33-
18-
-11-
-20-
12-
25
-9
6
11
12
13
14
15
16
17
18
19
20
21
22
23
-23
14
12
11-
17
-1
11
12
-1
-5
2
24
20
-20
-2
2
-5-
-12-
23
-8
-2-
10-
14-
10
12
5
-3
-7
1
12
4
-6-
27
-3
-4
4
-2
10-
12
25
8
-3-
19
-4
3-
-25-
-11-
40
-9
-2
-7-
32
1-
12
-1-
-32-
12-
26
1-
22
9
1
12
6
14
-8-
14-
16-
-21-
32-
38
21-
-35
3-
13
26
7
8
0
1
15
-9-
18-
28
9-
-23-
44
-6
-4
2-
17
6
5
28
-1
7-
25
-8-
14
-8
8
11
17
10
-2
0
7
1
6
-6
1-
11
-5-
25
3
-3
5
5
8
8
-6
6
-6
12
-2
-2
-4
13
8
11
-4
-3
-4
-6
-2
1
13
10
-4
-4
0
1
5
-7
-4-
12-
-12-
18-
-18-
-22-
19-
28
-9-
14
1
-4
8
14
-4
-5
3
-2
6
26
1
2
-5
10
4
24
10
-6
11
12
19
8
34
12
7
-4
2
17
11
9-
13
16
11
19-
11
-7
-9
-1
-2
0
14
8
7
-7
10
7
-1
11
7
9
1
12
11
25
-3
-6
4
8
-2
4
-2
0
-8
-7
-7
0
5
-4
-4
0
-1
4
1-
11
-6-
13
-1
11
1-
15
9
14
7
5
9
-3
-7-
-13-
26
-6-
10
-5-
10
-27
8
-4
-8
-7
-7
-6-
-17-
30
3
0-
-29-
-15
-7
1
3-
18
-6-
-21-
12
-8-
10
7-
-10-
47
-3
10
15
14
-9
14
-5
4
0
-9
5
9
1
3
5
6
11
11
1
1
8
12
-9
cn
cn


TABLE 14 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10 11
90
-7-
12
-8-
11
-2-
44
2 11
12-35-
30-32
85
27
2-
11
-6
12-
26
4 -6
1-32
-2-15
80
-5
20
-4
10
5-
11-
15-14
17 -3
18-14
75
-19
-2-
23-
26-
11
-2-
22
3
0 11-
16
4-
70
-9
0
10-
41-
13-
10-
10-24-
61 -4
-7 38-
65
-15
17
15
-5-
31
17
14
7
10-13
29-17-
60
-18
-3-
32-
28-
24
11-
17-11
6-23
5-26-
55
-26-
21-
22
-9
-9
-6
4-20-
19-11-
11-36-
50
-16-
22-
lO-
15-
40
-6
-7-14-
30-29-
20-21-
45
-12-
20-
ll
-9-
14
2
-6 -5
-5 -9
-8-14-
40
-6-
10-
16
2
2-
14-
13-21
0 -9-
10-24-
35
2
4
6
3
1
0
3-17
-6 -6
2 -3
30
8
22
13
6
0
11
-3-10
1 -9
-7-22-
25
24
24
13
11
17
9
11
7
4 15
12 25
20
6
7
7
13
6-
10-
10 -8
-2-18
-9
4
15
-7
-8
-5
18
-7
-5-
14-29-
11-35
-2
7
10
0
-1
6
8
-4
2
14 -1
18
5
11
7
5
-9
-1
9-
17
-3-
23
-3 -9
1-10-
12
6-
0
-20-
17
13
-1
18
-3-
17-16
9 -9-
14-19-
-5
-3-
21-
26-
29
-5
1
8-22
-6-42
-4-15
-10
21
-4
-4-
19
2
-8-
19-43-
25-17
5 -3-
13
14
15
16
17
18
19
20
21
22
23
9
32
36
13
-3-
-13-
28-
-49-
-46-
-38-
-21
6
11
18
24
14
4
-9-
-24
17
2
11
-20-
-31-
-24-
27
-3-
32
6-
-13
21
6
7
-25
0-
11
-2
4-
-12
15
-7
-5
19
9
14
26
26
-1
4-
10
1
18
3
12-
-53
-7
-2
-3-
-44
2-
-16-
17
29
-9
-3-
-48
35
13
-3-
-21
23
5-
19-
-21
3-
-11
4
-8-
-23
-2-
-13
34-
17
-6-
-53
6-
13
-9
-8
-4
21
13
20-
-18
-3-
-13
-6-
-10-
-10
0
4
6
-5
-8-
-14
2
0
-6-
-15
-9
1
9
1
0
3
3-
17-
-11
4
0
2
12
12
9
0
6
13
-3
0
3
-1
1
13
21
34
14-
12
11
8
30
2-
-11
3
22
25
16
37
14
26
-6
0
13
13
25
35
26
13
4
0
0
-7
0
15
7
1
-10
-2
-7
3
-3
-5
1-
-13
-5
-4
9
1
4
24
33
14
21
9
-3
5
8
13
6
-9
12
19
-5
17
2-
-15
7
7
18
-5
1
4
8-
13
8-
27
4
13
1
-9
-6
14
4
25
-9
15-
12
20
3
0
-7
-27
-6
-5
7-
-30-
-14
24
53
-2
14
0
cn
cr>
12
5
15
14
20
27
56
10
33
13
10
12
5
13
-9
-5
-4
6
26
39
7
25


TABLE 15
Corrections Applied to the GCH 1-50
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
25
-8
12
6-
-15-
-32
4
-6
-5-
-23-
-16
20
8
6
-6
-3
0-
-18-
-12-
-28-
-25-
-18-
15
14-
-16
14
11
-9
13
19
7-
-19-
-12-
10
44
16
28
12
-9
7
11
0
2
-7
5
26
17
26
21
12
37
17
11
-8
6
0
19
-7
32
31
20
26
13
10
-1
16
-5
0
0
0
0
80
99
99
99
59
26
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
25
42
16
28
25
17
39
-4
1
15
6
20
36
37
17
26
32
47
40
46
55
47
15
25
23
5
27
22
24
23
37
30
43
10
-2
9
-5
12
0
1
-7
9
28
11
5
33
26
9
23
21
46
30
34
46
25
0
19
27
-2
50
48
23
47
54
40
54
-5
0
0
0
0
-6
21
44-
-99-
-99-
-99-
11
12
13
14
15
16
17
18
19
20
21
22
23
-22-
-13-
-15
-9-
-34
3-
-22
12
6
7
6
-3-
-11
-29-
-43-
-24-
-10-
-18
0-
-14-
-17-
-31-
-20
-7
17
3
2
-8
0
4
4
11
11
3
-2
3
23
28
-2
6
0
-6
9
10
15
23
30
0
17
24
22
8
-9
10
11
26
7
3
13
22
16
25
25
33
28
17
-6
15
26
7
14
9
-4
10
3
17
52
23
86
38
15
99
10-
-18
99
99
99
99
99
0
0
11
12
13
14
15
16
17
18
19
20
21
22
23
28
36
35
3
9
20
32
38
38
46
41
35
30
35
34
25
25
49
38
30
34
46
42
47
36
32
29
25
24
22
22
35
38
28
48
30
32
22
24
12
8
11-
-13
13
17
14
18
38
25
35
30
17
-5
12
2-
-14
6
8
9
31
28
26
22
13
20
31
22
25
33
42
17
6
37
78
50
59
71
40
-89-
-99-
-99-
-98-
-99-
-99-
-99-
-99-
-54-
-54-
-54
0
0
10
5
14
17
7
9
7
77
10
50
27
39
14
29
43
99


TABLE 16
Corrections Applied to the Cape02 00
Right Ascension
dec\ra 0123456789
35 0 0-99 17 24 46 32 -9-40-99
30 16-99-39-68-59-76-80-99-99-99-
25 -76-62-74-73-80-89-85-99-91-99-
20 -55-37-55-54-88-87-83-95-91-99-
15 -58-47-62-55-78-69-75-99-99-99-
10 -61-48-68-67-87-68-73-99-99-99-
5 -45-46-50-51-54-65-99-99-99-98-
0 -38-68-66-99-77-99-28-57-44-99-
-5 -49-59-68-99-99-99-28-28 99-99-
Declination
dec\ra 0123456789
35 0 0 99 99 99 99 17-21-99-85
30 -99-12 73 99 99 95 31 15-38-20-
25 -59 -7 6 21 16 15 -2 2-13 -9
20 -17 8 12 27 19 11 3 13 26 7
15 10 15 29 33 40 45 60 40 36 8
10 14 2 27 9 27 6 93 11 16 11
5 13 18 34 31 41 -9-42 25 42 43
0 -1 12 6 24 12 43 12 16 95 25
-5 2 17 0 11 5 31 12 12 99 1
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-62
0
0
0
0
0
0
0
0
0
0
0
0
-99-
-99
0
0
0
0
0
0
0
0
0
0
99
-99-
-99-
99
0
0
0
0
0
0
0
0
0-
28
-95-
-83-
-99
84
0
0
0
0
0
0
0-
-99-
38
-70-
-72-
-95-
-99-
99
0
0
0
0
0
99-
-93-
-47
-79-
-81-
-85-
-90-
80-
99
0
0
0-
-99-
-29-
-40-
-42
-86-
-63-
-69-
-60-
-66-
37
0
0
0
99-
-41-
-24-
-41
-65-
-44-
-77-
-42-
59
93
0
0
0
99-
-52-
-43-
63
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
99
0
0
0
0
0
0
0
0
0
0
0
0
20
99
0
0
0
0
0
0
0
0
0
0-
-99
31
75
99
0
0
0
0
0
0
0
0
0
7
14
24
16
42
0
0
0
0
0
0
0-
-63-
-10
10
9
-1
0
99
0
0
0
0
0-
-99
46
-8
31
15
8
-3
14
70
0
0
0
99-
-30
-1
1
2
3
-6
6
4
85
0
0
0-
-99-
-42-
-20
-4
-8
-3
-8
15
21
61
0
0
0-
-99-
-55-
-34
0
10
0
70
99
86
77
72
77
82
47
10
0
43
0
19
18
19
36
19
-1
cn
00


TABLE 17
Corrections Applied to the Nice 10
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
20
-99-
99
99
99
6-
-53-
-99-
-20
99
99-
-35-
-99
11-
-18-
-99-
-99
30-
-99-
-99-
-99-
-99-
-45-
-99
15
-55-
46-
-67-
-89-
-59-
-19-
-90-
-97-
-94-
-82-
-81-
-84-
-68-
-85-
-60-
-18-
-99-
-80-
-88-
-78-
-32-
-53-
-68-
10
-99-
85-
-96-
-35-
-42-
-58-
-96-
-86-
-69-
-73-
-90-
-99-
-75-
-64-
-85-
-78-
-51-
-43-
-93-
-64-
-55-
-84-
-69-
5
-32-
85-
-64-
-68-
-10-
-56-
-88-
-79-
-97-
-99-
-99-
-86-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-98-
-50-
-90-
-78-
0
0
99
36-
-99-
-99-
-79-
-51-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-44
99-
-99-
-99-
-99-
-99-
-99-
-51-
-87-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
20
57
77
99
99-
-99-
-99-
-99-
-99
99
51-
-84
99
99
99-
-46-
-99-
-99-
-80
77
99
99
99
99
15
88
77
30-
-29
29
24
-2
15
28
85
35
48
34
99
96
74
98
49
41
78
-2
32
53
10
47
42
28
49
46
43
18
40
-9
3
37
45
44
90
93
54
44
13
33
46
35
51
10
5
99
79-
-59
29
42
82
28
41
46
69
5
49
51
41
90
79
46
42
14
40
57
87
43
0
0-
99-
-99-
-19
99
99
99
-5-
-99-
-99-
-74
99
99
99
59-
-84
99
99
99-
-28
99
56-
-99-
23
30
25
75
50
99
23
99
53
19
18
99
on


TABLE 18
Corrections Applied to the Nice 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -99-99 -8 6-12-61-99-99-99-99-99-99-99-99-99-95-79-88-99 2 23-15-70 5
5 -50-52-60-51-56-63-80-99-88-86-82-82-99-48-54-98-76-75-99-53-27-51-85-40
0 -55-54-68-50-94-96-81-99-99-62-86-89-82-75-66-75-76-70-73-71-69-56-56-53
-5 -68 13-63-90-69-89-97-76-91-99-99-92-99-90-62-83-99-60-68-74-71-77-84-92
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 21 72 11 -6 47 99-16-99-64 99 99 99 99 99-99-95-99-56 99-99-99-98 56 -4
5 40 13 8 39 36 68 43 11 32 31 56 60 62 42 33 80 49 52 66 67 63 34 64 54
0 1 23 13 16 3 4 4 44 51 18 33 58 18 25 79 71 50 38 10 24 48 64 28 46
-5 -13 29 3 44 36 65 45 2 57 11 39 4 55 47 29 64 23 55 77 37 61 38 46 0
TABLE 19
Corrections Applied to the GCH Z 10
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
35 14 2-39-99 5 45-23-81 6 2-55-67-95-66 7 24-39-71-12-34-32 4-19-18
30 -63-41-39-58-58-59-34-74-67-84-84-46-47-91-99-99-79-94-73-83-72-76-82-48
25 -73-67-74-52-74-64-76-87-64-66-60-52-81-69-53-76-89-72-50-71-89-65-74-55
20 40-43-99-85-70-32-99-99-99-99-99-99-99-99-99-99-57-99-99-99-17 61 38 55
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
35 81 98 19-14 29 12 2 50 6 20 90 40 37 22 10-20 18 8-37-19-14-30-39 0
30 -32-17-15-31-38-22-39-18-18-20-21-27-18-15-23-39-12 1-29-40-32-32 -9-25
25 -13-19-18-28-16-30 -9-13 -7 -3 -1 -3-15-28-15-10-20-22-44-27-32-37 -4-17
20 24 -3 32 14 9-27 20 -6 23 5 9 6 76 18-19 8-11 28 7-21-74-74-69-45
cr>
o


TABLE 20
Corrections Applied to the Paris 90
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
60 -46-99 44-99-99-99-99 000000000000 0-99-99-99 99
55 -18 52 99 99 32 42 99-80-21 47 90 99-62-40 99-99 11 99 99 81 99 99 99 68
50 27 99 99 99-99-99 -5 8 23 48 99 65-99 11 40 84-26 6-10-27 99 19 8 31
45 54 83-68 99 28-99-99-94-99-74 14-19-71 15-16 68 -4 21-55 59 99 31 66 99
40 7 8-13-57-99-99-99-63 37-44-18 65-20-46-85-50-60-67-14-43-32-21-49-28
35 -99-28 -3 32-41-95-93-99-99-43-32-53-79 4-99-99-93-79-17-32 2 99 87-79
30 -9 5 -4-77-99-99-99-86-99-99-16 -5-99-99 2-67-99-69-57-45-31 46 30-97
25 59 99-13-53-99-99-99-99-99-99-92-99-99-99-99-99-99-60-24-25-47-80-41 11
20 -39-25-61 54-27-99-99-99-99-99-87-31-21 4-99-99-92-67-99-65-23-99-51 -9
15 -40-42-49-14-99-99-99-99-99-99-60-99-99-99-99-62-22 -8-55-99-99-89 40 -6
10 -83-15-23-99-32 -8-90-99-99-99-89-63-99-89-99-99-99-84-42 14-17-65 2-51
5 -6-38-86-92-99-99-99-99-88-22-26-77-41-99-24 8-14 33-37 72 37 76 83-99
0 7 99 12-52-99-99-99-97-99-99-99-99-77-99-29-99-99-17-64-64-17-99 21 87
-5 35 99 39 -6-68-69-99-99-99-99-57-72-16-10-77-99 20-88-99-29 27-49 -3 99
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
60
-99-
-99
47
99
99
99
99
0
0
0
0
0
0
0
0
0
0
0
0
0
99
99
99-
-99
55
-20-
-61
99
99-
-37
15-
-31-
-57
71
32
60
99
14-
99
99
60
64
8
5
43
30-
-64-
-99-
-67
50
25
-9
14
58
-5
70
21-
-57
33
49
31
37-
-17-
42
-4
42-
-39-
-92-
-77-
-70-
-46-
-33-
-20
-8
45
25
44
27
11
-1
96-
32
8
66
99
27
-1
10
90
6
2
-7-
-40-
-46-
-90-
-70-
-59-
-34-
12
40
57
51
7-
-62-
70
-6-
22
14
31
4
9
40
42
89
1-
-14-
-99-
-99-
-99-
-52-
-86-
-87-
-22-
-40
35
-44.
-49-
-44
33
39-
-14-
-40
43
31
20
35
33-
-12
-3
27-
-20-
-53-
-50-
-45-
-28
0-
-10-
-28-
-99
30
-57-
-35
79
14
19
55
35
49
32
55
15
31
57
-5
41
-7-
-42-
-43-
-28-
-27-
-21
11-
-32-
-24
25
24-
-36
19
29
84
37
33
30
62
47
14-
-67
8
99
58-
-15-
-29-
-32-
-34-
-71-
-40
-8-
-30
24
20
8
52
15
47
44
59
77
27
-1
52
65-
-20-
-21
85
55
-3
-8-
-41-
-99-
-22
37
54-
-26
-8
15
-31-
-27
-1
48
25
57
88
39
62
45
37
94
64
43
27-
14
14
-3-
-48-
-59
3-
-28-
-54-
-21
10
-1
-4-
-14
30
-4
36
99
78
5
35
45
7
55
43
25
25-
-16-
-38-
-15-
-18-
-12-
-26-
-26
35
5
-22
25
45-
-45
27
73
66-
-15
33
46
51
53
29
68
44-
-37
-7
5
2-
-65
-6-
-51-
-99-
-93
0
26-
-43
49
-5
57
59
44
99
99
83
65
84
20
36
57-
-16
0-
-77-
-76
-8-
-56-
-18-
-38-
-22
-5
-59-
-11
99
19-
-34
19
93
99
51
32
69
18
-1
56
44
2-
-19-
-99-
-58-
-49-
-35
-2-
-16-
-99


TABLE 21
Corrections Applied to the Paris 00
Right Ascension
dec\ra 0123456789
30 2 75 57-14-99-90-47-12 4-68-
25 -62-48-57-83-99-99-99-99-99-99-
20 -81-94-82-99-99-99-99-99-99-99-
15 -88-99-72-92-99-99-99-99-99-99-
10 -85-99-93-99-99-99-97-99-99-99-
Dec 1ination
dec\ra 0123456789
30 -4-37 12 27 19 -4-17 18 31 22
25 28 4 32 31 18 3 -6 10 23 32
20 12 0 12 20 11 5-5-6 3 18
15 -25-34-38 -5-12-20-38-40-23 -6-
10 -72-99-99-99-96-99-99-83-25-14-
11 12 13 14 15 16 17 18 19 20 21 22 23
-99-96-99-99-99-51 30 55 0-71-99-99-54
-99-67-81-99-99-99-84-89-87-94-99-99-75
-99-88-99-99-99-99-99-99-99-87-82-82-81
-99-99-99-99-92-93-88-87-79-38-49-73-99
-99-99-99-63-43-33-28 19 11 72 30-23-99
11 12 13 14 15 16 17 18 19 20 21 22 23
17 -4 8 12 26 48 44 53 54 31 -2 15 3
6-13 3 -2 16 25 31 20 30 20 19 37 20
-4-10 0 1 12 6 13 -5 22 18 22 25 4
-27-30-27 -9-11-22-12-31 10 6 0 -7-27
-75-99-99-91-90-62-23-38-14-26-56-78-78
10
99
99
99
99
99
10
0
5
5
10
29
cr>
ro


TABLE 22
Corrections Applied to the GCH 2-25
Right Ascension
, dec\ra 0123456789
65 -4 -7 18 29-10 11 4 7 11 4-
60 -8-15-27 14 0 -9-17 0 -8 -5-
55 2-13-12-12-10-24-21-19-31-28
50 -33-23 0 -9-12-30 1 0-18-18-
45 -6 -8-15 -7-25 -9-23 -7 -2 5-
40 -22-28-27-31-20 -9-34-18 -4-21-
35 -33-28-15 -5-22-12-18-39-35 -8-
30 12-81-42-15-34-14 2-34-58-50-
Declination
dec\ra 0123456789
65 39 78 70 61 78 40 60 85 51 6
60 30 29 43 32 20 51 38 34 32 39
55 28 54 34 24 32 27 40 15 16 39
50 8 7-13 20 14 21 16 7 33 20
45 7 32 42 25 18 16 13 24 32 8
40 27 34 31 15 19 27 12 37 33 11
35 13 25 4 -4 10 12 -7 5 4 3
30 -5 24 46 6-13 -1 20 8 -8-19
11 12 13 14 15 16 17 18 19 20 21 22 23
13-17-33-38 -8 24-23-23-45-29 1 25 -5
-17-14 1 0-13-15-19-21-19-12-17 -4 -8
-19-21-24-16-18-14-26-10-27-41 4-13-21
-19-42-23-25-11 -8-46-23-20-20 -6 -5-11
-19-33-39-18-32-15-11-27-13-37-33-24-10
-8-33-27-28-20-29-30-31-24-27-24-13 -2
-23-31-13-20-24-43-39-38-21-29 -8-26-29
-18-44-16-15-33-54-36-24-41-67-48-46 45
11 12 13 14 15 16 17 18 19 20 21 22 23
11 5 3 -4 48 26 3 3 27 41 28 60 72
18 33 27 3 9 -3 -9-11-14 10 15 14 17
26 31 29 21 16 3 8 7-2 4 11 28 30
9 12 8-2 -7 15 0 -9-22 -8 14 11 5
-13 -8 -2 -7 5-13-18 -8-24 -5 -9 9 11
4 25 24 15 11 8 17-12 -1 -1 25 30 38
20 1 0-4 2-9 4-21-10 22 11 6 8
13-31-16 6 3-12 2-10-27 24 1 35 37
10
13
13
-8
19
18
28
22
28
10
30
11
40
0
-7
29
6
-7
cn
OJ


TABLE 23
Corrections Applied to the Berl 20
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 -84 99 79-99-99-78 71 20-99 63 84-82-88-88-38 99 99 37-19-99-99-99-99-99
40 -99-79-73-68-79-99-86-81-99-84-73-64-93-99-85-84-96-95-87-98-62-91-79-99
35 -99-99-99-92-84-99-99-99-99-99-99-99-94-99-99-99-99-99-99-86-99-99-99-99
30 -96-50-90-99-99-99-83-99-99-99-86-99-99-99-99-99-99-99-99-99-99-71-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 14-99-99 66 99 99 32 89-99-99-99 99 99-74-99-14 37-24 99 99 42 99 99 99
40 22-20-32-40-16-29-35 26-63-65-23 -4-12 5-31 20 18 0 9 6 27 28 17 47
35 -21-20 -3 13 -2-11-57-19-29 2 -3-11-24 5-13-25-12 21 0-16 -8 2 -4 -8
30 89 43 61 26 8 34 67 76 67 32-14 -9 25 47-25 42 35 81 85 35 52 6 75 89
TABLE 24
Corrections Applied to the GCH 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 99 10-13 83 58 71 94 54 50 54 69 99 46 35-32-34-28 4 18-12-62-65-27 26
85 12 -4-18 3-24 -9-14 16 13 6-24 11 -4-15-23-15 -1 43 2-64-50-45-32-45
80 -56-54-57-35-28 -7-40-61-31-20-40-55-26-13-52-45-50-42-53-54-65-29-72-76
75 -11-34-64-31 -9 -1-26-22-39-47-34-55-31-51-88-65-25-31-52-62-59-44-74-66
70 -48-38-32-41-60-49-20-35-39-33-51-46-61-85-63-64-51-72-48-54-73-78-66-38
65 -99-97-87-81-63-76-86-69-83-73-92-99-90-99-75-92-89-92-99-87-94-99-99-99
60 -27-99-99-89-99-99-99-99-99-99 56-55-99-99-64-99-99-99-99-99-99-99-99 -8
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 -7-15-44-28-37 12 30 58 21 12 7-42-10 34 28 26 20-19 21 -6 5 13 28 22
85 22-19-19 -1 12 21-15 1 9-25 -3-29-41 20 31 13-28 39-60 -9-20-12
80 5-14 -5-44-61-25 11 -3-19 -2-21 -9-13-23-26-23-24-43-24 3 0-34-27-20
75 44 5 -4 17 9 5 7-10 -4-11 3-33-13-14-57-33 3-12 1 27 12-14 10 40
70 14 38 43 29 40 28 41 16 -3-62-24-14 11 30 -2 16 21 -5 0 -6 30 74 41 23
65 10 11-18 6-13 7 18 -5 10 33 35-16-10 5 -1 15 23 2 1 3 29 54 28 -7
60 -35 63 99 52 26 45 25-40-15 21 32-61-54 20 48-31-47 40 3 -4 99 99 99 35
cn
-P>


TABLE 25
Corrections Applied to the Toul3 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
15 -42-71-97-99-99-99-99-99-99-99-54-99-99-83-93-99-88-99-99-99-98-90-65 -1
10 -69-82-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-74-82-74
5 -82-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-95
0 -99-59-69-61-87-99-99-99-99-99-99-84-99-99-57-41-99-99-99-99-99-99-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
15 -50 16-14-51-62 -2 25 0 6-51-31-28-67-23 6 8 10 11-34-20-34-28-55-74
10 -7 2 14 21 20 6 -2-21 2 -5 -7 -8-29 4 9 4 22 24 10 -1 -9 14 -1-11
5 7491 20 11 45 -5-12 -5-21 -4 -6-12 25 15 1 2-10-11 -6 -5 4
0 -39-28-23 -6 27 58 44 39 17 15 -6-27 -9 0-19 29 39 40 45 36 70 31 -6 8
cn
<_n


TABLE 26
Corrections Applied to the Cape 2-25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0
65
1-
94-
99
0
0
30
0
0-
99-
18
-1
-7
6
44-
36-
99
25
0-
-99-
52
-4
5
-9-
17
13
0-
13
20
99
83
19
19
10
-1-
13
5
14
-9
15
41
17
-2
4
-8
20
26-
21
10
-4
10
17
25
-2
0-
35-
99
99
80
-2
-4
5
-9
-7-
32
-1
99
0
0
0-
99-
21
0
16-
10-
28-
77
0
0
0
0
0-
99
-5
30
52
99
0
0
0
0
0
0
0
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0-
16
27
28
28
0
0
30
0
0
99
99
40-
21
1
17-
13-
41
25
0-
99
-2
43
21
15
10
11
26
4
20
99
46
39
46
30
1
15
6
29
34
15
81
51
22
29
32
4
61
50
25
37
10
53
28
41
32
9-
32
55
99
60
34
5
42
24
36
73
99
0
0
0-
99
32
0
51
26
31
99
0
0
0
0
0
54
-5
33
83
99
0
0
0
0
0
0
0
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
99
0
0
0
0
0
0
0
0
0
0
0
0
48
29
0
0
0
0
0
0
0
0
0
0
0
-8-
-45
0
0
0
0
0
0
0
0
0
0
0
2-
-26-
-91
0
0
0
0
0
0
0
0
0-
-68
-21-
-12-
-45-
99
0
0
0
0
0
0
0-
-99-
-45
-24-
-23-
-25
-6
99
0
0
0
0
0-
83-
-54-
-33
15-
-28
-5
22
36
0
0
0
0
0-
83-
32
-7
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-72
0
0
0
0
0
0
0
0
0
0
0
0
99-
-99
0
0
0
0
0
0
0
0
0
0
0
24
29
0
0
0
0
0
0
0
0
0
0
0
47
18-
-88
0
0
0
0
0
0
0
0
0
99
43
45
26-
33
0
0
0
0
0
0
0
23
53
58
45
32
31
92
0
0
0
0
0-
29
20
39
46
47
49
41
25
0
0
0
0
0-
29
44
44
10
0
0
6
11
6
11
10
48
99
10
0
0
44
71
28
50
50
67
45
cn
cr>


TABLE 27
Corrections Applied to the Cape 3-25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5 -54-18 0 -7 14 12 11-18-55-62-82-55-52-68-19-43-31-42-18-42-52-84-83-81
0 -25 -5 -3-20-17-29-17-22-26-19-25-14-19-29 0-27-29-42-49-55-46-52-55-42
-5 86 2-26-27-46-31-26-17 -4 -4 -1-22-17 -5-24-28-35-50-53-38-24-26 -1
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5 9 -3 58 84 68 15 0 3 -9 17 50 75 50 13 28 16 34 20 13 31 43 42 51 25
0 25 15 30 40 44 17 19 17 19 27 39 46 32 15 30 19 40 29 40 43 48 35 37 27
-5 35 26 19 22 34 25 30 26 31 32 32 28 22 21 33 21 42 33 57 55 60 38 38 38
CTl
^4


TABLE
Corrections Appli
Right Ascension
dec\ra 0123456789 10
35 0 0-99-50 1 15 36 13-12-64-99
30 0 99-32-42-18-11 3-17-36-54-57
25 -24 99 22 19-17-14-18-20-12 3-11
20 -16 5-18-12-31-18-30-22-23-34-59
15 -10-25-26-45-55-30-37-28-55-52-47
10 8-31-41-56-73-53-66-38-54-40-42-
5 -25-40-44-50-31-39-43-79-65-63-42-
0 -38-41-36-35-25-32-28-50-38-40-31-
-5 -30-22-32-33-35-42-33-43-29-24-28-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
35
0
0
93
28
15
16
3
12-
-55-
71-
-99
30
0-
-99
-1
-5
-4
-5-
10-
-15-
-50-
38-
-61
25
-99-
-99
9
15
20
-1
-6-
-17-
-10
11
7
20
-99-
-99-
12
21
8
5
-2
-4
-3
1-
-11
15
-78-
-30
4
26
6
19
20
28
18
-8
-9
10
6
31
15
34
39
54
65
38
18
1
11
5
2
20
7
-7-
-27
0
44
39
-2
11
-6
0
7
13
3
-4-
-22-
10
6
11
-4
7
12
-5
-1
1
13
26
1
-5
-7
7
2
12
15
to the W 40
12 13 14 15 16 17 18 19 20 21 22 23
000000000000
000000000000
95 99 00000000 0-24
49 99 00000000 0-33
26 93-40 0 0 0 0 0 0 0 0-82
31-23-39 79 0 0 0 0 0 99 99 99
33-29-24-29-24-81-36-37-16-12-18-14
33-30-29-38-35-57-29-40-41-39-44-47
46-35-42-44-39-42-28-47-60-52-51-43
12 13 14 15 16 17 18 19 20 21 22 23
000000000000
000000000000
99-99 00000000 0-99
74-99 00000000 0-99
12 28 88 0 0 0 0 0 0 0 0-99
6 12-49 99 0 0 0 0 0 97 4 37
18-21-20-29-21-40-49-61-16 025
-2-16 -9-15 1 0 2-22 1 -5 12 6
10 10 13 -7 7 14 33 18 34 10 24 -3
: 28
ed
11
0
47
15-
21
4
25-
31-
34-
30-
11
0
99
27-'
47-
-5
35
2-
-2
0
O'
00


TABLE 29
Corrections Applied to the W 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 000000000000000 0-21-21-21-21-21 0 0 0
45 -54-76-67-19 4 12-99-91-99 99 0 0-99-99-47 24 27 24-23-43-72-46-37-29
40 -23-47-69-19 11 29-81-46-73 99 0 0-99-99-57-20 -6 -1-32-46-71-21-15 -9
35 -13-39-73-30-16-33-68-30 -7 99 0 0-99-99-73-60-51-51-58-58-50 511
30 -1 51 10 16-17 -6-23 1-25 2-51 96-99-99-98-99-97-99-99-99 99 99 30 8
25 -14 -2 -6 -7-18-26-41-39-52-37-51-28-99 00000000000
20 -15-42-52-55-35-44-53-68-61-59-67-53-59 99 000000000 99
15 -22-21-37-36-45-45-49-57-55-54-54-35-35 19-99 000000 0-39 3
10 -49-39-52-39-68-64-99 -7-40-33-52-46-37-25 32-99 0000 0-99-68-40
5 -36-33-37-26-28 34-99 99 -9-26-48-53-45-38-30-22-99 000 0-99-55-47
0 -41-50-34-41 19 43 0 99 36 5-39-45-71-55-70-37-99 000 91-65-46-54
-5 -39-70-69-99-99 0 0 0 99 73-14-17-48-40-52-39-70 000 91-49-34-56
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 000000000000000 0-42-42-42-42-42 0 0 0
45 -4-17-64-71-70-88-15-99-71-99 0 0 99 99 84-16-24 -4-27-32-56 -8 -1 50
40 -29-16-29-42-23-50-13-99-93-99 0 0 99 67 15-32-36 -3-17-2.2-69-17-41-41
35 -37-26 -5-16 8-36-21-60-47-99 0 0 99 18-17-36-51-32-41-35-85-24-61-72
30 -72-64 -7-17-17-32-31-51-18-25 43-45 12 10-13-40-74-92-99-99 99-99-99-99
25 40 -9 8-17-11-45-57-61-32-42-24-53 36 00000000000
20 -41-36-30-29-20-48-51-43-26-39-27-22 22 99 000000000 56
15 -15-19-46-50-39-57-53-63-57-60-56-41-36 6-99 000000 0-99 46
10 -43-33-51-65-58-77-51-95-57-51-48-55-65-70-93 99 0 0 0 0 0 99-99-33
5 -50-48-62-80-99-99 99-99-25-45-43-67-72-62-46 53 99 0 0 0 0-61-58-47
0 -51-37-35-24-29-99 0-99-27-59-66-77-78-75-67-58 15 0 0 0 99-32-44-47
-5 -67-65-68-38-35 000 99-62-44-60-54-84-80-99-84 0 0 0 99 -6-29-52
cr>
id


TABLE 30
Corrections Applied to the W ZOD 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0-
-99-
-12
5
33
53
68
94
99
30
-69-
36-
22
2
6
16
10
5
-3-
-12-
25
-24-
34-
-19-
-17
-5-
-12
-6
-4
-4
-3
20
15
2
1
-9-
-12
-9
-9
2-
-21-
-15
15
-9-
10-
-11-
-17-
-13
-9
-6
-1-
-19-
-18
10
-19-
17-
-24-
-13-
-10
4-
10
-5-
-11-
-10-
5
-37-
29-
-41-
-15-
-19
99-
99
94-
-33-
-21-
0
-34-
23-
-32-
-22-
-65
99
0
99-
-95-
-53-
-5
-21
-7
9
28-
-99
0
0
0
66-
-43-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
99-
-22-
-11-
-25
5
14
63
54
30
-33
40
99
62
43
15
0
32
13
9-
25
19
13
34
19
12-
-15-
12
19
17
-4-
20
21
16
9
6
7
-8
-1
9
18
13
15
-8
-6
-7
-4
2
-8
-4
4
15
14
10
-21
-9
-6
-8
-6-
-30-
92-
47
-6
16
5
-11
0
-9
-2-
-11
5-
99
99
-3
6
0
-18-
26-
-41-
-52-
85
99
0
99-
-50-
-12
-5
-3-
37-
-51-
-99-
-99
0
0
0
99
99
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-90
0
0
0
0
0
0
0
0
0
0
0
0
-3
3
0
0
0
0
0
0
0
0
0
0
49
5
32-
-99
0
0
0
0
0
0
0
0
0
0
-18-
-18-
-51-
-23
0
0
0
0
0
0
0-
-99-
-10
-23-
-18-
-23
-3-
-99
0
0
0
0
0
44-
24
-9
-17-
-15-
-14-
-19-
-40-
34
0
0
0
0-
-19-
-37-
29
-39-
-37-
37-
-34-
-34
24
0
0
0-
99-
-58-
-47-
37
-27-
-17-
-44-
-25-
40
47
0
0
0-
99-
-94-
-64-
48
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-99
0
0
0
0
0
0
0
0
0
0
0
0
-69-
-30
0
0
0
0
0
0
0
0
0
0
17
1
-9
99
0
0
0
0
0
0
0
0
0
83
-14-
-14-
-60
99
0
0
0
0
0
0
0-
99
2
13
27
17
69-
99
0
0
0
0
0
99-
-63-
25
6
11-
-20-
-32-
99
81
0
0
0
0
79
0
8
-3
-2-
-15-
-12-
24
70
0
0
0-
43-
-14-
12-
-11
42
15
21
24
39
59
0
0
0-
43-
-14
-1
-1
10
99
18
-7
-2
-9
20
31
48
11
10
62
76
29
1
9
19
-4
-8
50
o


TABLE 31
Corrections Applied to the Cape 1-50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35 29 27 2 2 5 48 81 13-54 33 66-46-72-27 1 23-37-18 28-25-48 12 9
30 -6 24-14 5 2-16-30-21 6 26 10 24 -8-28 -4 0-13 18 11-21-44-12-19-
25 -10 30-40-65 62 -6-10-16 -7 38-27-12 4-28 10 11-13 -9 -8 22-34-38 18
20 -25 -9-12-31 -1 -2 -1 12 0 11 8 2-24-33-26 4-24-49-30 19 35 3 1
15 -8-19 -4 48 17 12 19 -8-11 -5-26 33 66 22 0 5-21 -8 -3-19 1-63-21
10 -13 -6 1-1 0 26-17-28 10-27 13 -6-45-17-53-47-44 25 50-49-30 -7 -7
5 18 9 16 -4 -8-13-30-18-32 5 8 15 4-3-2 3 26 6 9 -4-23 35 18
0 -15 -4-32 -8 24-19-14-14-17-11-33-23-22-16 31-65-99-15-26 15 -7-47 17-
-5 19 10 23 3-33-41 10 10 27 19-22-19 -9 8 36 6-45 20 -5 33 60 5 50
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35 -17-33-40-99-96-99-99-62-26-22-26 -9-13-47-18-46-51-13 24-12-35 72 55
30 18 32 45 21 10 5 11 17 8 1-11 2 0 2 41 12 18 0-10-12-10 98 30
25 9 27-13 11 65 32 0 8 34 23 20 39 53 46 54-30 -4 25 28-60 43 49 15
20 18-44-39 6 5 11 -8 12 14 9 10 6 -8 18 6-19 1 57 26-46-32 3 20
15 -7 17 53 80 21 9 36 3 28 35-33 13 33 55 44 40 21 8 3 8 -2 63 24
10 40 4 62 1-35 36 22 -9-28 3 7 43 41 23 35 10-14 5 43 63 10 -7 6
5 2 45 35 19 -5 41 83 -2 20 18 25 39 38 29 31 39 68 27 9 26 38 4 39
0 15 18-14 29 26 22 27 5 24 28 36 46 -4 11 -8-26 30 34 30 20 36 26 28
-5 32 22 41 36 12 10 35 32 36 51 77 26 11 47 21 43 41 25 31 48 44 9 31
23
6
35
25
-2
-5
-8
20
18
17
23
45
-5
-7
37
2
51
68
43
50


TABLE 32
Corrections Applied to the Bord 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
25 -16 41-91-99-99-61-64-99-99-99-99-99 99-20-99-99-99-99 27 99 60-71-99-15
20 -33-12-77-71-99-59-58-63-85-99-91-79-29-99-99-53-31-81-26 0-68-83-73-38
15 -54-52-71-68-44-47-60-59-89-98-73-56-53-89-86-49-51-59-70-62-77-73-74-58
10 -79-47-21-83-58-61-77-58-99-95-99-84-89-93-87-74-86-47-84-74-67-54-87-86
5 -96 22 99-99-99-99-99-77-99-99-99-99-99-99-94-77-66 -9-65-75-81-48-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
25 99 99 99 99 99 99 99 99 99 99 99 82 82 99 99 99 53-37-73 40 92 99 99 99
20 63 67 71 81 57 70 76 65 50 81 62 32 19 46 51 73 63 47 23 34 58 64 69 38
15 31 17 10 38 25 22 8 22 23 34 32 24 33 37 55 59 47 60 52 37 47 32 28 10
10 78 49 34 47 30-11 -5 28 33 4 12 26 56 50 80 82 75 93 76 52 60 52 48 48
5 99 99 99 81 36-52 35 64 44-44-29 12 52 65 99 99 99 99 99 69 68 99 99 99
TABLE 33
Corrections Applied to the ALB99 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -99-99-99-99 0000000000000000 0-99-99-99
5 -72-68-77-31-44 3-53-59-99-99-99-99-77-36 -5-20 -9-69-48-99-67-78-34-92
0 -63-11-47-14-44-16-70-60-87-53-83-75-61-31-25-49-48-81-58-99-77-69-33-45
-5 -83 23-27 -6-37-25-65-50-56-23-51-46-43-22-48-86-82-85-57-99-99-99-99-86
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 99 99-99-89 00000000000000000 99 99 99
5 30 29 1-39 -7 1 9 21 47 61 87 90 52 5 50-24-26 -6 27 99 99 99 85 59
0 -28 13 -8-39-23-11 0 19 32 33 33 57 26 8 45-30 -4 5 11 44 80 38-12-42
-5 -73 -5-18-40-38-18 -6 25 48 29 -4 12 -8 16 38-39 -1 7 7-25 -2-41-70-99
^4
rv>


TABLE 34
Corrections Applied to the Mun97 OOii
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
55 0 12 12 12 00000000000000000000
50 -91-46-49-46-70-99-99-99-77-74-77-99-99-20-16 -6-99-99-99-44-40-59-85-58
45 -58-57-67-80-76-85-82-78-84-89-74-86-89-89-92-65-73-87-67-78-87-95-95-72
40 -79-87-84-97-79-87-98-90-78-80-82-84-95-99-99-99-99-99-96-93-92-73-88-98
35 15 15 4 -4-76-29-31-94-87-99-99-88-77-87-27-49-99-99-99-81-75-37 26 0
Declination
dec\ra
55
50
45
40
35
30
25
20
15
10
5
0
0
0
17
-14-
-32-
40
0
0
0
0
0
0
0
12 3
11 11 11
37-25-27
15-23-24
25-19-27
40 99 99
0 0
0
0
0
0
0
0
0
0
0
0
0
0
4 5
0 0
-65-99-
20-44-
25-17-
41 13-
0 0
6 7
0 0
63 99
37-26-
30-26-
17-38-
0 0
8 9
0 0
-5 -7-
24-27-
30-16-
24 12-
0 0
10 11
0 0
31-99-
47-47
35-31-
19-44-
0 0
12 13
0 0
99-99-
-3-16-
18-16-
38 34
0 0
14 15
0 0
99-99
51-39-
20-15-
23-77-
0 0
16 17
0 0
18 24-
44-35-
14-23-
51-25-
0 0
18 19
0 0
18 10
10 0-
24-33-
16-37-
0 0
20 21
0 0
22 -9-
15-24-
27 -8-
29 2
22 23
0 0
96-99
38-68
14-52
29 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 19
0 19
19 19
19 19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
^4
CO


TABLE 35
Corrections Applied to the Mun97 OOii
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
70 00000 99 99 99 99 99 00000000000000
65 -37-40-45-38-34-33-35-30-29-31-31-14-29-42-52-35-13-19-15-25-28-37-30-32
60 -34-40-45-37-30-32-46-43-44-44-48-40-52-48-52-50-31-32-30-38-37-47-38-32
55 -29-44-51-40-27-25-43-42-47-50-55-49-57-42-49-55-46-41-39-48-47-53-42-31
50 -16-37-58-49-30-16-40-45-50-57-60-53-54-29-44-61-74-62-57-58-56-55-39-24
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
65 23 32 9 4 26 45 26-18-40-43-19-15 20 20 6 2 -3-10 6 16 26 22 2 11
60 -7 12 -4 -5 7 15 1-10 -8-17-10-21 -1 0-14-15 -9-13 -3 10 16 18 -6 -9
55 -31 -5 -9-12-10-11-21-21 -7-16-14-26-10-15-37-46-27-24-21-12-11 3-23-28
50 -73-57-43-62-58-59-54-45-28-35-33-33-15-29-67-93-61-41-57-66-81-42-59-62
TABLE 36
Corrections Applied to the Kon 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0
0
99
48
31
-8-
-35-
-41-
-57-
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
-99-
-88-
-39-
-47-
-52-
-70-
-91-
-85-
-99-
-99-
-99-
-99
0
0
0-
-58-
-56-
-54-
-51-
-45
25-
-99-
-99-
-99
25
-69-
-52-
-62-
-65-
-82-
-93-
-99-
-98-
-99-
-90-
-99-
-99-
-99-
-99-
-64-
-77-
-80-
-85-
-99-
-99-
-99-
-97-
-99-
-82
20
-38-
-44-
-61-
-69-
-85-
-98-
-99-
-99-
-99-
-95-
-99-
-99-
-99-
-13-
-85-
-70-
-72-
-79-
-94-
-89-
-94-
-82-
-99-
-29
15
-51-
-60-
-70-
-77-
-81-
-94-
-99-
-99-
-99-
-90-
-96-
-86-
-90-
-61-
-75-
-49-
-50-
-59-
-71-
-74-
-82-
-64
-1-
-40
10
-67-
-77-
-83-
-75-
-65-
-50-
-75-
-83-
-88-
-92-
-96-
-90-
-87-
-82-
-46-
-26-
-25-
-36-
-52-
-63-
73
16-
-21-
-58
5
-64-
-64-
-77-
-68-
-78
47
99-
-99-
-99-
-99-
-99-
-99-
-93-
-96-
-86-
-99
99
0
0
0
0-
-38-
-58-
-55
0
-63-
-55-
-64-
-66-
-99
0
0-
-99-
-86-
-99-
-99-
-99-
-89-
-85-
-78-
-75-
-70
0
0
0-
-68-
-99-
-80-
-70
-5
-66-
-72-
-71-
-96-
-12
0
0
0-
-99-
-99-
-99-
-94-
-75-
-63-
-67-
-65-
-99
0
0
0-
-68-
-99-
-88-
-77
^4
4^


TABLE 37
Corrections Applied to the Pulk99 00
Right Ascension
dec\ra 0123456789
20 -91-25-99-99-99-66 18-99-94-99-
15 -38 15 1-15-34 -5 -4-72-55-92-
10 -49-36-29-48-48-32-39-50-32-81-
5 -78-52-34-46-84-62-99-99-82-97-
0 -84-70-20-26-75-67-60-78-99-91-
-5 -19-46-31-77-75-87-55-61-85-44-
Declination
dec\ra 0123456789
20 99 -4 99 81 76 20 99 93 65 25-
15 59 -8 27 18 24 8 16 2 5 5-
10 22-14 17 26 49 45 16-28-16-18
5 38 13 23 22 39 49 40 -1 0-11
0 22 8 8-13 -1 9 26 12 -4 6
-5 -28-46-12-35 -5 0 11 11-45-36-
11 12 13 14 15 16 17 18 19 20 21 22 23
99 99 99 7 28 2-39-33-72-80-68-95-70
2-19-23-68-37-12-43-31-60-69-82-85-66
-84-90-70-60-39-37-63-64-65-11-50-31-74
-94-99-71-40-27-52-79-70-67-17-65-61-99
-81-99-81-57-33-53-76-81-99-63-72-67-99
-1-54-37-45-40-68-83-81-99-69-60-52-84
11 12 13 14 15 16 17 18 19 20 21 22 23
-55-71-28 -3 26 74 47 70 23 79 28 99 69
-19 -3 17 41 37 63 24 24 -1 35 21 62 25
-14 4 7 19 3 19 16 -9-11-24 13 14 0
8 2-3 9 25 44 57 39 23 22 30 35 34
-5-19 -9 7 29 26 13 1 -6 12 2 23 19
-32-25-22-21-14-19-23-37-15 -4-21 -9-34
10
26
73
67
54
86
44
10
41
22
-4
16
8
38
cn


TABLE 38
Corrections Applied to the Madn 10
Right Ascension
dec\ra 0123456789
35 78 83 0 0 84 84 84-99-99-99
30 -41-63 3 56-13-28-26-67-56-48-
25 -19-41-31-88-92-19 29 7 -1-88
20 2-21-14 37 70-35-99-99 3-71-
15 8-38-47-52-22-15 22-80-85-67-
10 -1 48-55-27-21 28 41-99-82-22-
5 -38-99 -8 44 18-59-11-38-82-29-
0 19 8 3-22-57-16 -2-68-29-49-
-5 -34-48-31-12-52-99-74-99-99-14-
Dec lination
dec\ra 0123456789
35 -94-99 0 0 99 99 99 97 97 97
30 28 10-34 99 53-20 19 58 48-97-
25 35 8 15 17-79 18-52-99-90 58
20 31 10 13 49 93 70 4 99 99 83-
15 39-17 -2 4-23 0 37 7-55-63
10 -19 63 61 7 51 34 12-40 50 8
5 35-40-35 8 8 71 94 48 99 52
0 65-14-18-27-34 19-30-77-33 34
-5 10 59 36 77 27 26 10 -1-99-99
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 0-44-44-87-99-50 51
-28-18-50 13-16-22 19-56-41 -6 6-34-34
55 44-44-41-66-66-34-79-40-15-17-15-15
-72-40-67 27-18-54-60-50-18-51-18-78-54
-19 19-71-41-16-14 25 0-59-36 1 11 14
-53-99-13-14-70 -7 14 23 -6-24 19-24-54
40-49-27-22-24 2-53-88-47 14 65-41 -1
0-27 -3-25-10-46-28 14-19-42-54 12 24
-66-43-48 -8 -9-33 11-28-72-32 6-64-70
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 0-34-34 94 99 99-24
58 7 -5-11-61 26 31 21 11-28 49 -6 12
15 10 22 33 50 63 5 5 14 27 20 7 24
24 -5 14 81 56 78 53-12 55 44-51 58 1
78 27 15 17 50 33-16 43 47 29 28 -2-13
15 96 0 -9 94 74 32 58 35 -4 39 45-21
-79 27 46 15 73 32 15 20 31 15 74 35 11
-9-28-26-32 -6 62 36 6 48 11 41 39 8
56 54 64 97 99 45 38 33 56 20 68-33-26
10
0
83
17
53
67
25
13
48
40
10
0
59
27
38
99
35
11
20
99
CT>


TABLE 39
Corrections Applied to the Berg 1-25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
75
-99-
-56-
-16
22
22
22
22-
-99-
-99-
-99-
-99-
-59
58
1-
-53-
-53-
-53
0
0
0-
-99-
-99-
-99-
-99
70
-87-
-92-
-58-
-37-
-36-
-36
10
1-
-34-
-50-
-58
0
11
8-
-47-
-47-
-46
-7-
-77-
-53-
-54
-6-
-37-
-33
65
-81-
-85-
-68-
-50-
-38-
-32
16
99
17-
-21-
-73-
-43-
-19
7
0-
-27-
-49-
-69-
-67-
-51-
-54
-7-
-23-
-37
60
-66-
-86-
-74-
-62-
-49-
-33-
-26
3-
-34-
-43-
-80-
-62-
-20
3
5-
-94-
-96-
-84-
-37-
-52-
-73-
-65-
-47-
-53
55
-91-
-95-
-83-
-61-
-49-
-50-
-81-
-53-
-69-
-54-
-92-
-87-
-60-
-49-
-83-
-99-
-94-
-71-
-40-
-52-
-56-
-55-
-38-
-49
50
-59-
-48-
-50-
-41-
-48-
-70-
-81-
-41-
-54-
-46-
-75-
-67-
-38-
-63-
-96-
-81-
-82-
-59-
-51-
-45-
-59-
-65-
-67-
-59
45
-23
-5-
-64-
-59-
-74-
-68-
-89-
-83-
-81-
-82-
-94-
-92-
-54-
-66-
-72-
-66-
-75-
-72-
-73-
-39-
-74-
-90-
-99-
-49
40
-57-
-62-
-92-
-80-
-70-
-65-
-90-
-99-
-99-
-99-
-99-
-99-
-75-
-90-
-99-
-99-
-79-
-74-
-78-
-50-
-91-
-94-
-99-
-34
35
-56-
-72-
-61-
-79-
-71-
-85-
-99-
-99-
-99-
-99-
-99-
-99-
-92-
-80-
-99-
-99-
-99-
-86-
-77-
-66-
-99-
-99-
-89-
-82
30
-51-
-61-
-55-
-80-
-99-
-66-
-72-
-99-
-99-
-97-
-96-
-92-
-67-
-10-
-33-
.44.
-98-
-86-
-74-
-79-
-61-
-92-
-37-
-89
25
-90-
-77-
-38-
-68-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-94-
-88-
-81-
-98-
-99-
-97-
-99-
-99-
-84-
-71-
-85-
-99-
-99
20
-90-
-69-
-64-
-82-
-79-
-82-
-99-
-99-
-99-
-99-
-99-
-99-
-92-
-84-
-92-
-84-
-99-
-72-
-98-
-50-
-69-
-69-
-94-
-75
15
-94-
-59-
-65-
-71-
-84-
-75-
-93-
-99-
-99-
-99-
-96-
-94-
-92-
-85-
-92-
-77-
-99-
-63-
-64-
-35-
-71-
-79-
-91-
-60
10
-80-
-52-
-52-
-84-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-87-
-99-
-99-
-99-
-99-
-86-
-68-
-46-
-33-
-62-
-86-
-83-
-75
5
-78-
-60-
-43-
-55-
-70-
-49-
-67-
-13-
-99-
-99-
-99-
-99-
-99-
-97-
-93-
-70-
-54-
-99-
-81-
-77-
-31-
-49-
-69-
-59
0
-88-
-57-
-89-
-68-
-77
18-
-63-
-99-
-99-
-99-
-77-
-68-
-90-
-57-
-84-
-63-
-83-
-99-
-93-
-77-
-58-
-92-
-99-
-64
-5
-93-
-37-
-24
34
14
99-
-99-
-99-
-99-
-34-
-99-
-94-
-98-
-61-
-75-
-77-
-81-
-84-
-77-
-87-
-99-
-99-
-99-
-87


TABLE 39 CONTINUED
Declination
dec\ra 0123456789
75 -99-99-66 61 61 61 61-35-35-41-
70 -52-53-61-11 0 0 60 55 50 37-
65 -30-44-65-95-28 -2 28 85 42 48-
60 -9-22 27-37 2-11 24-27-34-28-
55 -28-55 -6-57 2-16-43-67 19 17
50 -2-20 -3-28 22 -5-78-99 -1 23-
45 72 79 99 99 99 57 3 64 18 26
40 74 28 62 64 99 98 53 34 24 32
35 4-66 14 38 19-24-40-15-12
30 -29 77 62 94 31 -2-11 12 52 27
25 -1 19 50 70 17-37 20 -5 70 50
20 20 -7 8 43 48 27 58 -8 22 -4-
15 47 56 51 64 42 60 85 62 51 41
10 4 13 18 26-46-33-87 -8 -9 5-
5 -5-18-16 17 31 87-71-78-45-69-
0 13 11-52-75-82 99 74 -7-10 17
-5 -57 -9 13 90 99-99-40-40-18 15-
11
12
13
14
15
16
17
18
19
20
21
22
23
-99-
-99-
70
46
46
46
0
0
0-
-99-
-99-
-99-
-99
-76-
-97-
-48
38
27
37
75-
16
-6-
-15
39
-8
9
-13-
-40-
-21
-3-
-13
9
24
28
6
0
57
23
32
11
36
11-
-13
17
30
9
48
-4
29
16
39
10
28
85
23-
-14
27
58
29
34
7
31-
-19
-1-
-44
-11
27
24
56
29
45
29
7
3
2-
-42-
-10
9
18
32
68
81
32
40
49
-4
0
-8-
-17
21
61
61
82
98
36
9
53
71
81
34
43
47
99
80
65
57
64
25
19
52
40
38
13
34
48
10
26
39
35
99
2-
-36
45
65
37
31-
-19
61-
-76
44
38
26
73
28
31
38
44
36
22-
-27-
-14
-9
61
30
5
35
23
44
44-
-24
3
30
43
35
55
78
66
44
40
48
68
86
39
23
59
67
69
75
66
27
26
30
59
99
99
99
91
99
81
91
32
-3
-14
-9
-6
-8
15
99
60
11
24
30
28
-9-
-12
-16-
-22
13
3-
-30-
-34-
-85-
-52
-3
25-
-17-
-14
6
-32-
-35
56
36
31-
-29-
-43-
-21
-1
13-
-42
-7
6
10
61
11
10
20
-4
27
-5
28
8
12
35
12
22
26
42
-6
99
^*4
00


TABLE 40
Corrections Applied to the ABB-6 00
Right i
Ascension
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
0
-58-70-99-99-
99-
99-
99-
97-
92-
-63-
82-
99-
94-99-
99-
99-
-99-
86-
-80-
99-
99-99-
-99-
80
-5
-99-82-99-99-
99-
99-
99-
99-
99-
-99-
70-
99-
99-99-
85-
83-
-99-
93-
-73-
99-
98-89-
-99-
99
Declination
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
0
5-58-15-64
22
74
15
12
2
-5
9
58
91 80
84
75
85
86
84
99
0 51
32-
53
-5
7-17 9-27
34
50
27
12
28
2-
17
23
27 1
11
38
59
76
31
80
18 48
83
0
TABLE
: 41
Corrections
Applied to the
Buch 50
Right .
Ascension
dec\ra
0 12 3
4
5
6
7
8
9
10
li
12 13
14
15
16
17
18
19
20 21
22
23
15
-38 8-15-42
9-
77-
66
18
32
35
29
41-
17-36-
19
40
25
3'
-11
12-
40-30
31-
25
10
-5 14 11 13
11
22
18
24
9
16
22
12
25 7
16
26
15
18
12
15
24 15
35
15
5
10 11 6 9
12
5
7
29
25
11
19
14
24 17
28
29
5
13
10
28
11 26
17
2
0
8 -1 -7 -7
5
0
2
9-
15
11
25
5
16 3
10
14
4
8
9
14
3 5
13
13
-5
1 4 9-21
-7
9
11
20
18
2
15
4
13 8
5
4
-2
-7'
-20
17
1-12
-5
3
Declination
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
15
-99-57 53 20-
-17-
14
66
24
23
99
50-
29-
41-17
12
6
-11-
12
29
1-
52-99
-13
58
10
-13-20-16-17
-5
-6
-8
14-
14'
-10
-8
21
5 -9
-9-
11
6
-9
-32-
19
13 0
7
10
5
-9-17-20 9
2
-9-
16
-9
-7'
-13-
12
-3
4-10-
17
-8
-11
-2
-22-
-21-
-27-45
-34
-3
0
-2-15-15 1-
-10-
-28-
-26-
-14-
19'
-13
-8-
23-
17-12-
-30-
17
-20
-5
-11
5
-1-17
12-
11
-5
-21 -4-23 -6-
12
0
-4
6
19
6
-6
-9
15 2
5
10
7-
22
10
20
11 -9
-11-
32
LD


TABLE 42
Corrections Applied to the Bonn09 00
Right Ascension
dec\ra 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
55
7
8
0-
99-
99
51
79
99-
-22-
34-
99-
-99-
-66-
-46-
-99-
-99-
-99-
-99-
90-
-95-
-99-
-76-
-30
-1
50
-28-
29
-2-
50-
-50-
-99-
-99-
-73-
-80-
-22-
54-
-98-
-62-
-92-
-99-
-99-
-99-
-99-
-67-
-36-
-85-
-85-
-88-
-80
45
-37-
72-
-69-
-72-
-26-
-99-
-97-
-90-
-97-
-42-
-57-
-66-
-72-
-88-
-76-
-74-
-99-
-62-
-95-
-48-
-81-
-99-
-87-
99
40
-12-
71-
78-
-90-
-45-
-99-
-59-
-28-
-99-
-49-
-84-
-59-
-68-
75-
-58-
-53-
-91-
-51-
-96-
-31-
-37-
-73-
-38-
-79
35
7-
73-
-85-
-89-
-59-
-79-
-75-
-25-
-99-
-39-
-99-
-53-
-65-
-76-
-71-
-73-
-94-
-58-
-70
35
58
37
45
12
30
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
0
0-
-27-
-27-
-27-
-27-
-27
0
0
0
0
25
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Decli
mation
dec\ra 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
60
10
10
10
10
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
-31
-9
-2
-5-
-15-
-10-
-43-
-30-
-90-
-48-
-67-
-44
2
-7-
-15
-7
20
90
62-
-12-
-99-
-99-
-69
32
50
15
3
-4
-1
4
31
28
37-
-20
1-
-15
9
30
13
12
30
-6
5-
-11-
-30-
-60-
-12
15
49
45
48
21
18
0
-6
6
21
42
-1
2
-4
21
19
14
18
39
6
16
14
22
22
60
45
41
40
15
-5
17
15
10
6
6
34
-1
11
-5
27
11
51
28
41
14
41
39
17-
-21
27
3
13
35
-38-
34
15
50
65
54
38
38
18
36
24
62
45
99
68
51
-6
-6
21-
-41-
-99-
-83-
-95-
-38
30
0
0
0
0
63
63
63
63
63
0
0
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
25
0
0
0
0
63
63
63
63
63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
TABLE 43
Corrections Applied to the ABB+20 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
30 -48-85-99-30-99-99-72-18-13-67-99-99-99-99-99-99-99-75-99-84-99-99-99-99
25 -66-65-64-87-92-92-98-99-99-99-99-99-99-91-99-99-99-87-74-70-98-86-86-93
20 -53-55-52-83-99-99-99-99-99-99-92-99-99-99-99-99-99-80-65-76-81-82-83-71
15 -99-99-99-96-99-99-99-99-99-99-99-94-99-99-99-99-99-99-99-74-28-39-45-98
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
30 51 12-16 22 39 75-40-86 49 44 59-70-99-64-99-59-25 8 37 47 79 99 67 50
25 11 5 -8 23 13 7 -6-21 -2 9 11-15-11 1 24 7 19 16 8-9-8 2 0 20
20 27 21 13 23 37 23 15 19 11 32 31 11 30 24 34 21 35 42 28 39 46 19 19 46
15 36 14 43 45 77 10 -6 37 20 55 35-17 38 35 55 68 68 70 21 23 56 74 54 71


TABLE 44
Corrections Applied to the ABBO 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -76-99-89-46-99-99-35-99-99-99-72-35-71-99-99 5-81-99-84 50-61-99-99-99
5 -53-78-99-80-99-99-98-99-99-99-99-99-99-99-99-99-99-99-96-91-75-86-99-83
0 -71-58-67-85-99-99-99-99-78-94-99-99-99-99-99-93-77-98-99-99-98-99-99-98
-5 -99-99-98-85-92-99-99-99-92-99-99-99-99-73-99-99-70-84-99-99-99-99-97-93
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 99 99 -5 75 99 99 99 99-26 99 99 96 99 99 99 99 99 99 99 99 99 99 99 99
5 -5 -6-39-36-30 -9-40 1-36-15-57-28-24-21-54-23 -4 4 -4 -6-22-33 9-21
0 25 19 8-20-22 -2-18 -1-26 -4 7 0-9 25 27 28 3 14 34 24 30 30 19 -1
-5 -11-67-66-72-29-38-60-11-15-24-33-10-21-17-35 6-17-32-11 -8-15 -4 14 1


TABLE 45
Corrections Applied to the Lund44 50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 -46-22 77 24 -7-47-60 111 0-98-98-98 0000000000
45 -13-52-23 4-99 16 12-88 36-65-73-21 66 99-60-99-99-99-99-99 57 99 73 24
40 -1-17-42 15-47 13-21 18 -5-57 49-26-24-29-15 -1 99-20-17 26 3-36-48-34
35 -23-10 -8-20-20-13-40-18-17-17 -8-26 -8-44-39 88-77 14-14-29-20 -8 -8-24
30 -7-12 6 -4-11 -3-22 20-10-40-29 0-45 -3-13 -6 4 -6 13 1 7-10 5 -1
25 -36 6 10-17-10 20-14-32-21 10 -7 15-19-52 14 86 62 43 8 20-14 -1 6-14
20 -55 -1-71-15-24-10 28-38-30-46-39-11 17-68-56 30-50-14 25-18-20-32 -2-21
15 -76-87 15-30-67 -9 58 -9-53-44-83 -1-99-99 1 10 3-2 1-7 53 46 -4-25
10 39-60 16-64-57-35-99-98 19-35-30-41-13 40 31-63-96-14-19 21-26 44 59 99
5 99-99-92-41-92-43-36-14-13-66 -2 -9-52-34-24 14 36 51-77-77 9 14 5 99
0 -43-99-97 37-34 54 25-99 80 29 -7 28-52-99-99-88 99-40-50-62-71-99-50 30
-5 -99-99 0 0 0 0 0 17 17-37-54-31 99-41-99-99 0-87-28 18-69-28 21-80
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 -99-99-72 99 99 99-99-99-99-99 0-99-99-99 0000000000
45 -18 25 43-18-54-62 29-62-47 65-55-42-39 88 99 71 99 99-99-99-82 35 85 31
40 -41 75 38 22-26 -2 5 46 16 37 84 -8 41 30 -2 18 5-52 2 4 61 -4 9-4
35 -32-20-20-12-37-25 -3-26 20 24-16-10-29-20-61 69-30-76-11-20-21-24 -6-46
30 -7-42 24-15 -264 -5-36 16 4-36 -8-44 21 -6 18 21 9-30 -4 -6 -8-15
25 -64-74 -4-52-36-89-66 17-44-39-14-34-30-59-30 70-37 5-32-72 6 2-15-13
20 22 3 53 33 -2-20 19-32 -4-50-48-16 5-45-31-12-21 26-10-28-11 35-29-29
15 -41-52 30-53 22-74 94 85 29 16 41 39 34 31 17 24 55 35-49-28 8 -1-49-20
10 99 99 21 0 -7-39-17 -2 0 20-23 -6 99 18 9 26 4-22 35 21-78 49-95-89
5 21-97 34 70 41 20 34-11 14 11 51 26 43-53 -1 52 71-99-74 75 21 73 27 -2
0 15-26-73-92 33 22 89 27-27 36 40-63-99-99-28 25 88 22 19 7 5 4 13 47
-5 -99-86 0000 0-99-99-87-67-85-99-99-12 30 0-99-74 4 26 29 66-99
oo
ro


TABLE 46
Corrections Applied to the Stras 30
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
90
0
0-
-12-
-16-
-22
7
38
0
0
0
0
0
0
0
0
18
18
18
0
0
0
0
0
85
25
12
47
6
8
7
38
-8
-8
-7
23-
-13-
-20-
-20
0
15
15
19
39
16
32
6
15
80
28
12
39
24
20
35
52
6
3-
-30-
-27-
-43
-6
19
20
13
-1
-4
11-
-24
17
47
35
75
55
66
30-
-14
7
51
35
10
46
31
14
3
15
4
19
-9-
-15
-1
56
86
90
51
22
70
70
65
-2
5
27
2
-3
10
40
-6
24
58
15-
-11
46
24
10
5
30
12
39
29
51
65
57
81
44
17
25
67
52
-1
51
41
42
22
16
29
35
24
-2
29-
-27
12
62
45-
-10-
60
41
-9-
-53-
-59-
-64
-4
99
99
26
52-
-23-
-50-
-55-
-82-
-99-
-14
5
35
34
68
23
1
74
55
67
30
5-
-21-
17
1
-7
-8
-5
-9-
-37-
-65-
-24-
-14-
-84-
-46-
-55
51
46
-9
21
57-
-10
50
6-
-37-
-38
20
35
35-
-13-
-59-
-17
22-
-18-
33
49
19-
-15
22
1
35
39-
-34-
52
-5-
10
45
26
41-
-70-
-52
13
27
-1
8
24
35
35
95
24-
79-
-31
0
25
-5
0
0
0
99
4
40
55
18-
-99-
68
14
14
2
21
35
20
32
15
56
57-
-17
28
99-
-75
8
50
39
15
15
35
51
25
-4
-2
41
5
-4
32-
-11-
-13
10
8-
-10-
35
-2
9-
-21
25
14-
-20-
21
46
-8
30
-9
33
63
50
70
76
37
11
4
9
30
70
20
8
-2
-7-
24
14
17
31
37
84
39
25
10
23
27
2
-3
45
3-
70
55
60
23
83
62
-4
37
21
-7-
-11-
-12
12
49
55
-9
20
65
39
11
55
66
28
32-
-36-
-23-
-40-
-61
-3-
-34-
-37
-2
12-
-41
42
27
50
5-
-17-
-26
15
5
93
17-
-35-
-12-
-14-
-16-
-28-
-27
31
55
40
-9
5
13
6-
-52-
-48
37
53
32
99
99
10
0
-5
54-
-12-
51
43-
30
-2
-1
-2
14-
-14-
-20
12
13
42
22
80
99-
-24
2
9-
-19
5
19
40
21
8
5
13
8
2
-3-
-34
8
64-
-47
4
17
0-
-35
34
6-
-14
23-
-13
26
0
60-
-43-
-39
13
18
70
16-
-37-
-15
15-
-19-
-21
4-
-15-
-30
5-
-12
9
40
21
10
11
20-
-5
13
15
1-
-14-
-11
5
35
30
12
41
51
53
59
7
31
-7
20-
-13-
-15-
-20
3
16
7
23
0
23
27
27
18
10
99
39
0
-4
62
-2
55
24
11
99
-8
-7
12
16


TABLE 46 CONTINUED
Declination
dec\ra 0123456789 10 11
90 0 0 31 24 -1 -2 22 0 0 0 0 0
85 13 -2 37 13 -5 -2 22 2 2 32 85 34-
80 -52 -2 46 25-51-80-59 41 38 5-44-54
75 -53-58-16 99 57-31-46-31-75-60-69-99-
70 -74-47 9 -4-14 -8-56 51 43-48-67-34
65 -2-40 78 85 38 14 32 44 17 60-21-70-
60 3-97-99-99 86 84 37 -9-42-55-31 23
55 8 45 17 0 28 10 53 -5-14-16-57-72-
50 -27 7 -1 57 39 -5 53-88 -9 15 -7 -6-
45 53 88-21-26-21 -1 7 58 38 -7 -7-99-
40 -52-24 32-23 5 35 59-11-50-17-25-92-
35 -46-38 89 99 26-18 -5-99-66-48-63-62-
30 3-11-11 14 9 18 75 33-14 12-47-20
25 -19 -5-26 12 27-12 10 25 -7 22 38-70-
20 -60-78-38 73-99-96-99-88-99-79-81-47-
15 5 39 14-54-66 99 99-13-86-84-62-33-
10 53 13 1 99 25 24 50 18 30 2 7-27-
5 -13 16 37-51 34 7-24 16 2-32-31 -8
0 32-31 -2 2-66 8 52 6-66-86-38-83-
-5 -52-41-26 -2 37-20-28-38 -3 45-69-99-
13 14 15 16 17 18 19 20 21 22 23
00111000000
-84 0-41-41-40-55-50-68-44 44 40
99-29-99-86 5-21-13-21-39-48-54
-66-37 5 14 23-86-99-26-77-96-54
-99-99-99-38-48-84-91-45-40 1-29
-88-29 28-19-99-31 36 46 97 65 27
99 -3-70-87-99-99-31 16 53-78-99
-12-85 27 9-46-11 -1 -6 4 53 14
-52-45-13 99 99 62 89 95 23 23 9
-3 26-33-99 99 0 0 0 15 -1 10
-58-31-56-99 99 43-99-99-99-99-61
-64 1-45-26 65 46-32-58 80 74 16
-28-55 25-16-29 -2 70 6-86-32 -1
-33-53-38 20-70 31 4-99 9 36-18
-93-54-84 46-99-99-87-99-99-93-52
67-68-99 11 30-83-41-19-99-24-49
-55 25 7-10-41-41 47-63-56 12-49
33 55 -5 1 74 37-99-21 22-34 19
-7 1 61-77-99-19-37 49-14 -8 52
-32-95-18 12 30 99 25 -6 49 69-45
oo
12
0
84
52
23
59
51
70
21
13
92
96
53
0
99
99
49
56
1
82
71


TABLE 47
Corrections Applied to the Cin 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
80
0
0
0
0
99
79
79
7
49
73
75
35
-8-
-24-
-67
30
-8
25-
-35-
-14
11-
70
-38-
-21-
-49-
-64-
-24-
-24
21-
-47-
-28-
-22-
65
-98-
-73-
-78-
-24
27
23-
-27-
-77-
-48-
-13-
60
-99-
-99-
-90-
-41
53
9-
-39-
-14
0-
-34-
55
-71-
-99-
-99-
-97-
-40-
-91-
-99-
-66-
-37-
-99-
50
-95-
-11-
-97-
-99-
-99-
-81-
-99-
-99-
-82-
-99-
45
-99-
-85-
-99-
-99-
-99-
-99-
-77-
-54-
-41-
-99-
40
-99-
-99-
-83-
-49
3-
-47-
-67-
-86-
-78-
-99-
35
-83-
-46-
-80-
-71-
-68-
-52-
-99-
-58-
-99-
-72-
30
-61-
-35-
-99-
-58-
-51-
-25-
-88-
-93-
-92
9
25
-99-
-30-
-98-
-71-
-65-
-70-
-99-
-99-
-99-
-99-
20
-87-
-44-
-41-
-59-
-99-
-99-
-99-
-97-
-95-
-99-
15
-99-
-67-
-99-
-66-
-82-
-99-
-99-
-99-
-99-
-99-
10
-98-
-47-
-99-
-72-
-76-
-74-
-79-
-99-
-99-
-99-
5
-99-
-99-
-82-
-59-
-82-
-80-
-99-
-99-
-99-
-98-
0
-99-
-90-
-93-
-99-
-99-
-99-
-99-
-99-
-99-
-55-
-5
-99-
-55-
-63-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
11 12 13 14 15 16 17 18 19 20 21 22 23
-3-99-99-99 76 76 76 76 76 0 0 0 0
-11-19 33 9 99 25 41-99-99-99-91-11-17
-8 -5-15-78 3-38 -7-73 2 -9 9-63-48
-33-99-99-98-57-99-99-99-65-56-40-54-42
-61-45-99-78-99-99-99-83-49-20-42-69-99
-99-28-31 41-88-99-74-19 53 18 18-25 -6
-99 -3-78-60-99-99-99-99-99-99-99-99-74
-99-64-99-99-99-99-99-42-51-88-99-99-99
-95-99-99-82-84-72-92-69 21 -3-65-58-76
-59-47-84-48-39-61-97-99-49-34-25-99-90
-82-59-99-86-99-90-92-83-67-92-49-99 8
-99-99-99-90-99-99-99-99-99-99-26-99-79
-99-99-63-71-75-99-34-87-71-92-60-74-99
-99-99-99-99-99-99-61-99-74-99-99-99-99
-77-99-99-99-99-99-99-63-77-99-99-97-85
-89-99-99-99-99-99-99-80-99-99-73-29-67
-99-99-99-99-91-39-85-64-99-99-99-99-75
-95-96-94-99-94-89-99-99-64-59-99-99-99
10
18
46
60
13
32
93
97
99
65
43
-9
79
99
99
99
99
90
99
00
cn


TABLE 47 CONTINUED
Declination
dec\ra 0123456789
80 0000 0-37-37 59 99 99
75 -99-83 42 89 99 99 95 57 99 74
70 -69-27 11 31-15 15-29 28 73 66
65 64 37-36-19-99-23-78 26 63 67
60 9 26-69 -1-99 16-20 2 44 32
55 11 0-51-86 4-92-55-61 17-17
50 -17-99 -9-12 99-99 -7 4 42-41
45 -27 0-64-55-82 99 82 99 -7 12-
40 -15 92-19 28-99 76 9 88-23 59
35 -1-13 36 77 59 -1-23 -9 55 60
30 33 3 66 78 99 87 99 46 20 7
25 50-11 50 88 51 1 83 53 5 40
20 78 97 54 99 95 90 31 15 51 78
15 80 99 51 66 79 63 37 -7 10-26
10 41 4-12-37 -5-21 25 22 10-25-
5 -36 7 -1 52 6-53-29 4 10-15
0 -27 43 -9 97 29-39 -9 50 85 0
-5 -53-32-99 55 99 68 59 18 13-63-
11 12 13 14 15 16 17 18 19 20 21 22 23
-99 43 39 99-83-83-83-83-83 0000
-54 99 34 99-99 44 81 99 76 99-99-99-99
11 99-64 50-62 14 26 14-37-53-76-79-70
47-17-38 59 47 65 44-27 44 4 86 99 98
20-69-33 -4 1 5 90 27 99-20-14-99 32
-54-68-15 99 29-28-32-99 11-99-86-78-38
-3 42 5 97 6 88-17-53-93-84 0 71-21
-48-77-92-57-99-10-29 53 7 24 21 54 -8
-24-30 61 73 12 21 -4 -6-55-28 -2 99 69
23-61 49-17 79 -5 11 4 16-73-69 18 34
48 25 50 14 62 9 72 21 29-48-43 26 44
54 61 30 9 39 59 21-55-14 38 5 88 78
65 41 7-14 81 44 52 9 71 99 75 51 96
18 35 68 16 99 42 84 8 9-12 32 20 54
17 29 86 44 48-26-24 15 70 61 21 10-32
-5 1-62 2 39 65-36 52 19 47 2-16-52
-15 -2-25 -9-33 41-47 30-29 8 33 20 33
-33-49 20 22 29 44 45 62 8 17 17 15 30
10
1
23
60
72
37
-1
2
18
22
6
46
32
85
17
52
-2
14
68


TABLE 48
Corrections Applied to the PFKSZ
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
41
10
24
19
31
20
9
4
3
4
-8-
-12-
-29
15
44
60
54
55
40
34
15-
33
-2
1
85
32
5
6
-6
-9-
-26-
-26-
-17
-2
-1-
-11-
-18-
-18
0
25
20
22
3
-8-
-24-
-16-
13
22
8
80
4
16
5-
-12
-9-
-28
12
7
38
20
4
5
-4
-5
12-
-14-
-19-
-32-
14-
-24-
-12
16
6
27
75
8
25
2
11
30
15
58
36
19
2-
-12
13-
11
-7
7
19
19
2
8
6
-1
11-
15
33
70
30
31
5
16
28
37
38
29
18
15
1
18-
13-
10
-5
10
-1
4
-5
17
-3
0
-5
16
65
4
7
3
17
16
15
18
43
48
59
34
28
3
-2
11
-4-
14
-9-
26
-4-
-18
10
16
6
60
29
12
9
24
18
29
16
48
27
25
20
26
19
-8
1-
-24-
11
0
-4
10-
12
7
14
26
55
24
20
8
24
7
5
7
8
9-
18
4
-8
4-
12
19-
14
-5-
18
0-
-15
-5
8
2
14
50
-19
-4-
13
ii-
17
9
21
2
11
-7
16
24
-2
1
12
0
-9
-1
6
1
-1
-5-
12
-7
45
-13
12
2
ss
-8
22-
-15-
-18
-1
7
12
25-
-23-
-15-
24
2-
25
5
-6
10
-9
-4
0
11
40
7
10
4
8
-9
4
5
13
14
3
6
8
3
8
-4
3
-5
-5
-1
-6
15
9
5
14
35
9-
12
11
7
11
-3
7
10
13
-3
8
-2-
11
-9
-5
-9-
11-
39
-9
0
46
-2-
10
-1
30
31
4
2
7
4
1-
-11-
-10
16
5
26
22
-3-
-16-
-20-
16
-5-
21
1
10
16-
17
-2
2
25
39
21
4
-9-
18
6
12
-1
18
-6
25
29
11-
-16-
-23-
20
-9
-8
9
15
24-
12
11
2
20
-2
11
9
7-
24
0
-3
-3
14
5
13
-2-
-19-
23
-6
10
-8
2
5
17
7
-5
-9-
18
15
14
22
0
32-
21
-6-
-42-
11
38
13
35
-1
-7-
17
10
27
3
17
3
19-
10
-2
-7
19
10
6
22
6
32-
-11-
-42-
16
6
38-
22
27
9
10-
13
8
-4
4
-7
-2
5-
22
-1
-4
21
5
-12
0
10-
10
2-
-13
4-
-10-
-15-
-28-
-13
5
-3-
11
17
13
11-
-13-
11
3
-5
29
6
-6
0
7
0
20-
19
-5-
-19
6-
-33-
-15
7
12
10-
-13-
-21-
11
8
-6-
16
-7
27
9
22
-2-
-20
-5
-16-
20
-1-
14
15
3
31-
-39-
-13
2
13
4-
20-
-15-
17
6
0
0
17
10-
-72-
-63-
-37-
-46
oo


TABLE 48 CONTINUED
iec\ra
0
1
2
3 4
5
6
90
-38-
20
18
60 79
-2-
67
85
0
21
24
19 1-
36-
55
80
-3
-4-
23-
18-43-
18
13
75
-70-
45-
21
22 -9-
14
8
70
-46-
14
-1
22 16
11
33
65
-15
11
-8
-8-23
9
45
60
-14
10
6
39-20
6
-1
55
-35-
11
1
25 -9-
10-
14
50
-16
3
5-
26-25
-2
18
45
-14
27
40
1-41
28
' 8
40
6
18
15-
24-50-
12-
20
35
29
-6
12-
11 26
4
12
30
4
-5
8
-8 18
1
-6
25
8
13
6
-9-11
4
15
20
-11
-4
-4
5 26
0
3
15
-5
2-
13
-5 5
18
24
10
11
3
1
-4 9
73
43
5
-12
9
29
2 -7
-1-
34
0
-2
17
17
9 9
17-
10
-5
-27-
22-
13
8 37
35
19
8 9
-27 -7
-17 -8
-9-27-
-16 -6
23 21
25 23
14 34
-6 0
10 0
-15-26
1 4
11 10
12 -4
-5-21-
8 10
16-12
58 19
-12 18
-38 -2-
14 49
10 11 12
8 5 5-
2-17 0-
11-24-15
12 2-54
35 39 11
19 16 -9-
51 19-33-
3 11 -6
-4 16 7
10 3 10
17-15-16
18 9 9
24 10
5 2
12-18
15 14 -5
30 6 -4
-8 18 20
18 -7 5-
23-21-71-
7
19
1
13 14
40-18-
14 13-
3 22-
18 11
-3-17
24-17
16 -5
0 8-
0 1-
14 12-
-1 13-
-9 6
6 20
12 48
5 18-
5 -2
63 30
39 19
36 -7
99-30
1-
-8
2-
15 16 17
15 28 7
25 23
28-12 -1
16-17 2
21-17
32 -3
15 21 27
13 27 25
24 54 50
24-23 3
17-24-21
13 24 3
17 -2-37
-8-14-27
10 14 -3
6 35 8
32-11 6
4-21 5
-4 8 3
18 19
14 -3'
13-49
-9-33
3-15
-6-31
-15 -6'
20 14
29 5
31 35
-2 8
15 4
17 -1'
29 -9
13 5
20 -3
20
12
6
2
6
-1
18 45 25
18 24
1 11
20 21
-12-50-
-30-27
-12-21
7 -8-
1 14
-24-12-
4 5
12-13-
11-29
-1-21
2 4
-24-20
-5 3
14 4
10-23-
32 0-
-7 -9
1-13
37 20
6 13-
22 23
64-68
22-18
36 27
19
14
15
12
-6
-9
-7
9
24-20
-9-31
25-22
11 2
-4-18
-2 -7
12 0
23-25
18 12
-9 21
-4-14
6 21
22 6
CXI
00


Full Text
RIGOROUS COMPILATION OF THE
NORTHERN INTERNATIONAL REFERENCE STARS
BY
CARL STEPHEN COLE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

ACKNOWLEDGEMENTS
I would like to thank Drs. T. Corbin, J. Hughes and C.
Smith of the Astrometry Division of the U.S. Naval
Observatory and Dr. W. Warren the Astronomical Data Center
at the NASA Goddard Space Flight Center for providing those
data required to carry out this research. I would also like
to acknowledge the support which I received from the
Division of Sponsored Research at the University of Florida
in the form of a graduate research assistanceship.
Dr. Heinrich Eichhorn suggested the topic of this
research and has guided me through its execution. He has
also introduced me to the international community of
astrometrists and has gained their co-operation on my
behalf. I am very grateful for Dr. Eichhorn's advice and
for the knowledge which he has imparted to me.
Finally I owe many thanks to Leslie Gilbert for her
patience and the emotional support which she has given me
throughout my tenure as a graduate student.
11

TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS ii
LIST OF TABLES v
LIST OF FIGURES ix
ABSTRACT x
CHAPTER
I. INTRODUCTION 1
The Establishment of an Inertial Reference
Frame 1
The International Reference Star Program ... 4
II. CATALOGUE COMPILATION 7
The Estimation of Systematic Differences ... 7
Critique and Analysis of the Tabular
Procedure 10
Description of Simultaneous Reduction .... 16
III. REDUCTION PROCEDURES 20
Precession 20
Model Parameter Estimation 22
Star Parameter Estimation 25
Sequence of Iterations 27
IV. RESULTS 110
Residuals Between the Two Versions of the
NIRS 110
Internal Errors 118
Perth 70 Residuals 122
V. CONCLUSIONS 129
iii

REFERENCES 131
BIOGRAPHICAL SKETCH 133
iv

LIST OF TABLES
TABLE PAGE
1. Succesive Corrections Computed with Biased
Estimates 15
2. Smoothing Coefficients 25
3. Iteration Sequence 30
4. Independent Catalogues Used in the Compilation
of the NIRS 32
5. Corrections Applied to the AGK3R 39
6. Corrections Applied to the AGK2A 41
7. Corrections Applied to the W20 43
8. Corrections Applied to the Albany 10 45
9. Corrections Applied to the Bonn 00 47
10. Corrections Applied to the Bord 50 49
11. Corrections Applied to the Sch 50
12. Corrections Applied to the Bonn 25 52
13. Corrections Applied to the W2-50 53
14. Corrections Applied to the W3-50 55
15. Corrections Applied to the GCH 1-50 57
16. Corrections Applied to the Cape02 00 58
17. Corrections Applied to the Nice 10 59
18. Corrections Applied to the Nice 25 60
19. Corrections Applied to the GCH Z 10 60
20. Corrections Applied to the Paris 90 61
v

21. Corrections Applied to the Paris 00 62
22. Corrections Applied to the GCH 2-25 63
23. Corrections Applied to the Berl 20 64
24. Corrections Applied to the GCH 00 64
25. Corrections Applied to the Toul3 00 65
26. Corrections Applied to the Cape 2-25 66
27. Corrections Applied to the Cape 3-25 67
28. Corrections Applied to the W 40 68
29. Corrections Applied to the W 00 69
30. Corrections Applied to the W ZOD 25 70
31. Corrections Applied to the Cape 1-50 71
32. Corrections Applied to the Bord 00 72
33. Corrections Applied to the ALB99 00 72
34. Corrections Applied to the Mun97 OOi 73
35. Corrections Applied to the Mun97 OOii 74
36. Corrections Applied to the Kon 00 74
37. Corrections Applied to the Pulk99 00 75
38. Corrections Applied to the Madn 10 76
39. Corrections Applied to the Berg 1-25 77
40. Corrections Applied to the ABB-6 00 79
41. Corrections Applied to the Buch 50 79
42. Corrections Applied to the Bonn09 00 80
43. Corrections Applied to the ABB+20 00 80
44. Corrections Applied to the ABB0 00 81
45. Corrections Applied to the Lund44 50 82
46. Corrections Applied to the Stras 30 83
47. Corrections Applied to the Cin 00 85
vi

48. Corrections Applied to the PFKSZ 87
49. Corrections Applied to the Lund42 50 89
50. Corrections Applied to the Cin 25 91
51. Corrections Applied to the Moscow40 50 93
52. Corrections Applied to the Tri 25 95
53. Corrections Applied to the Bruss 25 96
54. Corrections Applied to the Leid21 25 98
55. Corrections Applied to the Leid24 25 99
56. Corrections Applied to the Lund 25 100
57. Corrections Applied to the Leid27 25 100
58. Corrections Applied to the Berl Z 10 101
59. Corrections Applied to the Konl9 25 101
60. Corrections Applied to the Toul3 00-II 102
61. Corrections Applied to the Pulk 10 102
62. Corrections Applied to the Lick 17 103
63. Corrections Applied to the Lick 28 103
64. Corrections Applied to the Turin 10 104
65. Corrections Applied to the Bord 00-11 104
66. Corrections Applied to the 0ttw28 25 105
67. Corrections Applied to the Ottw42 50 107
68. Corrections Applied to the Konl7 25 109
69. Mean Right Ascension Residuals, Corbin minus
Cole 114
70. Mean Declination Residuals, Corbin minus Cole . . 115
71. Mean Proper Motion in Right Ascension Residuals,
Corbin minus Cole 116
72. Mean Proper Motion in Declination Residuals,
Corbin minus Cole 117
vii

73. Mean RMS errors 119
74. Position Residuals, Perth 70 minus NIRS 123
75. Mean Right Ascension Residuals, Perth 70 minus
NIRS 127
76. Mean Declination Residuals, Perth 70 minus NIRS . 128
viii

LIST OF FIGURES
FIGURE PAGE
1. Distribution of Right Ascension Residuals,
Corbin minus Cole Ill
2. Distribution of Declination Residuals, Corbin
minus Cole Ill
3. Distribution of Proper Motion in Right Ascension
Residuals, Corbin minus Cole 112
4. Distribution of Proper Motion in Declination
Residuals, Corbin minus Cole 112
5. Distribution of Right Ascension RMS Errors .... 120
6. Distribution of Declination RMS Errors 120
7. Distribution of Proper Motion in Right Ascension
RMS Errors 121
8. Distribution of Proper Motion in Declination RMS
Errors 121
9. Distribution of Right Ascension Residuals, Perth
70 minus NIRS 125
10. Distribution of Declination Residuals, Perth 70
minus NIRS 125
ix

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
RIGOROUS COMPILATION OF THE
NORTHERN INTERNATIONAL REFERENCE STARS
By
Carl Stephen Cole
December 1986
Chairman: Heinrich Eichhorn
Major Department: Astronomy
The tabular method of determining the systematic
differences between two star catalogues is discussed. It is
noted that the tabular method is subjective in nature and
that the estimation of the model parameters does not use all
available model constraints. Furthermore, these estimates
are not least squares estimates nor are they unbiased.
The simultaneous estimation of both target parameters and
model parameters is applied to the compilation of a complete
star catalogue. By simultaneously using all available
constraints on all available data, more precise estimates
for the target parameters are obtained. The input material
x

of the Northern International Reference Stars (NIRS) is used
and the resulting catalogue is compared to the NIRS
catalogue compiled by Corbin using standard techniques. It
is shown that the new estimates of the star parameters have
smaller formal errors than estimates derived from the same
material but using conventional procedures. Both versions
of the NIRS are used to predict the star positions of the
later observed Perth 70: A Catalogue of Positions of 24900
Stars and these predicted positions are compared to the
actual observed positions. It is found that a simultaneous
reduction results in a slight but significant improvement in
the predicted positions.
xi

CHAPTER I
INTRODUCTION
The Establishment of an Inertial Reference Frame
One of the goals of kinematic astronomy is the empirical
establishment of a frame of reference in which Newton's
first and third postulates of motion are valid. To those
involved in this endeavor, two important facts become
readily apparent. First, in all areas of science which
involve dynamics, such as lunar and planetary theory,
galactic dynamics, astronautics, among others, the
determination of an inertial reference frame to some
required accuracy is essential. Second, the complexities of
the determination of this inertial reference frame are often
completely ignored. The fact that the determination of an
inertial reference frame has been taken for granted is a
tribute to all the astronomers who have, over the centuries,
performed this indispensable service for their fellow
scientists. This work, however, is never finished. As
science progresses so does the precision of measurements
increase which in turn requires an increased accuracy of the
standard.
Due to the rotational and revolutionary motion of the
Earth, it has long been realized that stars can be used to
1

2
define, in practice, an inertial reference frame. The
sighting of stars has been used by sailors for centuries to
determine their latitude and longitude on the rotating Earth
and, more recently, star positions are being used to
navigate the Voyager spacecraft past Jupiter, Saturn, Uranus
and Neptune. In kinematic astronomy, the most frequently
used coordinates are not cartesian coordinates but spherical
polar coordinates. This is so because the position of an
object, which is defined by two angular coordinates (e.g.
right ascension and declination), can be accurately
determined to a fraction of a microradian while the radial
distance is known only to one or two significant figures if
at all. The position of a star, defined by these two
angular coordinates, fixes its place on the imaginary
"celestial sphere." Conversely, any two non-diametrically
opposed stars whose position and proper motion estimates
are given in a star catalogue, uniquely define the
coordinate system of that catalogue and provide the basis
for the establishment of an inertial reference frame.
A coordinate system (or simply a "system") in connection
with a star catalogue, is not necessarily inertial; rather,
estimates for the parameters needed to transform the system
to an inertial reference frame are assumed known. If
estimates for the distances and radial velocities of some of
the stars in a catalogue are known, this information can be
combined with the positions and proper motions in order to

3
estimate Oort's constants of galactic shear and galactic
rotation as well as the solar motion. Thus the kinematics
of our Milky Way galaxy are described and an inertial
reference frame is established.
A fundamental star catalogue contains the positions and
proper motions of at least several hundred stars and
therefore overdetermines, in a sense, the system which is
defined. In light of this, certain concepts related to a
catalogue's system need further clarification. Eichhorn
(1982) has given concise definitions to these concepts.
First, it must be borne in mind that the "star positions"
which are listed in a star catalogue are only estimates. If
the errors in these estimates are purely random, the system
is defined by any randomly selected subset of star positions
to the precision of the individual positions. However, if
there are systematic errors of star positions dependent on
which part of the sky is under consideration, or other
parameters charcterizing the stars such as brightness or
color, the system will be dependent on which subset of star
positions is used to define it.
It is often found that there exist differences in the
systems of catalogues which are functions of the sections of
the sky under consideration. In order to combine
independent star catalogues into a compilation catalogue,
these systematic differences must be modeled and the
parameters of these models must be estimated. In this way

4
it is possible to correct the systematic trends of each
independent catalogue in order to bring them all onto a
common "system."
This research investigates the techniques used to model
the systematic differences between the systems of star
catalogues, as well as the procedures used to estimate the
parameters of these models.
The International Reference Star Program
The International Reference Star program (IRS) is a
multinational effort whose execution has required more than
a quarter of a century. Its aim is to provide more than
40,000 accurate and precise star positions and proper
motions over the entire sky (Scott 1967, Scott and Schombert
1970, Smith 1979, Corbin 1985). Transit circle catalogues
from around the globe are being compiled into compilation
catalogues with a density of about one star per square
degree. With these catalogues, the fundamental system of
the Fourth Fundamental Catalogue (FK4) (Fricke and Kopff
1963) can be extended to fainter magnitudes such that over
300,000 star positions of all stars to the 9th magnitude can
be tightly related to the fundamental system.
The northern half of this program (NIRS) can be traced
back to the Catalog of Reference Stars for the Dri tter
Katalog der Astronomischen Gesellschaft (AGK3R). One of the
aims of the NIRS was to provide proper motions for the AGK3R

5
stars. Unavoidably (and fortunately), this also led to
improved positions. The NIRS was compiled from observed
positions in 64 independent meridian catalogues whose mean
epochs date back as far as 1889.
The catalogue of Northern International Reference Stars
(NIRS) (Corbin 1974, 1977, 1982) contains positions and
proper motions of 20194 stars in the declination zone -5 to
+90 degrees of apparent visual magnitude 6.5 to 9.5. NIRS
was compiled from independent catalogues (ICs) which only
contain star positions measured at a given epoch. Corbin
constructed this catalogue in a two-step process. First,
the systematic differences between the star positions in
each of the ICs and the reference star positions of the FK4,
which is the target system, were calculated. Systematic
corrections were computed from these differences and applied
to all star positions in the ICs in order to bring them onto
the system of the FK4. Second, from the thus corrected and
weighted IC positions, a complete catalogue of appropriate
stars was constructed.
It must be noted that Corbin used no intercomparisons of
ICs to calculate systematic corrections. That is, when
estimating the parameters of the models of systematic
differences, the only constraints which were used were those
which minimized the systematic differences in star positions
between ICs and and the reference catalogue. The
constraints which require that the systematic differences in

6
star positions between independent catalogues also be
minimized were not used. In light of this fact, it is
apparent that better estimates of the parameters are
available with procedures which use all available
constraints on all available data (cf. Eichhorn and Cole
1985).

CHAPTER II
CATALOGUE COMPILATION
The Estimation of Systematic Differences
The difference between the position estimate of a star in
two catalogues originates from the random errors of the
observations from which the positions in each of the
catalogues were computed and the inconsistencies of the
systems defined by the star positions of the catalogues. In
computing corrections to bring a catalogue onto a system,
one seeks to minimize the differences between the defining
systems without changing the accidental errors in the
individual position estimates. In correcting for systematic
errors, the usual procedure is to model the source of the
error, guided by the geometry and, when indicated, the
physics of the actual measuring situation. In the case of
star catalogues this technique is impossible, in practice,
because there are too many small sources of systematic
errors which occur at different stages of the data reduction
process. Often, their presence is either unsuspected or
reasonably accurate models for them are difficult to
establish. Systematic errors can, for example, be
introduced by an inaccurate refraction correction. Likewise
it is difficult to determine the optical characteristics of
7

8
an instrument which was destroyed in the Second World War.
It is thus easier to lump errors from all sources together
and model them by some empirical interpolary function.
We see that the systems defined by star catalogues, since
they are only estimates, can only approximate the
unobtainable ideal target inertial reference frames.
Therefore the actual, true systematic errors of a catalogue
can never be rigorously and unambiguously found or even
defined. What can be defined and estimated are model
dependent systematic differences between the systems defined
by any two catalogues. Once systematic differences^ are
found, they can be applied to the positions in one catalogue
as systematic corrections in order to bring the two
catalogues ideally onto the same system. Regardless of the
functional form of the model for the systematic differences
between two catalogues, when two or more catalogues are
being combined, there are, in principle, two distinct
methods to compute these systematic differences.
The traditional methods utilize the comparisons of the
positions of only those stars common to each IC and the
reference system (the FK4 in this case) for the derivation
of the systematic corrections for that IC. Systematic
corrections are then determined from these individual
comparisons only. Since the star density in a typical IC is
1
For the purposes of this research, the term "systematic
error" will be used to denote the systematic difference
between an IC and the FK4.

9
much higher than that of the reference system, systematic
properties of an IC have often been estimated from as few as
5 percent of the star positions in that IC.
Traditionally, position differences averaged over blocks
of the sky and smoothed with adjacent blocks are applied as
systematic corrections. It appears that several problems
arise with this traditional tabular method. First, the
smoothing coefficients are chosen on a subjective basis.
Second, not all of the available model constraints are used
in estimating the model parameters. This means that the
procedure which estimates the model parameters does not
constrain these model parameters to minimize some measure of
the systematic differences between all ICs but rather the
model parameters are constrained only to minimize a measure
of the systematic differences between each IC and the
fundamental system. Finally when estimating the parameters
in the tabular model, the estimates obtained are not least
squares estimates but estimates used only because, from a
computational standpoint, they are easily accessible. While
this results in an acceptable star catalogue, the process
involves a high level of subjective judgement which is
undesirable and uncommon in most scientific investigations.
More sophisticated models (Bien et al. 1978) define as the
measure for the systematic differences the sum of orthogonal
functions (Brosche 1966, Schwan 1977, 1985) and then use
individual positions in a least squares algorithm to
determine the parameters of these functions.

10
On the other hand, a simultaneous reduction sets up all
condition equations in closed form and solves for target
parameters (star positions and proper motions) and model
parameters (systematic errors) at the same time. The
advantage here is that all available constraints on all
available data are used to estimate both sets of parameters
and that all estimates are least squares estimates.
Critique and Analysis of the Tabular Procedure
In spite of the fact that the tabular method has been
producing very good results for over a century, it is poorly
defined and the underlying assumptions have never been
explictly stated. That is, the tabular method, with
smoothing included, has never been defined in terms of a
model, but only as a "cookbook recipe" as it were. Without
the benefit of a model and specifically, without the benefit
of the assumptions concerning the joint probability
distribution of the random quantities, it is impossible to
assign a meaning to terms such as the bias and variance of
the estimated parameters. One cannot speak of the bias of
an estimate unless one knows the expected value of that
estimate. One cannot know the expected value of an estimate
unless one knows the probability distribution of that
estimate. One cannot know the probability distribution of
an estimate unless there exists a model which specifies the
dependence of the estimate on the random quantities.

11
In the simplest case of a tabular method without
smoothing, the systematic error of an IC is considered a
fixed constant in each subjectively delineated domain. The
model for the observed error of the position of star y in
domain v, a /is
MV
A =p +e , u=l,2...n , v=l,2...m (1)
yv Kv yv v
where p is the fixed but unknown systematic error in domain
v
number v and is an independent and normally distributed
random error with mean zero and constant variance a^ for all
yv Under these assumptions one invokes the principle of
least squares and minimizes the sum of all £^v- In this way
one obtains estimates p for p as the mean of all A :
v v yv
n a
v A
A
p = z -
v -in
1=1 v
IV
(2)
n , of course, being the number of differences formed in the
2 2
vth domain. An unbiased estimate, s , for a is
n
v
2 iÍlAiv'nvPv .
- —H7T
(3)
So far this is statistically sound, because the estimates of
the systematic errors are uncorrelated under the given
assumptions. The estimate of their (diagonal) covariance
matrix is
S2 = diag(S^/n,, S2/n_...S2/n)
11 2 2 mm
(4)

12
where m is the number of domains involved in the process.
Unfortunately, the model in (1) proves inadequate.
Experience has shown that the domains cannot at the same
time be chosen small enough to model with sufficient
accuracy the structure of the systematic differences and yet
large enough not to mask the random errors of the
observations. The accepted solution to this problem calls
for choosing smaller domains and then "smoothing" each
A
estimate, p , with its immediate neighbors. It is during
this process of smoothing that the reference to a model and
its underlying assumptions is lost. However, this procedure
will still produce some kind of a numerical result.
If smoothing is involved, one can only infer a model
working backwards from the "recipe." It is implied that the
model for the observed error of the position of star ^ in
domain v is
m m
A
tv
. . a.p,+e ,
j=l uv
. .a.=l
1 = 1 3
(5)
where the p.s are again fixed constants, r is again an
3 UV
independent and normally distributed random error and the
a_.s are subjectively chosen smoothing constants with
smoothing occurring over domains in the neighborhood of v .
A
The method of least squares would yield the estimates, p ,
by minimizing the quantity
m n.
3
Z Z e
j=l i=l
2
ij
m
n
m
Z Z (Aii- Z a p )Z.
j=l i=l 13 k=l K K
(6)

13
In practice this is, however, not done; rather the pv s are
obtained from equation (2)!
The assumptions of the model function and those of the
procedure for estimation of the model parameters thus
contradict each other. The model function (5) is predicated
on the assumption that the p s are correlated, thus giving
v
justification for the smoothing process, while the
estimation of the model parameters from (2) is based on the
assumption that the p_s are independent.
Assuming the model (5), the estimates of the model
parameters from (2) are therefore biased. The bias of an
estimate is the expected value of the estimate minus the
true value of the parameter or
m
Z
j = l
a .p .
J3
(7)
which is, in general, not equal to zero. One result of
these estimates being biased is that once systematic
differences are calculated, smoothed and applied as
systematic corrections, if systematic differences were again
calculated and smoothed using the same coefficients, the
resulting corrections would not be zero. That is, after a
catalogue is "corrected" using these biased estimates, if
systematic corrections were again calculated in the same
manner, the second set of corrections would be different
from zero.

14
As a demonstration of this phenomenon, the Catalogue
Meridien de 2024 Étoiles Reperes de la Zone +11° a +18°
(Bord 50) was corrected to the system of the FK4 using the
tabular method with smoothing as described in chapter 3.
The upper part of table 1 lists the corrections to the
declinations of the Bord 50 in hundredths of arcseconds at
gridpoints separated by one hour in right ascension and five
degrees in declination. The individual positions of the
Bord 50 were corrected with this table using two-way linear
interpolation. The lower part of table 1 lists the
corrections to the declinations of the Bord 50 in hundredths
of arcseconds, computed with the same smoothed tabular
method, using the "corrected" Bord 50 and again only the FK4
as a reference system. Although the second set of
corrections is smaller than the first, the second set would
be identically zero if the first set had not been biased.
The concept of a covariance matrix of the model
parameters is very problematical in this contradictory
environment. Without an estimate of this covariance matrix,
the tabular method cannot be objectively compared to other
methods. Only a subjective comparison of the "goodness" of
results is available with the tabular method.
When one discuses and-inevitably-criticizes these
methods, one must remember that they were established at a
time when most calculations had to be performed with
logarithm tables and only later with mechanical desk

TABLE 1
Succesive Corrections Computed with Biased Estimates
Corrections computed for the Bord 50 declinations:
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
30
2
7
10
13
13
9
12
16
18
17
13
9
8
6
5
2
1
1
-1
0
-1
-3
-4
-1
25
6
8
12
13
17
15
17
19
18
17
13
9
8
7
7
7
5
5
4
4
3
2
2
4
20
4
2
3
5
7
9
12
15
14
12
10
7
6
5
4
5
3
0
-2
-4
-3
0
1
3
15
-1
-5
-5
-3
-2
2
2
3
4
6
8
5
2
1
2
4
2
-2
-6
-8
-6
-5
-1
-2
10
-4
-7
-7
-7
-5
-3
-3
-5
-2
-1
1
0
-2
-1
0
1
-1
-4
-5
-5
-3
-2
-1
-3
5
-8-
10-
•12-
-13-
-11
-9
-8-
10
-9-
•10
-9
-8
-7
-6
-5
-5
-5
-5
-7
-7
-6
-3
-3
-4
0
13-
14-
â– 17-
-19-
-18-
17-
17-
15-
-12-
-12-
•11-
10-
10-
•11-
•10-
11
-8
-8-
10-
12-
â– 13
-8
-8
-8
Corrections
computed
f or
"corrected1
1 Bord
50
declinations
30
-2
0
1
2
0
-4
-3
0
1
1
0
0
0
0
-1
-2
-3
-2
-2
-1
-1
-3
-4
-3
25
1
2
3
2
4
2
2
3
2
2
0
-1
0
1
2
2
1
2
2
3
2
1
1
1
20
1
-1
-2
-1
0
1
2
4
2
0
0
-1
0
0
0
1
0
-1
-1
-1
-1
0
0
1
15
0
-2
-3
-2
-3
0
-1
-1
-1
1
3
1
-1
-1
0
1
1
-1
-2
-3
-2
-1
0
-1
10
1
0
0
1
1
2
1
-2
0
1
3
2
0
1
2
2
1
0
0
0
1
1
2
0
5
0
0
-2
-2
0
0
0
-2
-1
-2
-1
-1
-1
0
0
0
0
0
-1
-1
0
1
1
1
0
-3
-2
-4
-4
-3
-4
-4
-4
-1
-2
-2
-2
-2
-3
-3
-4
-1
0
-2
-4
-5
-1
-1
0

16
calculators. Often, the necessary computing effort was the
deciding factor as to whether a project was feasible or not.
With the advent of computers, it is now practical to
undertake enormous data reduction problems which require the
simultaneous estimation of tens of thousands of parameters
without taking any computational shortcuts which degrade,
even if ever so slightly, the results. It is now possible
to reduce the avoidable subjectiveness of a scientific
investigation so that its results can be judged on an
objective basis.
It must also be noted that there are many vital interests
in the results of astrometrists. For example, the time
standard provided by astrometrists is relied on to
syncronize global satellite communications and calibrate
radio navigation. Thus astrometrists must be absolutely
certain of their results. With this in mind one might argue
that caution should be exercised in the acceptance of any
new procedure. While this is a legitimate concern, because
of the importance of this work, catalogue astrometry does
deserve the full analytical treatment which is now
available. There is no excuse for not using a rigorous
reduction in the compilation of a complete star catalogue.
Description of Simultaneous Reduction
As mentioned above in regard to estimating the systematic
errors of a catalogue, there are two distinct methods to

17
compute these estimates. In the tabular procedure, one
estimates the systematic characteristics of a catalogue and
adjusts the catalogue in order to correct these systematic
trends. Once all the catalogues are on the same system,
estimates for the individual positions and proper motions
are calculated.
In a simultaneous reduction, systematic corrections
(model parameters) and positions and proper motions (target
parameters) are estimated simultaneously. In this way not
only are the systematic differences between the independent
source catalogues and the fundamental system of the FK4
minimized, but the systematic differences between all
catalogues are minimized as well. The incorporation of all
available information for the derivation of systematic
corrections yields a result more precise and accurate than
that achieved by traditional methods. The idea that all
parameters, used in the construction of a complete
catalogue, should be solved for in a single adjustment was
first suggested by Eichhorn (1974) and later described by
him in more detail (Eichhorn 1980).
Within the framework of this research I have employed
this principle to estimate simultaneously systematic
corrections for all ICs used to construct the NIRS on the
basis of exactly the same model and from exactly the same
raw material as those used by Corbin. Corbin's model
computes differences on a grid at each hour of right

18
ascension and each five degrees of declination and then uses
two-way linear interpolation to compute corrections to
individual IC positions. The smoothing coefficients and the
weights of the individual catalogues were also the same as
in the model used by Corbin. The only difference between
the the reductions was the method of computing systematic
differences.
Consider the linear matrix equation
Y = xe + ZP + e (8)
where Y is a vector of observations, j3 and P are the target
and model parameters respectively, X and Z are their
respective coefficient matricies and £ is a vector of errors
with covariance matrix Z . This equation could be
alternately and more compactly written
Y = [XZ] [|] + e = A£ + e.
(9)
A simultaneous reduction estimating both model and target
parameters would yield least squares estimates
✓\ rp » 1 rn

(10)
P
If model parameters are estimated first and target
parameters second, the least squares estimates are
P = (ZTZZ)_1ZTZ(Y-XS')
and
(ID

19
- T _1 T ~
1 = (X IX) X I(Y-ZP)
where g' are preliminary estimates for g. In trying to
perform a simultaneous reduction of the NIRS using the same
model as Corbin, I had to decide how to handle two problems.
First there was the computational difficulty of inverting
the A2A matrix in (10). Since I have approximately 40,000
star parameters and 20,000 model parameters, this means that
a 60,000 by 60,000 element matrix must be inverted.
Although there exist procedures (cf. Lawson and Hanson 1974)
which render a solution without the direct inversion of this
matrix, a problem of this size requires more virtual address
space than the Fortran application, which was at my
disposal, had available. This work was performed on a VAX
11/750. The second problem was that the model parameter
estimates that Corbin used were not least squares estimates
but the estimates described above. The obvious solution to
both of these problems was to iterate on a solution. An
iterative process converges toward the same solution as the
closed form (cf. Faddeeva 1959) but with less computational
difficulty and also allows for the use of traditional
tabular method of estimating model parameters.

CHAPTER III
REDUCTION PROCEDURES
In the previous chapter, I have criticized the tabular
procedure on three grounds: 1) the process is subjective in
nature, 2) not all available model constraints are used and
3) the estimates for the model parameters are biased. The
premise of this research is that by using all available
model constraints, a more precise and accurate result is
produced. Therefore, I have used the same subjective model
and the same biased parameter estimates as Corbin used for
my compilation of the NIRS. The differences in the two
versions of the NIRS are thus due only to the fact that I
have constrained the model parameters to minimize the
systematic differences in star positions between independent
catalogues as well as the systematic differences between
independent catalogues and the FK4. The aim of this
research was not to produce the best possible catalogue but
rather to show that a simultaneous reduction produces
superior results to those of the classical method.
Precession
The first step taken to recompile the NIRS was to precess
all of the independent catalogue positions to the coordinate
20

21
system orientation of the FK4. The catalogues used in the
recompilation of the NIRS are given in table 4 at the end of
this chapter. The precession was carried out using Newcombs
constants of precession. Three angles, £ , z and 0, were
computed for each catalogue epoch, these are (cf Eichhorn,
1974)
; = [(23402.253 + 139.75^ + 0.061t2)tf
+ <30-23 - + 18.0t3J
z = c + [(79.27 + 0.66ti)tJ + 0.32t2] g^óó (12)

i i f
- (42.67 + 0.37tilt2 - 41.8t3l
where t. is the initial epoch of orientation relative to
i
1900.0 and t is the difference, final minus initial epoch
of orientation. Both t and t are reckoned in Bessel
i f
millennia. The constant tt/648,000 is necessary to convert
from arcseconds to radians. Next, the IC positions are
precessed to 1950.0 with the above angles and the following
formulae
X = cosó cos(a + £ - j)
Y = cosó sin(a + Q - j) cos9 + sin<5 sin0
Z = -cosó sin(a + z, - —) sin0 + sinó cos0
a5Q = arctan (Y/X) + z + j
(13)

22
6_q = arctan (z/^x^ + y^)
where X, Y, and Z are temporary cartesian coordinates, and
a, 6 and a , <5 are the right ascension and declination at
50 50
the initial and final epoch respectively. A vector
resolution arc-tangent function was used to insure the
proper quadrant for a
Model Parameter Estimation
After all IC positions had been precessed, the next step
was to compute systematic corrections. Right ascensions are
used in the following discussion but an analogous procedure
was applied to declinations. It must also be noted that
right ascensions were first multiplied by the cosine of the
reference declination before differences were calculated.
First differences in positions were computed for each star
in each IC using the reference position and proper motion.
These differences were summed over blocks of one hour by one
degree centered on the hour and the degree. That is a block
that covered 13^ would extend from 12^ 30m to 13^ 30m.
These sums are
Aa (a, 6) = L
a+0^5 6+0.5 cos6 ^
^ -V^taref - Pa(1950.0-Ta)-a] (14)
a-075 6-0.5 r
where ¿a(a , 6 ) is the systematic difference, is the
estimated variance of the reference star position at the
epoch of the IC position, a
ref
ref
and 6
are the reference

23
right ascension and declination, ya is the reference proper
motion and a is the IC position observed at epoch Ta. The
estimated variance of an FK4 position was calculated using
the errors and central epoch given in the FK4 and the epoch
of the IC position. The variance for an NIRS position was
calculated in a like manner except that an additional
variance term was included to represent the error of the
system of the NIRS. That is, the reference system of the
FK4 is defined only in terms of the set of FK4 stars. If
that set of stars is altered, then the ideal reference
system, which the altered set approximates, is no longer
exactly that of the FK4. Even though the system of the NIRS
is an approximation to that of the FK4, they are not
identical. Therefore, the variance of an NIRS position
consists of two parts. The first is due to the error of the
star position within the system of the NIRS and the second
is due to the error of the system of the NIRS itself.
In order to estimate the variance due to the error of the
system of the NIRS, the Perth 70 and Corbin's version of the
NIRS were used. After matching 3324 stars between the Perth
70 and the NIRS, the one sigma dispersion of Perth 70
positions and the NIRS predictions of the Perth 70 were
found to be 0.22 arcseconds in right ascension and 0.30
arcseconds in declination. This dispersion is due to the
position errors within the catalogues as well as the errors
of the systems of the catalogues. Since the mean error of a

24
position is published in each catalogue, the errors of the
the systems of the catalogues can be estimated.
2 _ 2 2 2 2
£NIRS + £P70 + £SNIRS “ £SP70
(15)
The square of the dispersion, , is the sum of the squares
of the mean errors of a catalogue position, and e'
:2 and e2
NIRS P70
plus the squares of the estimated errors in the catalogue
2 2
systems, e „ and e . The residual variance could be
SNIRS SP70
split equally between the systems of the two catalogues, but
I chose to have the ratio of system errors equal the ratio
of the mean position errors. The system error used for an
NIRS position was .064 arcsecond in right ascension and .070
arcsecond in declination.
Once tables of differences for each IC were calculated,
these differences were smoothed with adjacent differences
according to the following scheme:
h 0
+3n +6
A' a (a,ó) =
Z Z A.B.Aa(a + i, 6 + j)
• ,h . ° 1 3
i=-3 i=-6
(16)
h °
+3n +6
Z Z A.B.n(a + i,6 + j)
i j ' J'
i=-3 j=-6
where A. and B. are the smoothing coefficients in table 2
i 3
and n(a, 6) is the sum of the reciprocal variances for the
appropriate IC, hour and degree. The smoothing coefficients
used (regular or light) for each catalogue are listed in
table 4. After differences have been summed and smoothed,
they are then averaged over zones of five degrees:

o
25
A ' ' a(a , ó )
y 0 D A'a(a 6 + j)
j=-2 J 1
+ 2
where D . is the denominator in
3
associated A'a(a/ 6)-
equation
(16)
(17)
of the
TABLE 2
Smoothing Coefficients
i
Regular
A.
l
1
B .
J
i
Light
A .
l
3
Bj
Oh
4
O
0o
10
0h
8
0°
10
lh
2
1
8
lh
3
1°
8
2 h
1
2 o
8
2h
0
2°
5
3 °
5
3°
2
4 °
5
4°
0
5°
2
5°
0
6°
2
6°
0
Once tables of systematic differences are computed for
each catalogue, they were applied to the IC positions as
systematic corrections using two-way linear interpolation.
Right ascensions were first multiplied by the cosine of the
declination, corrected and then divided by the cosine of the
declination.
Star Parameter Estimation
After correcting the systematic errors of the ICs, the
position and proper motion were calculated for each star

26
using a weighted least squares algorithm. Corbin (1982)
calculated weights for each IC used in the construction of
the NIRS using three different methods. Method A was based
on the deviations of an IC from the final NIRS compiled with
each catalogue receiving equal weight. Method B was
similarly based on deviations from a mean NIRS but this time
the mean NIRS was compiled without the particular IC whose
weight was being determined. Method C was based on the
deviations of an IC from the reference system which was used
to calculate its systematic corrections. Corbin then used
the arithmetic mean of these three methods in the final
compilation of the NIRS. I have used these same weights,
listed in table 4, in my compilation of the NIRS.1
The following algorithm was used to calculate star
parameters. First the central epoch, T, and position, P,
were calculated:
P =
l
.w.P.
1=1 i i
Z w.
i=l 1
T =
l
L w.T.
i=l 1 1
¿i^
(18)
1
For a discussion of selecting weights used in catalogue
compilation, see Khrutskaya 1980.

27
where T\ is epoch and P^ is the position of the star in
catalogue i and is product of the the weight associated
with catalogue i and the number of observations for that IC
position divided by the mean number of observations per IC
position for that IC. Next the T. were referenced to the
central epoch:
ip I = iji _ rp
i i
(19)
and the proper motion was calculated:
4 =
Z w . T . ' P .
i=l 1 1 1
l
l w . T â– 
i=l 1 1
,2
(20)
Finally, estimates for the variance of the position and
proper motion, V and V^, were calculated:
l
.2, w.(P - P - yT ')
v = =^-=-
l
(1-2) Z w.
i=l 1
m2
Vy =
i=l wi(Pi “ P ~ yTi')
i \ 2
(1-2) Z w.T.
,2
i=l
i i
(21)
Sequence of Iterations
Now that the basic mechanics of the reduction have been
described, a discussion of the iteration sequence is in
order. Within an iteration the first step was to eliminate

28
outliers (IC positions with large residuals), the second was
to determine and apply systematic corrections and the third
was to compile a new version of the NIRS.
Corbin used several criteria for selection of AGK3R stars
to use in the NIRS. Among these was the requirement that a
star with only two observations must have those two
observations separated by a minimum of 28 years. Because of
the convolution of these criteria with the selection of
outliers, I chose those stars which appeared in Corbin's
final NIRS catalogue to use in the compilation of my version
of the NIRS. This, however, did not eliminate the problem
of identifing the outliers.
In duplicating the model and method used by Corbin, I
chose the same criterion for rejecting outliers. Corbin
rejected an IC position if the absolute value of its
residual was 3.5 times the mean absolute residual for
positions in that catalogue. Corbin established residual
limits for each IC and I have used these same pre-set limits
in my compilation of the NIRS. Residual limits for each IC
are listed in table 4.
The problem here is that one must compute systematic
corrections before residuals can be analyzed. In using an
IC position with a large residual to calculate corrections,
the corrected system of a catalogue can be distorted such
that other positions, which would not normally be excluded,
now exceed the residual limit. I decided to take an

29
iterative approach to this problem. The largest outliers
were removed first such that the systems of the catalogues
were not influenced by them in the next iteration. Then the
residual limit was lowered and the next largest outliers
were removed. This process was repeated until the residual
limit was lowered to that of the individual catalogues. In
iterations one and two, no IC positions were removed. In
iteration three, only IC positions whose residual absolute
values were greater than five arcseconds were removed. The
iteration residual limit was lowered in succesive iterations
as given in table 3 until the residual limit for an IC was
the individual limit given in table 4.
For the first iteration, the only reference system was
the FK4. Only catalogues 1 through 10 had FK4 observations,
thus only these first ten catalogues were corrected. For
the second iteration, the reference system included the FK4
as well as 6317 NIRS positions and proper motions computed
in the first iteration, thus allowing all ICs to be
corrected. For the third and subsequent iterations, the
reference system included the FK4 and 20194 NIRS positions
and proper motions.
Only the first ten ICs were corrected in the first
iteration; thus for the first computation of the NIRS, only
positions from the first ten ICs were used. In addition,
only those stars with three or more IC positions were
compiled into the first version of 6317 NIRS positions and

30
TABLE 3
Iteration Sequence
Iteration
Residual3
Limit
Number of Stars
Compiled into NIRS
1
none
6317
2
none
20194
3
5.0"
20194
4
2.0"
20194
5
1.8"
20194
6
1.6"
20194
7
1.4"
20194
8
1.2"
20194
9
1.0"
20194
10
0.8"
20194
11
0.6"
20194
12
0.4"
20194
13-25
b
20194
a. The residual must be greater in absolute value than
both the iteration residual limit and the individual
catalogue limit in table 4 in order for an IC position
to be rejected.
b. For the 13th through 25th iterations the individual
catalogue limits in table 4 were used.
proper motions. For the second and subsequent iterations,
all IC positions were used to calculate 20194 NIRS positions
and proper motions.
Tables 5 through 68 at the end of this chapter give the
corrections applied to the independent cataolgues for my
compilation of the NIRS. Each IC position was corrected
with values from this table using two-way linear
interpolation. The units are hundredths of arcseconds and
the right ascensions corrections have been multiplied by the
cosine of the declination. Furthermore, corrections whose

31
absolute values exceeded 99 hundredths of an arcsecond were
replaced by 99 hundredths with the appropriate sign.

TABLE 4
Independent Catalogues Used in the Compilation of the NIRS
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
1
AGK3R
Catalog of Reference stars for the
Dritter Katalog der Astronomischen
Gesellschaft
1.00
1.00
0.46
0.45
regular
2
AGK2A
Katalog der Anhaltsterne für das
Zonenunternehmen der Astronomischen
Gesellschaft
0.52
0.36
0.53
0.68
regular
3
W20
Catalogue of 9989 Standard and
Intermediary Stars
0.26
0.46
0.71
0.62
regular
4
Albany 10
Albany Catalog of 20811 Stars for
the Epoch 1910
0.21
0.32
0.83
0.71
regular
5
Bonn 00
Katalog von 10633 Sternen
0.25
0.46
0.73
0.59
regular
6
Bord 50
Catalogue Méridien de 2024 Etoiles
Rephres de la Zone +11° a +18°
0.70
0.64
0.41
0.50
regular
7
Sch
Katalog von 3356 schwachen Sternen
1.00
0.88
0.36
0.45
regular
8
Bonn 25
Katalog der Intermediaren Sterne
von +50°Declination bis zum Nordpol
0.23
0.31
0.68
0.71
regular
9
W2-50
Catalog of 5216 Stars for 1950.0
1.05
0.69
0.42
0.59
regular
10
W3-50
Catalog of 5965 Stars for 1950.0
1.09
0.88
0.42
0.50
regular
11
GCH 1-50
First Greenwich Catalogue of
Stars for 1950.0
0.42
0.45
0.62
0.62
light

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
12
Cape02 00
Cape General Catalogue of
Stars for 1900.0
0.22
0.32
0.71
0.68
regular
13
Nice 10
Catalogue Deduit des Positions
Observées a 1'aide du Cercle
Méridien de 1'Observatoire de
Nice de 1912 a 1914
0.30
0.29
0.56
0.68
light
14
Nice 25
Catalogue De 1020 Étoiles
Intermediaires
0.59
0.34
0.45
0.62
light
15
GCH Z 10
Greenwich Catalogue of Stars for
1910.0
0.13
0.22
0.86
0.77
light
16
Paris 90
Catalogue de 11Observatoire
de Paris, Seconde Partie
0.04
0.07
1.50
1.20
light
17
Paris 00
Paris Catalogue de 10656 Étoiles
de Repére de la Carte du Ciel
0.07
0.19
1.13
0.89
regular
18
GCH 2-25
Second Greenwich Catalogue of
Stars for 1925.0
0.35
0.41
0.59
0.65
light
19
Berl 20
Berlin-Babelsberg Katalog von
8803 Sternen zwischen 31° und
40° Ndrdlicher Deklination
0.28
0.19
0.65
0.89
light
20
GCH 00
Greenwich Second Nine-year catalogue
of Stars for the Epoch 1900.0
0.25
0.34
0.68
0.59
light
21
Toul3 00
Troiséme Catalogue de Toulouse
0.30
0.47
0.65
0.56
light
CO
CO

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
22
Cape 2-25
Second Cape Catalogue of Stars
for the Equinox 1925.0
0.30
0.39
0.65
0.62
light
23
Cape 3-25
Third Cape Catalogue of Stars
for the Equinox 1925.0
0.38
0.51
0.56
0.53
regular
24
W 40
Washington Results of Observations
made with the nine-inch
0.77
0.78
0.50
0.41
regular
Transit Circle
25
W 00
Washington-Results of Observations
with the Nine-inch Transit
Circle 1903-1911
0.28
0.41
0.65
0.53
regular
26
W ZOD 25
Washington-Catalog of 3520 zodiacal
Stars based on Observations with
the Six-inch Transit Circle
1928-1930
0.35
0.37
0.63
0.68
regular
27
Cape 1-50
First Cape Catalogue of Stars
for the Equinox 1950.0
0.88
1.31
0.50
0.35
light
28
Bord 00
Second Catalogue de L'Observatoire
de Bordeaux
0.07
0.13
1.24
0.92
regular
29
ALB99 00
Albany Zone Catalogues for the
Epoch 1900 - Catalogue of 2800
stars between 2° of South and 1° of
North Declination
0.11
0.20
0.83
0.68
regular
30
Mun97 00ib
München Sternwarte - Katalog
1.13
1.29
0.39
0.35
light
von 1867 Sternen (+37°5 to +47?5)

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
31
Mun97 OOil3
München Sternwarte - Katalog
von 1867 Sternen (+55° to +60°)
1.14
0.83
0.35
0.40
regular
32
Kon 00C
Konigsberg - Rektaszensions -
Beobachtungen von 4066 Sternen
0.45
0.00
0.56
0.00
regular
33
Pulk99 00
Pulkovo - A Catalogue of 8820
0.07
0.19
1.20
0.80
regular
Stars between 5° South and 15°
North Declination
34
Madn 10
Madison Catalogue of 2786
Stars for the Epoch 1910
0.17
0.17
0.85
0.80
light
35
Berg 1-25
Erstes Bergedorfer
Sternverzeichnis 1925.0
0.33
0.20
0.53
0.80
regular
36
ABB-6 00
Abbadia - Catalogue de 7443 Etoiles
0.13
0.17
0.71
0.71
light
37
Buch 50
Bucharest KSZ Catalogue of
Faint Stars for 1950.0
0.49
0.34
0.62
0.80
light
38
Bonn09 00
Bonn Katalog von 2199 Sternen
für 1900.0
0.17
0.51
0.71
0.56
regular
39
ABB+20 00
Abbadia - Catalogue de 14263
Etoiles
0.17
0.28
0.86
0.62
light
40
ABB0 00
Abbadia - Catalogue de 13532
Étoiles
0.14
0.17
0.86
0.80
light
41
Lund44 50
Meridian Observations of Faint
AG Stars
0.12
0.13
1.00
1.05
light
oo
cn

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
42
Stras 30
Strasbourg Catalogue de 2251
Etoiles Faibles
0.39
0.21
0.60
0.80
light
43
Cin 00
Cincinnati Catalog of 4683
Stars for the Epoch 1900
0.12
0.10
1.00
1.10
regular
44
PFKSZ
Preliminary General Catalogue
of Fundamental Faint Stars
1.87
1.46
0.40
0.40
regular
45
Lund42
50
Meridian Observations of
Miscellaneous Stars
0.16
0.08
0.75
1.40
regular
46
Cin 25
Cincinnati Catalog of 2300
Stars for the Equinox 1925.0
0.11
0.12
0.92
0.90
regular
47
Moscow
50
Catalog of Faint Stars
0.26
0.32
0.80
0.80
regular
48
Tri 25
Catalogo di 2390 Stelle Osservate
al Cerchio Meridiano
0.09
0.07
1.10
1.20
light
49
Bruss ;
25
Brussels - Catalogue de 1339
Étoiles Fondamentales
0.40
0.32
0.55
0.66
regular
52a
Leid21
25
Leiden - A Catalogue of the
Positions and Proper Motions
of 1533 Red Stars
0.29
0.26
0.55
0.60
light
53
Leid24
,25
Leiden - General Catalogue
of Positions and Proper Motions
0.76
0.82
0.40
0.40
regular
of 1190 Standard Stars

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
54
Lund 25
Katalog von 11800 Sternen der
Zone +35° bis +40° AG Lund
0.11
0.16
1.05
1.00
light
55
Leid27 25
A Catalog of 1073 Stars in the Zone
of North Declination 55° to 60°
0.34
0.20
0.50
0.67
regular
56
Berl Z 10
Katalog von 1886 Sternen
zwischen +79° und +90°
0.35
0.17
0.59
0.80
regular
57
Konl9 25
Konigsberg-Katalog von 2043 Sternen
0.38
0.47
0.70
0.55
light
58
Toul3 00-I
Appendice II du Troisiéme
Catalogue de Toulouse
0.11
0.15
0.89
0.80
regular
59
Pulk 10
Katalog von 3396 Sternen zwischen
39° und 46° nórdlicher Deklination
0.30
0.44
0.59
0.56
light
60
Lick 17
Publications of the Lick
Observatory, Vol. XV
0.67
0.73
0.35
0.41
regular
61
Lick 28
Meridian circle Observations
of 1188 Stars between 20°
and 30° North Declination
0.47
0.35
0.56
0.62
regular
62
Turin 10c
Catalogo d'Ascensioni Rette
di 697 Stelle fisse
0.11
0.00
0.90
0.00
regular
63
Bord 00-11
Nouvelles Observations Des Étoiles
contenues dans le Second Catalogue
0.10
0.14
0.89
0.86
light
de 1'Observatoire de Bordeaux

TABLE 4 CONTINUED
(A)
(B)
Title
(C)
(D)
(E)
(F)
(G)
64
0ttw28
25
Results of Observations
the Reversible Meridian
1923-1935, Catalogue of
made with
Circle
1589 Stars
0.54
0.34
0.53
0.60
regular
65
Ottw42
50
Results of Observations
the Reversible Meridian
1935-1950, Catalogue of
made with
Circle
1525 Stars
0.54
0.32
0.53
0.62
regular
66
Konl7
25
Katalog von 546 Sternen
0.43
0.38
0.50
0.60
light
(A) Catalogue reference number as provided by Corbin
(B) Catalogue abbreviation as given by Corbin
(C) Right ascension weight
(D) Declination weight
(E) Right ascension residual limit in arc-seconds
(F) Declination residual limit in arc-seconds
(G) Smoothing coefficients used
a. Reference numbers 50 and 51 have no catalogue associated with them.
b. The Mun97 00 was observed in two seperate zones and is treated as two seperate
catalogues.
c. The Kon 00 and the Turin 10 are transit instrument observations of right
ascensions only.
to
oo

TABLE 5
Corrections Applied to the AGK3R
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
1
0
0
0
-1
-5
-1
3
-2
0
85
0
0
0
0
-1
-1
0
1
-1
0
80
-1
-3
0
0
1
2
1
-1
0
0
75
-1
-2
-2
-2
1
2
0
-1
-2
0
70
-2
1
-2
0
3
11
5
3
2
3
65
-4
-7
-9
-4
-2
3
2
7
5
6
60
1
-1
-1
4
1
3
-1
5
-2
1
55
1
1
1
2
-4
4
0
0
-4
-2
50
1
2
0
-1
-8
-4
-1
0
-3
3
45
3
1
4
-1
4
1
6
4
5
3
40
5
0
4
-1
2
-7
-1
0
2
-3
35
5
4
-3
-5
-4
-5
-2
-5
1
-1
30
5
8
0
0
-1
-1
-1
-2
0
0
25
2
1
-2
-2
-1
-2
-1
-1
1
2
20
0
0
0
-1
2
-2
-1
-3
1
2
15
1
2
1
6
2
-5
0
1
4
7
10
2
3
4
2
1
-2
4
2
7
4
5
-6
-3
-2
-2
-3
-6
4
0
3
4
0
-1
-2
-3
-4
-6
-4
-5
-2
-1
2
-5
2
6
3
0
-3
1
-2
0
0
0
-10
-8
1
3
3
0
0
6
4
10
10
11
12
13
14
15
16
17
18
19
20
21
22
23
1
2
0
4
7
6
2
1
-1
4
5
11
5
-3
-1
0
1
3
2
0
0
-5
0
0
1
-1
-5
-2
-5
0
1
1
0
0
2
2
4
2
-1
1
3
2
1
0
0
-4
-2
-2
3
4
2
-5
3
1
1
0
-4
-1
-3
-3
-1
5
7
2
0
2
-5
-5
-1
-1
4
3
-2
-2
1
4
3
0
6
1
0
-6
-2
-2
0
-1
0
4
2
2
1
1
0
2
-3
-1
-1
1
1
3
6
1
-1
0
3
1
3
2
2
1
6
0
2
-6
0
-5
2
2
5
3
1
2
-1
5
2
8
3
7
1
4
-5
-4
-2
-5
5
0
5
2
5
2
0
-5
1
-1
-1
-2
-7
-3
-7
-7
-4
-5
-2
-3
0
2
1
2
1
-1
0
2
4
14
6
5
-6
-1
1
1
0
0
0
1
3
4
11
6
3
-3
-1
1
-2
-2
-8
0
1
2
1
-2
0
0
-1
-1
-2
2
0
-3
0
2
5
1
0
0
6
2
1
1
-4
-1
0
6
3
3
1
0
-6
0
0
4
1
5
0
1
2
2
3
1
1
0
0
1
2
-1
5
0
4
4
6
-1
-1
1
5
0
0
0
1
-1
-1
1
-4
-2
-6
-4
-1
1
0
-4
-5
0
-1
-2
6-
12
4
-4
2
6
6
9
6
-4
-2
10
-4
0
0
0
1
2
0
1
2
1
-2
2
2
2
1
2
2
2
0
-3
-7
CO

TABLE 5 CONTINUED
Declination
dec\ra
0 1
2
3
4
5
6
7
8
9
90
0-15
-1
-3
-2-
46
-4
-4
17
7
85
26 0-
â– 10
3
7-
15
11
-2
10
-1
80
-26 1
-8
4
4
0
1
-5
7
8
75
-33-11
-5
1
-2
-7-
â– 10
-8
1
-7-
70
6 2
10
-1
-2
-7
-3
0
6
4
65
4 4
8
3
2
7
4
0
8
10
60
-7 -2
-5
-5
2
8
1
-6
0
4
55
-3 -2
-2
-3
-2
1
-1
0
1
2
50
-7 -2
-1
2
-2
2
3
7
0
-9
45
-2 -3
0
3
0
1
3
9
3
-1
40
0 -2
-1
-2
-3
-2
0
3
8
6
35
3 2
3
2
1
1
0
-5
-1
-1
30
-1 2
8
3
-2-
10
-8
-8
0
-4
25
2 2
3
3
6
0
0
5
2
6
20
0 1
1
3
2
0
-1
0
-1
-8
15
-5 -8
-6
-2
-1
-2
-4
0
3
1
10
0 -7
-3
-1
6
5
6
0
6
9
5
0 -6
6
0
3
-5
0
-6
-1
-5
0
2 -2
7
5
1
0
-3
0
1
3
-5
1-12
-2
-1
1
2
5
5
-2
0
-10
15-22
2
-3
1
-1
0
-7-
12
3
11
12
13
14
15
16
17
18
19 20 21 22 23
-26
14
18
8
8
8
4
1-
11-20-25-22 -4
-6
12
-1-
15
-1
12
12
7-
15-11 -5 -3 19
5
7
-3-
10
-9
-9
-8
-9
-9 -7 8 -9 -7
-6
-1
2
2
-1
-6
-3
3
2-1-1 2 -6
0
1
1
0
5
-1
3
9
6 5 0 11 7
-3
-4
0
0
-4
-4
0
2
2-3 1-2 -1
-3
3
11
5
-2
-1
6
3
3-2 3-6 -2
-2
-1
2
2
-5
0
1
8
5 -3 -4 -8 -3
-6
0
3
7
3
2
6
5
7 -3 -8 -5 -6
-1
0
0
5
0
-3
4
-4
5514-1
-2
0
-1
-1
-1
0
7
-3
-8-2 0 2 -1
-3
1
0
3
-1
-3
2
1
-1 -1 -5 -3 -3
-3
-2
-3
-2
0
3
6
9
-4 0 -2 -4 -4
5
-1
-2
-2
-1
2
3
6
1 2 4 0 2
-8
-3
-2
1
0
-1
-1
1
2 -1 -1 -2 -1
0
-1
-7
-7
-4
-1
-1
-3
-2 -7 -6 -3 -6
9
4
5
1
7
7
4
3
2 7-2 0-3
3
2
1
-2
0
6
1
-5
0-3-2 1 -5
2
0
-2
-8
-9
-1
1
4
10 8 11 12 4
2
4
7
8
-2
1
1
11
11 2 -1 6 2
9
3
-5
6
-7
-9-
10
-5
2-10 -4 -1 -6
10
-7
14
17
11
6
9
6
2
-9
-3
3
4
1
3
-8
2
7
-2
0
2
8
-p>
o

TABLE 6
Corrections Applied to the AGK2A
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
13
9
6
3
11 64
26
-5
-2
29
85
-1
-2-
-15-
â– 20-
â– 17 29
12
-3
1
4
80
17
5
6
3
0
7
5
12
21
13-
75
28
4
18
24
16 17
12
19
18
32
70
14
8
14
18
14 12
10
15
22
22
65
11
13
21
21
14 10
10
14
23
12
60
4
7
11
14
9
7
11
12
23
11
55
4
11
7
5
8
7
3
14
18
22
50
5
4
6
0
4
0
4
8
15
11
45
5
1
-3
-8
-6 -6
-3
-4
2
5
40
4
2
-6
-8
-8
4
5
5
-5
11
35
-6
-5
2-
â– 11
-7 -4
-3
1-
â– 14
-7
30
-6
6
5
-5
-2 -6
4
4
0
1
25
-2
2
-1
4
-1 -6
-6
1
-3
6
20
1
4
7
6
4 -2
-1
-1
1
5
15
-5
-4
8
-2
-3 -8
-3
-4
-3
-4
10
5
0
1
0
-1 -6
-9-
•10
-2
-2
5
4
1
3
-4
1 -4
-6
-5
5
4
0
-5
1
7
0
1 -1
2
-2
1
1
-5
-2
6
6
4
0 -3
5
6
10
2
-10
2
-4
4
-5
-3 -9
-6
-3
4
-5
11
12
13
14
15
16
17
18
19
20
21
22
23
53
44
15
-8-
â– 31
16
10
15
4-
35-
â– 51-
48
9
8
13
23
25
24
39
9
0-
â– 17-
39
1
-5
12
11
7
22
6
5
2
7
-4-
•15
4
5
9
6
23
9
8
6
1
-3
5
-1
-1
6-
•17
2
3
11
7
0
8
3
-1
-5
-3
-4
-3-
â– 13
1
1
14
14
6
5
3
0-
â– 10
-5
10
-2
-2
-9
9
16
18
1
1
1
1
-3-
13
-6-
12
-1
-3
7
11
10
-3
0
-1
2
-4
-4.
â– 13
-6
-5
-2
4
15
2
2
-6
-5-
â– 13-
â– 10
-4
-3
4-
â– 10
-8
-4
2-
â– 11
-5
-6
-1
-6
-3
-2
-1
-7-
â– 13-
11
-5
8
-2
-2-
â– 11
-6
-4
-6
2
-5
-8
-6
-7
-7
3
5
-4
-4-
â– 10
-5-
â– 13
-5
-3
-1
-8-
18-
â– 17
8
4
-9
2
-4
2
-4
6
-2
7
-2
-4-
â– 12
6
3
-5
-5
-4-
â– 10
-9
3
9
7
3
2
-3
4
4-
â– 11
-8
-5
-9
-7
-6
12
4
-5
-3
5
5
-4
-8
-4
0
-7
-5
-5
2
-4
2
-1
-2
2
-7
-2
7
-1-
-13-
â– 11
-6
8
-1
5
1
-5
8
-4
0
2
-3-
â– 11-
â– 11
1
3
10
6
3
-1
9
0
0
-6
-3
-6
-6
-7
-2
6
14
3
1
15
5
5
1
1
-3
-2
-2
5
-3
10
5
9
-2
5
3
15
8
6
5
1
3
-4
2
0-
â– 11
10
62
-7
12
15
22
26
19
13
7
0
6
7
13
5
14
1
-3
11
8
6
-3

TABLE 6 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-13-
12
1
28
0
15
0-
10-
16
4
25
39-
52-
-32
-2
-1
4
-4
-5
8
31
24
-5-
â– 39
85
14
5
5
30
-3
12
19
13
5
5
-4
18-
26
13
45
-4
6
-6
-3
5
20
-1
20
2
80
-3
1
-6
-3
7
8
11
6
9
15
-4
9
-9
14
16
-4
0
0
-5-
-13-
-11-
•17
2
-7
75
-16
1
-6-
12
1
12
-3
-8-
11
9
6
17
9
7
-2
3
-3
1
-8
-7
-9
1-
11
-6
70
10
12
2
7
10
3-
11
4
27
10
2
0
5
-2
-7-
10
-5
-4
-1
0
-8
-2
-1
9
65
-2-
16
-8-
16
15
-9
-9-
10
15
5
3
-2
-3
7
8
3
6
-4
2
-9
-2-
â– 10
3
-7
60
-1
0
4-
13
10
0
17
-3
-3
-4
-4
5
5
2
7
5
5
-7
1
-1
3
-3
-2-
â– 10
55
1
0
3
1
7
4
6
5
-4
2
-8
1
-5
-9
-2
7
6
-6
5
6
9
0
4
4
50
2
-1
-1
-1
0
-6
7
-6
-1
14
-4
1
-3
4
-6
-4
-9
-6
-8-
â– 11
4
-1
6
18
45
0
6
4
1
0
-4
3
-9
3
5
2
-6
-6
4
5
1
6
-2
4
0
-1
0
-2
-3
40
-5
-2
-2
3
3
2
-1
-1
5
4
10
-8
1
-7
-6
0
7-
•12
6
6
6
-6
-7
-4
35
-10
2
-2
-4
0
2-
15
-5
-3
-3
2
-3
2
-8-
•19
-2
7-
â– 14
-6
-7
-3
-9-
11
-6
30
-2
9
8
-2
0
-2
-8
-6
3-
•10-
12-
•18
4
21
2
5
9
6
0
4
0
1
-7
-7
25
-6
3
7
7
3
5
9
6
2
0
8-
•15-
14-
â– 12
-9
3
2
11-
13
9
-4
0
-1
6
20
4
-6
3
-8
-5
-9
2
-3
11
-2
0
-4
-2-
â– 10
-5
9
-3
6-
10
10
-3
0
-4
-4
15
12
4
16
0
4
-3
8
6
25
11
8
2
5
14
13
13
4
2
6
6
-1
-5-
12-
•19
10
13
-5
-5
-1
2
6
-6
4
-6
3
1
-1
-3
-1
17
14
15
-1
0-
â– 11
-3-
â– 12
-1
-7
5
3
-1
-1
-6
-5
4
1
17
9
8
-6-
â– 18
-4
-4
9
9
6-
â– 12
1-
â– 10
-2-
-14-
15-
â– 14
0
-3
-6
-3-
12
-7-
•11
-2
2
-3
6
-6
-9
4
-6
1
7
8-
â– 14
-3-
â– 15
2
-9
2
-7
-5
-20
-7
-4-
15
-8
-5
-5
-6-
10
0
-9-
â– 23-
16
-7-
â– 12
6
5
2
5
-1
1
-7-
17-
â– 13
-10
-15-
11
7
-6
8
2
0
-1
3
14
7
-2
-3
30
-7
3
-9
4
8
16
7
13
5
11
ro

TABLE 7
Corrections Applied to the W20
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
-10-
-14-
-14-
-12
-5
6
-5
-3
3
7
-6-
-11-
-36-
-14
-8-
-19
-7
-1
4
-6-
-20-
-49-
-35-
-17
85
32
8
4
-7
-1
-1
-5
0
10
19
3
-4
-9
11
20-
-15-
-27-
-27
-2
12
-3-
-11
-4
15
80
-2
-6-
-14-
-42-
-23-
-33-
-17-
-29-
-26-
-24
-6-
-18
15-
-16-
-14-
-28-
-12
11
27
22-
-30-
-13-
â– 14
-1
75
-37-
-39-
-40-
-35-
-32-
-39-
-27-
-54-
-41-
-54-
-15-
-45
-8-
-71-
-34-
-62-
-57-
-37-
-49-
-36-
-50
-5-
-14-
â– 11
70
-19-
-32-
-36-
-24-
-29
-9-
-36-
-44-
-33-
-38-
-37-
-45-
-34-
-34
-4-
-18-
-53-
-29-
•47
-5-
-23-
-24-
-38-
-26
65
-34-
-45-
-42-
â– 21-
-48-
-14-
-41-
-67-
-63-
-75-
-66-
-41-
-29-
-38-
-21-
-36-
-62-
-27-
-63-
-16-
-20-
-59-
-44-
-31
60
-38-
-32-
-13
46-
-13-
-16-
-35-
-63-
-42-
-43
-9-
-27-
-43-
-75-
-40-
â– 22
-3-
-52-
-59-
-75-
-26-
-57-
-26-
-11
55
-19-
-38-
-43-
-27-
-39-
-32-
-41-
-27-
-22-
-61-
-28-
-70-
-29-
-46-
-48-
-44-
-42-
-29-
-56-
-27-
-17-
-64-
-39-
â– 30
50
-61-
-19-
-29-
-15-
-43-
-49-
-30-
-32-
-12-
-50-
-41-
-55-
-36-
-17-
-28-
-17-
-41
-5-
-48
1
-9-
-41-
-58-
-53
45
-53
-9-
-54-
-38-
-55-
-40-
-41-
-45
-8-
-25-
-59-
-33-
-65-
-52-
-39-
-27-
-33-
-41-
-15-
-39-
-26-
-22
-9-
-16
40
-39-
-43-
-84-
-40-
-26-
-14-
-36-
-42
_4.
-20-
-45-
-26-
-29-
-22-
-11-
-21-
-20
-4
11-
-15-
-24-
-40-
-12-
-24
35
-12
8-
-19
5-
-13
7
-9-
-21-
-40-
-15-
-19-
-10-
-16
12
29-
-35
-1-
-45-
-26-
-15-
-10-
-17
-7-
-31
30
-42-
-33-
-42-
-26-
-40-
-25
-7-
-32-
-17-
-19-
-23-
-46-
-51-
-39
2-
-35-
-26-
-45-
-40-
-39-
-31-
-32-
-20-
â– 43
25
-25-
-54-
-39-
-38-
-30-
-48-
-26-
-47-
-23-
-32-
-28-
-42-
-28-
-19
11-
-20-
-63-
-44-
-33-
-21-
-19-
-43-
-64-
-32
20
-44-
-64-
-50-
-35-
-43-
-40-
-33-
-44-
-41-
-62-
-78-
-42-
-36-
-42-
-35-
-46-
-38-
-35-
-33-
-40-
-41-
-37-
-47-
-17
15
-49-
-66-
-67-
-39-
-40-
-35-
-46-
-54-
â– 66-
-61-
-82-
-41-
-39-
-37-
-33-
-31-
-43-
-27-
-36-
-46-
-62-
-73-
-46-
-41
10
-49-
-60-
-56-
-50-
-50-
-32-
-56-
-57-
-68-
-37-
-52-
-53-
-40-
-60-
-49-
-66-
-48-
-55-
-50-
-57-
-51-
-58-
-38-
-47
5
-56-
-57-
â– 52-
-60-
-67-
-43-
-55-
-58-
-71-
-42-
-69-
-63-
-55-
-62-
-62-
-57-
-45-
-52-
-55-
-42-
-43-
-54-
-51-
-51
0
-55-
-47-
-49-
-51-
-70-
-74-
-58-
-86-
-76-
-54-
-87-
-54-
-63-
.44.
-32-
-52-
-70-
-78-
-81-
-86-
-58-
-65-
-61-
-57
-5
-64-
-48-
-52-
-53-
-64-
-62-
-46-
-54-
-60-
-73-
-90-
-66-
-71-
-63-
-32-
-60-
-42-
-42-
-41-
-70-
-51-
-64-
-58-
-55
-10
-77-
-60-
-65-
-62-
-40-
-64-
-54-
-81-
-45-
-78-
-16-
-30-
-19-
-75-
-50-
-62-
-36-
-39-
-57-
-41-
-46-
-55-
-62-
-50
CO

TABLE 7 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-3
7-
-17-
10
-2
36
9
-8
-6
-3
85
2
9-
-13
-5
-5
23
8
9
14
14
80
33
0
-1
8
-3
-9
1
-7
14
14
75
41
4
5
-2
13-
-10
28-
â– 26
-4
19
70
17
11
20
32
35
3
23
-8
-8-
â– 21
65
16-
-11-
-25
2
10
-4
-7-
26-
-28-
-17
60
7
19
-7-
20
2
11
31
-8
-6
-2
55
-7
-3
12
4
-1
-7
5-
26
-3-
-12
50
34-
-34
2-
17
-1
10-
-15
-2-
â– 18
17
45
10
-5
12
5-
16
9-
-19
7
-4
12
40
3-
-12
-4
12-
11
37
7
7
-9-
-12
35
-1
10
-7
6-
28-
-39-
-41
-4
12
-5
30
-6
22
15
-9
-2
1
-9
0-
â– 13-
-11
25
-8
11
-5-
13
5
4-
-17
2-
•10
18
20
-2
1
-5
-4
-2
-4
-6
-5
-7-
-21
15
2-
-20
0
-7
-1-
â– 22
-7
-8
2-
-20
10
-8
-4-
â– 12
-3-
13
3
10
-2
5
-5
5
6
28
-7
-1-
17
10
-2
-7
-5-
-25
0
-8
12-
â– 17
5-
39-
-16-
â– 13
-5
2-
â– 10
-5
30-
-14-
â– 13
-1
-5
-6
26
-5
10
-5
-10
1
32
-5
6
2
13
22-
14
-3-
â– 13
11 12 13 14 15 16 17 18 19 20 21 22 23
17-29-20-16-17-17-11 3 -5 27 11 2-27
11 -6 22 39 22 -9 1 1-14 15 18 0-31
-24 12 10 0 -4-13 13 5 30-33 11-13 -4
-24 2 -2-19-20 12 14 -2 36-15 12-11 1
-21 7-14 -9 -8 35 -5 -8-26 5 28 26 19
0 26-25-18-13 8-26 2 -4 -2 23 17-14
-25 14-27-20-34 18 16 -3 10-11 20 2 14
-27-23 27 -3-15 -8 3-19-13 -5 15 -5 38
-22 3 13-11-30-27 -1 -4 3 13 2 9-33
-17 21 1-15 -7-13 15-11-10-16 -8 15 2
-20 -3-22 -1 16-12-20 -4-14 -5 -5 -4 8
-16 18-14 -9-23-27-10 -3-22 -1 3-17 1
-41 -7-13 23 -9 1 -5-11-22-11 3-45
8-20 -7 10 -7 3-13-15 392-70
4-20-13 -8-13 -5 0-16 -3-14-12-26 1
-8-13-11 6-22 3 -7 -5-12-13-19 1 5
3 3 2 21 -1 27-13 1-8 2-9 2-5
-6 -4-18-28 -5 15 1-11 0-13 1-82
4 2 0 21 -3 -4 -3-15 4 8 10 14 9
-12 -3-11 23 -8 -1 4 -4 16-11 676
3 37-33 10-11 586 49-10 8-12 7
10
0
10
-4
-1
-1
1
-6
10
12
21
1
15
24
0
18
6
4
12
4
13
15

TABLE 8
Corrections Applied to the Albany 10
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-3
8-
-10
6-
-19
6
-7
3-
-20
3
85
-25-
-10-
-32
5-
-26
-6-
-26
-2-
-29
-2-
80
-39-
-48-
-60-
-29-
â– 39-
-30-
-41-
-27-
-29-
-19-
75
-42-
-28-
-53-
-31-
-40-
-39-
-59-
-35-
-56-
-39-
70
-34-
-15-
-43-
-17-
-28-
-31-
-66-
-15-
-70-
-18-
65
-36-
-48-
-33-
-18
1-
-32-
-44-
-51-
-59-
-38-
60
-30-
-47-
-30-
-24-
-18-
-39-
-34-
-60-
-17-
-36-
55
-27-
-36-
-29-
-27
-5-
-36-
-24-
-31-
-10-
-18-
50
-31-
-22-
-29-
-35-
-28-
-13-
-17-
-22-
-33-
-29-
45
-43
7-
-26-
-31-
-35-
-34-
-50-
-25-
-38-
-51-
40
-44-
-48-
-54-
-60-
-38-
-52-
-73-
-39-
-39-
-41-
35
-65-
-66-
-60-
-45-
-73-
-74-
-96-
-75-
-77-
-51-
30
-73-
-61-
-56-
-40-
-62-
-51-
-53-
-64-
-65-
-74-
25
-72-
-71-
-76-
-59-
-51-
-65-
-70-
-85-
-55-
-75-
20
-73-
-64-
-63-
-66-
-72-
-70-
-76-
-80-
-66-
-77-
15
-76-
-71-
-53-
-60-
-60-
-62-
-64-
-65-
-73-
-68-
10
-71-
-77-
-85-
-69-
-89-
-66-
-53-
-55-
-59-
-62-
5
-74-
-65-
-70-
-59-
-66-
-62-
-66-
-69-
-65-
-76-
0
-64-
-82-
-74-
-68-
-58-
-75-
-83-
-94-
-56-
-54-
-5
-52-
-70-
-67-
-71-
-47-
-71-
-49-
-71-
-60-
-83-
-10
-70-
â– 73-
-73-
-66-
-56-
-86-
-55-
-65-
-53-
-64-
11 12 13 14 15 16 17 18 19 20 21 22 23
99 46 47-38 -6 -1 -4 -8-12-24-13 4 21
35-31 16-38 -9 -4 1 5-16-32-25-11 5
-25-18-25-37-32-31-32-46-40-43-37-40-45
-21-25-40-30-49-36-38-29-24-30-46-39-51
-18-44-75-42-54-31-28-21-31-40-62-28-31
-4-27-46-38-33-28-31-46-37-52-36-35-25
-19-27-26-34-40-49-41-30-22-44-27-33-20
-20-39 12-15-31-42-32 13-24-25-27-17-13
-14-46-28-45-36-55-56-34-39-30-38-26-14
-30-18-51-57-36-40-38-58-39-66-55-62-33
-44-30-31-42-55-52-51-66-59-68-45-52-41
-72-55-44-53-93-71-65-61-53-55-66-50-61
-26-26-72-66-70-57-66-74-67-84-85-53-70
-48-38-36-56-65-63-58-50-54-76-72-75-74
-58-67-53-65-81-72-76-58-91-68-65-82-95
-36-50-59-62-63-51-56-46-80-72-70-77-89
-42-47-64-77-71-77-65-60-64-60-80-75-65
-51-54-69-62-63-67-67-73-66-57-78-85-79
-59-57-76-65-87-75-78-90-95-94-94-75-75
-63-51-50-54-81-83-76-79-82-90-99-77-79
-29-65-54-67-79-70-65-74-60-70-73-71-81
10
3
66
53
61
33
25
24
21
27
34
36
58
29
55
72
56
54
79
50
41
25
<_n

TABLE 8 CONTINUED
Declination
dec\ra 0123456789
90 1 -6 -5 20 1 60 17 2 11 23-
85 -22-15-20 20-22 36 16 8 0-17-
80 2 5-27-25-39-11 17 23 1 2
75 23 15-27 1 16 21 29 32 15 16
70 -8 17 2 42 34 33 0 -4 -9-12-
65 11 26 12 -2 13 4 31 31 37 29
60 -4 6 -6-10 23 0 10 6 6 15
55 -6 -5 -6 -3 22 30 12-21-20-25
50 -19-12 -8 -5-10 12 -7 9 15 2
45 -14-12 82-3 4-19-14-16 5
40 8 13 8 -1 -2 -3-11-13-26 -4
35 -21 -4-36 -7-33-12-53 -8-14 -7-
30 -15 7 -8 17 -8 14-42-15-21 5
25 -32 -9 -9-15 1-29-27-26-22-15
20 -21 -4-15-43-13-32-27-33-25-33-
15 -23 -5-20-14-12 -9-42-28-24-11
10 -24-24-44-29-47-25-53-40-36-36-
5 -19-14-27-28-36-13-22-22-13-32-
0 -31-31 -1-15 -7 -2-40-36-29-14
-5 -29-22-30-25-44-28-41-24-47-29-
-10 -36 -5-31 -4-24-31-28 -5-28-26-
11
12
13
14
15
16
17
18
19
20
21
22
23
-28
41
40
46
45
45
32
27
11
-4-
-31
26
-7
-45
0
0-
-20
-3
-1
-3
12
-6
4
5
11-
-23
12-
-10
-9-
-20
-6
0
-5
7-
-15
29
8-
-27-
-26
7
-1
29
3
9
22
25
26
32
55
42
18
8
-22-
-21
-6-
-15
14
11
22
12
16
16
12
11
-8
3
-4
7
10
26
-4
9
6
3
30
25
31
9
-10-
-28
8
7
3
16
3
12
-4
14
-2-
•12
-3
13
0
-3
1
12
33
17
31
11
25
17
1
6
-1
-2-
-30
-5
8
13
21
6
11
17
34
15
-6
-22-
-19-
-22
1
9
-5
17
4
2
-9
0
-2-
-12
12
14
9
5
17
3
20
15
14
4
16
18
13
0-
-13-
-12
6
-2
-6
4
-4
10
0
3
-8
-9
4
3-
-17
24
-6
6
9
4
11
2
-3
-9-
-18
-23
7
2
8
-6
4
13
-7
5-
-19-
-32-
-13-
-11
-33-
-14
-5
_4.
â– 16
-7
-7-
-21
-8-
-15-
-22-
â– 20
-5
-14-
-11-
-14
-9
-3
-6-
-15
-8
3
-3-
-15-
-15
-8
-32-
-27-
-34-
-43-
•17
26-
-10-
-20-
-14-
-13-
-36
-9-
-32
-17-
-10-
-25-
-37-
â– 16
8-
-19
-4
-9
3-
•16
-9-
-12
-25-
-45-
-34-
-31
9-
-41-
-43-
-10
7
1
-2
-9-
-14
-41-
-55-
-39-
â– 28
0-
â– 13
5-
-14-
-14-
-33-
-30-
-20-
â– 28
-30
-2-
-19-
-23-
-35-
â– 13
8
8-
-28-
-20-
-10-
-13-
•30
10
11
40
14
14
10
14
-7
-5
3
-9
0
13
-1
-6
22
5
31
11
-6
41
45
-P>
cr>

TABLE 9
Corrections Applied to the Bonn 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
65
-99-
•99-
-99
99
99
99
99
99
0-
•78-
-99-
-99-
-99-
-99-
-99
0
-7
-7
-7-
-14-
-80-
-51-
-99-
60
-72
42-
-85-
-99-
-99
15
20
47-
-45-
-64
1-
-50-
-70-
-26-
-50
6
8-
-34-
-19-
-34-
-70-
-56-
-99
55
-82-
-36-
-64-
-99-
-57-
-18-
-53-
-21-
-83-
-58-
-26-
-44-
-75-
-41-
-99-
-97-
-71-
-99
-4-
-24-
-30-
-59-
-99-
50
-58-
•59-
-31-
-35-
-41-
-39-
-48-
-57-
-63-
-72-
-43-
-58-
-83-
-48-
-42-
-38-
-77-
-99-
-25-
-33-
-53-
-58-
-58-
45
-78-
-34-
-65-
-64-
-79-
-67-
-75-
-79-
-48-
-88-
-63-
-71-
-75-
-64-
-45-
-40-
-71-
-90-
-60-
-43-
-60-
-60-
-87-
40
-96-
-65-
-77-
-53-
-47-
-55-
-62-
-81-
-54-
-78-
-73-
-63-
-53-
-60-
-53-
-72-
-56-
-72-
-50-
-73-
-36-
-48-
-70-
35
-76-
-81-
-45-
-51-
-60-
-58-
-72-
-79-
-72-
-79-
-70-
-75-
-56-
-69-
-48-
-80-
-57-
-82-
-57-
-60-
-32-
-60-
-64-
30
-77-
-80-
-54-
•64-
-48-
-50-
-83-
-89-
-97-
-89-
-97-
-72-
-79-
-53-
-81-
-84-
-82-
-80-
-38-
-42-
-62-
-78-
-69-
25
-50-
-43-
-45-
-54-
-75-
-98-
-99-
-80-
-82-
-52-
-87-
-75-
-99-
-47-
-72-
-69-
-99-
-69-
-30-
-27-
-74-
-84-
-67-
20
-54-
-52-
-57-
-21-
-67-
-57-
-97-
-73-
-99-
-66-
-71-
-70-
-89-
-55-
-66-
-64-
-73-
-60-
-41-
-56-
-46-
-75-
-53-
15
-43-
-47-
-41
-9-
-48
-8-
-94-
-56-
-95-
-94-
-51-
-46-
-59-
-38-
-58-
-50-
-43-
-49-
-58-
-47-
-38-
-80-
-63-
10
-20-
-44-
-14-
-10-
-44-
-48-
-89-
-70-
-92-
-94-
-61-
-52-
-60-
-59-
-69-
-58-
-37-
-41-
-34-
-29-
-16-
-70-
-41-
5
-36-
-34-
-24-
-22-
-73-
-44-
-30-
-44-
-53-
-56-
-52-
-42-
-42-
-31-
-67-
-67-
-56-
-36-
-37-
-29-
-13-
-12
-9-
0
-43
-7
8-
-21-
-46-
-45-
-17-
-82-
-57-
-60-
-45-
-81-
-53-
-29-
-34-
-26-
-28-
-12-
-19-
-33-
-32
-2-
-18-
-5
-42-
-21-
-61-
-89-
-88-
-47-
-30-
-40-
-58-
-45-
-31-
-93-
-62-
-29
-5
-1-
-24-
-23-
-16-
-15
-3
25-
-45-
-10
41
56
20
17
19
29-
-16-
-32-
-65-
-28-
-11-
-10-
-15-
-18
-2
-4-
-23-
-25
7
-6-
-27-
-41-
-90-
23
52
2
35
52
70
72
88
84
64
63
52
36
19
18
47
53

TABLE 9 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
65
44
54-
-99-
-99-
-99-
-99-
-99-
-99
0-
-58
16
16
98
98
99
0-
-99-
-99-
-99-
-99-
-99
35
60
99
60
42
38
5-
-12-
-38-
-67-
-38-
-23-
-95-
-99-
-97-
â– 20
48-
â– 29
-4-
â– 48
47
11
2
-5-
-14
37
63
99
55
8
20
1
64
45
38
1
26
10
77
8
34
91
32
67
17
43
9
38
37
37
37
44
75
50
21
38-
-17
20
14
24
9
24
7
41
5
-2
36
17
45
-4
40
19
8
27
31
49
31
44
45
40
51
26
24
36
34
45
26
12
1
28
26
34
38
57
51
50
63
30
28
25
67
70
66
40
11
-2
-7
9
16
19
1
-6
-2-
-11
8
6
5
19
32
18-
-20
-5
-4
22
-1
32
27
41
35
0-
-10
-7
10
0
2-
-37-
-39-
-29
-4-
-23
9-
-20-
-21-
-33-
-24
18
-1
39
21
23
0
10
14
30
1
9
2
17
39
31
35
-3
-4-
-19-
-31
11
13
35
5
21
50
18
30-
-19
14
27
42
28
25
2
15
-3-
-13
17
17
0
2-
-14-
-20
-1-
-14
9
18
5
2
8
-1
27
-6
17
15
23
20
20
2
-8
16
-6
28
-4-
-23-
-14-
â– 20
-4
14
-3
11
6
11
6
7
1
29
-7
4
1
24
21
15
34
3
32
11
41
-5
25
12
7
5
3
-5
8
24
37
52
47
26
9
28
-4
47
44
43
10
22
12
25
27
12
26
14
29
-2
16
8
13
21
14
13
11
9
18
11
27-
-19
23
26
9
5
25
22
22
17
29
48
14
21
-7
14
21
17
58
30
51
27
22
18
10
6
26
19
34
2
0
11
10
44-
-12
32
29
84
18
15-
•16
2
-3
16
19
22
58
34
51
25
6
49
66
87
22
-5
3
30
53
56
66
31
78
41
22-
-12-
-38-
-40-
-46
25
8
49
-1
34
50
62
38
93
38
89
-10
25
80
17
16
11
4
1
-2
-3
0
-6
13
44
76
30
49-
-25
15
50
81
0
24-
-58
86
-p.
oo

TABLE 10
Corrections Applied to the Bord 50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35
-25
24
4
10-
•31-21-
16
-3-
â– 13-
•21-
•54-
31
0
3
0-
•13-
22-
â– 22-29-
•34-
33
-9-
•12
30
3
18
3
12
1 1
7
12
8
6
8
13
13
9
1
-6
-9
8 27
18
7
5
7
25
15
10
8
1
0 0
-6
7
4
4
21
-1
-5
8
-4
-3-
10
1 0
14
13
12
11
20
1-
â– 12
6
-5
2-12-
15
4
-5
0
16
0-
14
-8-
12
-9
-2
-2 -9
11
16
5
4
15
9
7
15
12
3 -2
2
13
12
15
22
10
12
4
4
6
18
16 18
22
26
21
18
10
3
1
-5
-2-
16 -8-
11
-2
11
6
0-
•18
4
-2
4
-2
11
6 12
9
14
16
12
5
2
-2
-6
-8
2 -1
-4
-8
-2
6
-2
-1
4
2
-5
-1
-3
4 9
12
11
8
7
0
14
6
16
-8
22-12
16
-7
0
24
28
27
11
5
-8
8
8
24 19
15
5
12
21
-5
38
10
14
-2
40-1
38
17
71
74
32
1
-6
1
7
22
21
34 20
1-
13
33
51
Declination
dec\ra
0
1
2
3
4 5
6
7
8
9
10
11
12
13
14
15
16
17 18
19
20
21
22
35
-8
29
24
50
-8-31-
25
17
45
46
7
7
21
0-
25-
43-
47-
•38-17
3
0-
â– 48-
51
30
-15
9
6
15
4-11
3
17
16
18
9
12
1
9
0-
11-
21-
10-16
-6
-6-
13-
14
25
10
19
21
20
36 12
19
28
25
29
18
3
3
8
15
20
3
19 14
24
12
10
4
20
8
0
-3
1
-4 11
11
32
25
0
13
-1
11
9
-1
4
-5
-6 -4
-2
-7
-1
0
15
4
-5
-5
-3-
13 9
-2
3
-4
-3
13
-1
-7
1
1
4
3
-4-13
-9
-6-
â– 10
2
10
0
-3
-7
-4
0 4
4
-9
9
9
11
2
-6
5
4
2
-6
-2 -3
-2
4
-4
7
5
-11
-3-
•15-
â– 20
-6-13
-5-
â– 27
-9-
â– 23-
â– 15-
•12
-5
-6
0
-6
-2
3-12
-5-
13
-2
0
0
-40
-8-
•19-
â– 25-
22-24-
30-
•19
-4
-7
-3
-8-
14-
32-
18-
26
-1
11-16
-2-
35
-5-
15
-5
-90-
•73-
•97-
â– 97-
80-71-
87-
â– 50-
â– 26
28
10
3-
14-
20-
25-
35-
•43-
â– 38-49-
â– 33-
82-
•67-
•75
23
20
2
6
-8
12
8
-4
10
59
23
22
-6
11
-3
10
-9
9
2
65
-P*
to

TABLE 11
Corrections Applied to the Sch
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
5
8
-2-
â– 18
3
19
15
26
20
23
13
9
14
8
9-
â– 10
-9
-8
-1
-6
-3
-4
-1
3
85
-6
-8-
â– 17-
â– 28
-3
5
2
10
9
14
7
0
0-
â– 15
-5-
â– 10-
â– 15-
18
-6-
•19
-9
-6
1
0
80
-2-
-10
4
23
27
20
4
4
5
13
18
8
6-
â– 12
-2
-5
3
-9
6
-5
3
9
19
16
75
18
15
17
16
16
22
17
21
17
24
33
45
33
11
5
-5
7
-3
1
3
4
1
9
15
70
13
15
26
25
24
23
19
22
24
33
21
31
12
16
8
-3
1
-6
-8
3
3
8
5
2
65
6
5
14
14
16
20
24
25
34
39
24
19
-1
4
5
-6
-2
-2
-1
2
-7
12
4
3
60
21
23
19
21
7
16
18
22
18
20
23
17
20
2
6
-2-
â– 12
-5-
-13-
â– 12
-6
3
4
6
55
13
11
9
12
1
16
9
23
11
20
17
9
11
-9
4
-4
-8-
12-
â– 11
-5
1
-3
-3
-6
50
12
9
12
-5
-8
1
2
12
3
24
15
6
4
-6
2
1
1-
18
5
4-
â– 10
-7
-8
-3
45
10
8
7-
-12-
â– 12
-5
1
18
21
19
6
10
11
7
-3
0
-6
-4
10
20
3
-4
-4
-4
40
8
16
4
-3
-7
-9
-6
1
30
8
6
-1
0
1
-5
-8-
â– 12
-6
-2
-5
-7
-8
-6
-1
35
5
3
-6
-2
-1
2
15
5
28
2
14
3
6
-4
0-
â– 11
-5
-9
8
-4
-1
-7
-4
2
30
8
7
-3
-4-
â– 14
-2
4
-9
9
9
12
0
10
-1
9
-4
-1
4
13
2
7
1
0
5
25
4
-1
0
5
0
1
-2
5
14
14
3
9
2
0
0
4
-4
6
10
8
11
5
7
0
20
9
3
3
1
-5
3
3
7
12
8
5
17
-5
-2
-9
3
1
7
7
15
16
7
6
-8
15
7
9
13
6
-8
-4
1
5
9
6
18
8
2
0
-2
10
5
6
2
19
14
15
3
3
10
-3
1
-6
7
-4
-6
2
11
3
0
3
-3
6
0
2
-1
-5
7
-4
6
2
18
-3
7
5
7
0
0
-8
-6-
â– 18
1
-1
7
4
0
4
2
6
4
8
1
4
6
7
5
7
-4
1
0
5
-2
2
-7
-9-
â– 12
-5
-6
14
5
-1
-3
-8
-1
-3
14
1
6
10
7
15
3
-2
3
-5
-1
5-
â– 14
-2-
â– 12
-4
-7
-6
0
6
1
-2
-3
2
-6
2-
•14
5
5
4
4
-1
4
9
-10
-1
13-
â– 12-
-12-
â– 15
-4-
â– 21-
-10
-5
17
5
5
5
13-
15
5
3
21
12
10
7
12
13
11

TABLE 11 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-22-
-39-
â– 38-
-28-
•23-
-44
-1
19
14
-7
85
8
-6
19
4
7-
â– 23
2
1
-8-
•18
80
-26-
-21
11
4
8
-4
4
-1
15
-6
75
-21
13
22
24
-6-
â– 18
-9
7
11-
•35
70
2-
-15
7
-7
5
-5
-8
-2
8
16
65
1-
-13
22
-6
10
1
0
-1
8
21
60
-1
-3
9
5
-2
6
-2
3
8
9
55
9
14
9
10
18
21
7
-1
11
9
50
-14
-4
-8
3
-1
3
11
4
9
-3
45
-12
10-
•14
-1-
•14
-6
11
10
8
16
40
-1
2
-4
3
4
7
14
-3
6
5
35
8
-7
-4-
â– 17
9
15
26
-5
18
7
30
-6
-7
7
2
12-
â– 18
-5-
21
-6
4
25
3
13
10
8
4-
â– 10
4
0
9
18
20
-5
-3
1
-6
1
7
15
3
-2
0
15
0
-9
16
10
5
15
16
6
3
6
10
7
7
-2
11
1
3
7
-3-
•11
3
5
1
-3
-9
-1
1-
-13
5
-9
-5
4
0
-5-
â– 18
15
-7
-5-
â– 28
8
7
4
0
-5
0-
â– 34
-6-
â– 32
-2-
â– 26
1-
10
-8
3
-10
-22-
â– 52
0
-9
34-
â– 16
6
-7
0
0
11 12 13 14 15 16 17 18 19 20 21 22 23
29 45 23 -8 1 11 10 7 1 9-36-56-12
11 17-20-37 -6 27 40 19-44-25-36-12 15
-14 -1 -4 25 9 10 -7-11 -6 -5 6 47 6
9 17 9 30 -6 -7-42-17 42-1 9-24
33 -8 2 3-10-12 -7 17-14-16-20 -7 1
-5-28-10 12-14 -4 -9 10-13-19 -787
3 2 25 21 11 -1 1 11 6 2 -3 -3 -2
-2-15 8-6 9-7 0 5 10 8 -8-16 0
0 11 5 12-12 -6-17 12 7-1 0 10 6
1-11 -2 15 5 2-17 22-5 4 3 25 12
7 1 4-2 3 5-6 1-4-5 8 4 7
-6 13 10 12-6-3 5 3 9 -6 -6 1-11
13 -4-14 35-448903 7-22
6 2 6-10 4-818 8-12 -8 -2 -2
-14 8936-5 6-11 19 -3 7-10 -7
7 2-12 -4 -4 10 4-14 -2 -7 14 5-13
1-5 5 13 5-6 8 6-2 5-7 2 0
-4-16 5 5 11 -6 -8 -3-11 1-17 -6-18
-5-3 2 3 -8 -3-8 8 5 23 -6 7-26
27-3 10-11-14-30 15 -6 14-17 9 -6
15 17 13 21 20 0-22 5-18 -2 -7 -4-14
10
20
9
15
-4
15
9
22
6
-1
11
-3
-6
4
17
8
12
-2
4
-1
-3
14

TABLE 12
Corrections Applied to the Bonn 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
90 -15 3 8 11 17 7 -4-24 3 25 35 99 63 54-24-45 4-20 0-34-74-99-
85 -6 6 17 27 27 17 15-10 13 -4 -9 16 8 -9-26-10 19 1-15-24-49-45-90
80 11-41-15-22 -1 -8-13-20 -5-1 0 0 -5 -7-18-52-73-49-56-75-48-53-40
75 -2-47 12 -9 -1-33-47-25-31-13-16 8-11-22-20-37-64-31 21-16-15-51-29-
70 -44-31-29-34-14-37-46-46-31-33-29-41-34-43-26-25 -8-35-38-53-58-79-30-
65 -46-45 -6-33-30-47-45-69-50-51-34-40-34-34-46-61-39-60-65-26-48-42-46-
60 -37-42-13-57-27-73-45-80-59-65-81-28-57-49-65-65-19-57-73-82-72-61-88-
55 -67-35-52-64-48-99-55-99-25-72-83-62-47-33-53-56-52-86-93-99-75-77-88-
50 -90-75-57-60-72-80-88-87-72-84-86-99-42-56-71-71-86-98-50-84-44-78-78-
45 -99-99-99-99-97-20-86-96-99-99-94-88-13-40-43-61-99-99-90-89-35-85-99-
40 -99-99-99-46 29 99 99 81 -1-59-74-94-59-87-63-92-99-99-99-99-71-89-83-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
90
-9
6-
•26
8-
â– 45
18
20
24-
â– 16-
•26-
â– 18
11
41
32
37-
-11
-6-
-18-
â– 21
2
11
35-
â– 62
85
60
47
1
33-
â– 41
9
3
-1-
â– 38-
-25-
â– 35-
â– 10
11
38
53
14
13
-7
3
32
14-
-26-
â– 42
80
22
16-
-16-
â– 30-
-38-
•21-
-10-
-26-
-17-
-13-
-32-
-38-
-69-
â– 20
-8
-1-
•46-
â– 21
-9
24-
-33-
-34-
-33
75
-30
-5
7
6
15
-2
17
26
12
20
32
-3-
-31
5-
-27
27
-8
17
-3
27
-9
20
-8
70
32
9
-8
0
4
-6
-4
20-
-19-
-21
11
-9
5-
-12-
-so¬
-18-
-42-
-27-
-21
-9
-2
15
8
65
15
12
1
6
23
3
11
14
15
18
17
-8
12
-7
is
12
7
15
16
39
22
41
5
60
-9
27
8
17
19
6
8-
â– 10
-2
3-
-14
-2
28
12
10
-6
-7
5
23
22-
-14
11-
-23
55
10
28-
-14
60
45
10
10
7
13
21
-9
-4
16
-5
11-
-11
17-
-12
42
28
-7
40
38
50
51
67-
•29
38
41
42
31
24
13
37
26
41
-1
15
35
34
39
31
51
57
22
76
18
45
69
78-
-22-
â– 32
-9
9
38
48
61
10
28
52
19
60
57
53
47
65
33
69
26
99
-7
40
99
99
95
61
51
28
99
99
99
99
99
96
70
99
63
73
73
80
46
99
99
99
99
23
31
8
-7
46
47
55
57
47
87
99
98
23
0
29
15
13
51
14
21
53
74
77
99
cn
ro

TABLE 13
Corrections Applied to the W2-50
Right Ascension
dec\ra 0123456789
90 11 -1-11 1 4 23 6 22 7-10-
85 11 12 19 15 11 16 -8 4-5 5
80 -9-11 -2-15 -8 -3-17-14-32-20
75 -15-13-24-10-11-13 -9 -7-23-15-
70 -2 6-16 2236 -2-16 -3-
65 -3-15-30-25-13 2 -4 -2-11 -1-
60 -6-16-19 -5 -7 -9 -6-12-18-13-
55 -18-18-17-20-21-27-17-25-32-28-
50 -4-14-14-36-25-29 -5-10-21-29-
45 -1-19 -5-24-12-14 -6-23-18-36-
40 -18-25-25-30-21-24-34-42-28-29-
35 -17-26-33-42-34-35-46-43-18-25-
30 -11-34-36-47-18-23-12-21-19-19-
25 -15-18-27-46-19-32-19-28-28-28-
20 -30-33-33-41-28-28-22-28-26-25-
15 -37-37-30-15-26-27-29-32-34-38-
10 -19-35-40-42-41-52-33-39-31-33-
5 -40-52-50-44-43-52-37-37-40-32-
0 -46-52-61-66-64-46-44-46-69-46-
-5 -38-27-27-52-48-51-41-47-47-46-
-10 -64-46-45-47-44-56-44-51-24-36-
11 12 13 14 15 16 17 18 19 20 21 22 23
-55 -4 5 20 0 1 6 2 2 12 30 58 26
-13 10 10 9 4 5 1 2 15 22 15 30 4
-26 2 -5 -9 -6 -3 -7-7-2 5 8 1 -9
-18 -3-12-21-13-19-12-12-16 -3 21 7 0
8 -6 -9-12 -2-6 2-7 4 5 23 8 5
-8 -8-18 -2-13 -7 -8-23-14 -4 5 16 3
-10 -2-21-14-25 -4 -2 -9 -8 -1 -4 9 10
-4 -1-16-17-23-16-15-13-12 -5 -3 -1 -7
-18-19-14-15-22-13-12 -8-18-31 -5-12-14
0 -6 -9 -7 -9-17 -1-14 7-21 5-43-25
-22-23-32-14-11-29-11-29-17-21-27-42-19
-31-41-33-42-43-35-15-18-27-15-22-23 -3
11-15-14-37-17-16-13-24-19 -8-22-22-18
-19-38-45-37-14-13-12-25-18-23-18-24-18
-29-14-47-14-19-25-26-35-31-29-22-35-30
-47-29-53-22-27-15-21-29-34-22-28-38-36
-37-34-34-31-31-12-31-31-39-35-31-38-34
-36-48-42-40-44-26-43-25-43-41-32-33-45
-36-40-41-28-27-32-33-35-39-53-53-43-45
-62-46-50-52-40-37-37-53-42-39-48-46-42
-51-45-28-47-37-31-29-29-42-45-64-54-51
10
34
5
-6
10
15
31
26
28
31
16
28
53
17
27
33
62
44
47
55
53
45

TABLE 13 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
-27-
-25-
-23-
•14
-8-
-47
-4-
-10-
-19-
-51-
85
33
-6-
-10
-6
8-
-20
10
0
-5-
-16-
80
-42-
-41-
-21
-1
-2
-3
-2
4-
-11
-6
75
-38-
â– 18
-5
-2-
-26-
-26-
-21
12
7
-2-
70
-13
5
-2
-8
-8
-5
-3-
-12-
-17
-2-
65
-20
1-
-17-
â– 21
-1
-2
16
6
-3
14
60
-20
1-
-11
-9
0-
-22-
•23
-7
1
1
55
-43-
-19-
-17
-2-
-13-
-15-
-11-
-21
-8-
-17-
50
-12
-4-
-13
6-
•33
-1
8-
â– 11
-7-
-23-
45
-32-
-22-
-30
11-
-13-
-21
13-
â– 15
-3
-1-
40
7
5
-4
1
5-
•22
25-
â– 10
28
4
35
-10-
-10-
-20
0-
-12
-3
33
-8
35
11
30
9
7
0
29
11
9-
-17-
â– 10
14
59-
25
33
19
22
24
25
37
28
6
25
26
20
14
5
9
14
14
5
22
2
3
-2
15
8
-6-
â– 14
8
19
-7
-6
2
7
46
10
19-
â– 11
0
14
11
37
16
17
25
33
5
15
-5
21
7
21
44
22
0
7
5
0
-7
6
4
9
-7-
-27-
-11
5
30
23
-5
8
11-
-10
15
21
40
23
2
17
28
-10
20
32
14
7
15
19
9-
-24-
â– 17
3
11
12
13
14
15
16
17
18
19
20
21
22
23
-13
8
-7
13-
-15
-9
-2
-1
0
-8-
-28-
-54-
•28
12
19
16
20
4
3
8
3
-3
8
10
0
20
19
22
7
23
6
-3
8
6
-6
27
-4
5-
-10
-22-
-11
-8
38
-4
3
0
8
4
11-
-17
2
1
-10-
-12
14
33
10
-5
11
1
8
-3
7
2
5
4
-6
10
12
7
7
21
0
-6-
â– 12
20
1
9
-5
-5
15
4
-8
12
2
2
5
-3
11-
-14-
-11
-6
-7
20
-1
-8
8-
-13
4-
â– 17-
-19-
-21-
-31-
-42
7
1
4-
-10
6
13
4
36
-3
13
11
7-
-11
20
-2
9
13
19
SO¬
-25
27
-5
40
14
-7-
â– 17
16
-1
16
7
25
SO
18
23
6
7
4-
-21
4
10
22
14
5
-6
12
31
13
14
-6
_4_
-11-
â– 11
6
12
6
35
20
31
41
9
6
24
15
31
-1
17
29
22
37
24
48
44
27
22
5
22
11
13
25
4
27
32
40
50
31
37-
â– 13
2
12
16
10
28
11
35
29
20
3
15
34
4
16
-6
11
2
16
19
51
32
39
38
39
14
11
24
2
22
-9
21
18
15
5
29
31
35
8
20
1
-8
14
4
5
27
17
12
28
7
18
31
25
3
-2
13
21
-24
29
19
17
25
12
16
14-
â– 13
6
-1
15-
â– 12
-22
23
11
16
26
1
13
-1
31
51
41
34
2
10
34
12
18
22
26
12
-9
22
12
29
15
18
19
7
20
24
4
23
16
11
15
cn
-P^

TABLE 14
Corrections Applied to the W3-50
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
6
8
0
13
6
12
4
18
1
6
85
1
15
27
26
14
12
1
15
-8
3
80
-19
-9
14
6
9
10
2
-2-
â– 20
-3
75
-18-
•10
14
-5
14
-4
-2-
â– 31-
•33-
•16
70
15
26
29
-2
5
1
22
11
13
20
65
0
1-
â– 27
-9-
-25-
-14
-4-
â– 10-
•11-
â– 34
60
6-
â– 24
-4
22
42
13
6
-8
-7-
•38
55
18
0
6
-2
4
14
-4
-1
-5
4
50
10
1
3
2
-3
13
4
-5
-7
1
45
17
8
12
6
13
16
16
5
7
-4
40
12
9
9
1
10
-6
4
3
9
-5
35
11
4
0-
•10
3
-7
4-
•13
5
-6
30
18
5
1
5
19
10
17-
•17
10
-7
25
29
24
7
15
14
13
18
7
15
10
20
5
24
5
6
15
10
12
11
18
9
15
4
17-
•12
22
17
0
7
5
7
8
10
12
17
-3
5
-1
6
9
-7
9
7
5
-1-
â– 14
-3
-5-
-10-
•14
6-
â– 23
-4
0
0
5-
â– 18
7
3-
-15-
â– 32
4-
•14-
â– 12
-3
-5
-17
9-
•18
-4-
-12-
â– 17
2
-9
-7
-6
-10
-21
15-
â– 33-
â– 18-
-11-
-20-
•12-
â– 25
-9
6
11
12
13
14
15
16
17
18
19
20
21
22
23
-23
14
12
11-
â– 17
-1
11
12
-1
-5
2
24
20
-20
-2
2
-5-
-12-
â– 23
-8
-2-
â– 10-
14-
â– 10
12
5
-3
-7
1
12
4
-6-
â– 27
-3
-4
4
-2
10-
â– 12
25
8
-3-
•19
-4
3-
â– 25-
-11-
â– 40
-9
-2
-7-
•32
1-
â– 12
-1-
-32-
â– 12-
â– 26
1-
â– 22
9
1
12
6
14
-8-
•14-
16-
-21-
â– 32-
â– 38
21-
-35
3-
13
26
7
8
0
1
15
-9-
-18-
â– 28
9-
-23-
â– 44
-6
-4
2-
â– 17
6
5
28
-1
7-
â– 25
-8-
â– 14
-8
8
11
17
10
-2
0
7
1
6
-6
1-
â– 11
-5-
25
3
-3
5
5
8
8
-6
6
-6
12
-2
-2
-4
13
8
11
-4
-3
-4
-6
-2
1
13
10
-4
-4
0
1
5
-7
-4-
12-
-12-
â– 18-
-18-
-22-
-19-
â– 28
-9-
â– 14
1
-4
8
14
-4
-5
3
-2
6
26
1
2
-5
10
4
24
10
-6
11
12
19
8
34
12
7
-4
2
17
11
9-
13
16
11
19-
â– 11
-7
-9
-1
-2
0
14
8
7
-7
10
7
-1
11
7
9
1
12
11
25
-3
-6
4
8
-2
4
-2
0
-8
-7
-7
0
5
-4
-4
0
-1
4
1-
â– 11
-6-
â– 13
-1
11
1-
â– 15
9
14
7
5
9
-3
-7-
-13-
â– 26
-6-
â– 10
-5-
â– 10
-27
8
-4
-8
-7
-7
-6-
-17-
â– 30
3
0-
-29-
-15
-7
1
3-
â– 18
-6-
-21-
â– 12
-8-
â– 10
7-
-10-
â– 47
-3
10
15
14
-9
14
-5
4
0
-9
5
9
1
3
5
6
11
11
1
1
8
12
-9
cn
cn

TABLE 14 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10 11
90
-7-
•12
-8-
11
-2-
44
2 11
12-35-
30-32
85
27
2-
11
-6
12-
26
4 -6
1-32
-2-15
80
-5
20
-4
10
5-
11-
15-14
17 -3
18-14
75
-19
-2-
23-
26-
11
-2-
22
3
0 11-
16
4-
70
-9
0
10-
41-
13-
10-
10-24-
61 -4
-7 38-
65
-15
17
15
-5-
31
17
14
7
10-13
29-17-
60
-18
-3-
32-
28-
24
11-
17-11
6-23
5-26-
55
-26-
•21-
22
-9
-9
-6
4-20-
19-11-
11-36-
50
-16-
•22-
lO-
15-
40
-6
-7-14-
30-29-
20-21-
45
-12-
•20-
ll
-9-
14
2
-6 -5
-5 -9
-8-14-
40
-6-
10-
16
2
2-
14-
13-21
0 -9-
10-24-
35
2
4
6
3
1
0
3-17
-6 -6
2 -3
30
8
22
13
6
0
11
-3-10
1 -9
-7-22-
25
24
24
13
11
17
9
11
7
4 15
12 25
20
6
7
7
13
6-
10-
10 -8
-2-18
-9
4
15
-7
-8
-5
18
-7
-5-
14-29-
11-35
-2
7
10
0
-1
6
8
-4
2
14 -1
18
5
11
7
5
-9
-1
9-
17
-3-
23
-3 -9
1-10-
12
6-
0
-20-
â– 17
13
-1
18
-3-
17-16
9 -9-
14-19-
-5
-3-
•21-
26-
29
-5
1
8-22
-6-42
-4-15
-10
21
-4
-4-
19
2
-8-
19-43-
25-17
5 -3-
13
14
15
16
17
18
19
20
21
22
23
9
32
36
13
-3-
-13-
28-
-49-
-46-
-38-
-21
6
11
18
24
14
4
-9-
-24
17
2
11
-20-
-31-
-24-
•27
-3-
â– 32
6-
-13
21
6
7
-25
0-
â– 11
-2
4-
-12
15
-7
-5
19
9
14
26
26
-1
4-
â– 10
1
18
3
12-
-53
-7
-2
-3-
-44
2-
-16-
17
29
-9
-3-
-48
35
13
-3-
-21
23
5-
19-
-21
3-
-11
4
-8-
-23
-2-
-13
34-
â– 17
-6-
-53
6-
â– 13
-9
-8
-4
21
13
20-
-18
-3-
-13
-6-
-10-
-10
0
4
6
-5
-8-
-14
2
0
-6-
•15
-9
1
9
1
0
3
3-
17-
-11
4
0
2
12
12
9
0
6
13
-3
0
3
-1
1
13
21
34
14-
â– 12
11
8
30
2-
-11
3
22
25
16
37
14
26
-6
0
13
13
25
35
26
13
4
0
0
-7
0
15
7
1
-10
-2
-7
3
-3
-5
1-
-13
-5
-4
9
1
4
24
33
14
21
9
-3
5
8
13
6
-9
12
19
-5
17
2-
-15
7
7
18
-5
1
4
8-
•13
8-
27
4
13
1
-9
-6
14
4
25
-9
15-
12
20
3
0
-7
-27
-6
-5
7-
-30-
-14
24
53
-2
14
0
cn
cr>
12
5
15
14
20
27
56
10
33
13
10
12
5
13
-9
-5
-4
6
26
39
7
25

TABLE 15
Corrections Applied to the GCH 1-50
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
25
-8
12
6-
-15-
-32
4
-6
-5-
-23-
-16
20
8
6
-6
-3
0-
-18-
-12-
-28-
-25-
-18-
15
14-
-16
14
11
-9
13
19
7-
-19-
-12-
10
44
16
28
12
-9
7
11
0
2
-7
5
26
17
26
21
12
37
17
11
-8
6
0
19
-7
32
31
20
26
13
10
-1
16
-5
0
0
0
0
80
99
99
99
59
26
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
25
42
16
28
25
17
39
-4
1
15
6
20
36
37
17
26
32
47
40
46
55
47
15
25
23
5
27
22
24
23
37
30
43
10
-2
9
-5
12
0
1
-7
9
28
11
5
33
26
9
23
21
46
30
34
46
25
0
19
27
-2
50
48
23
47
54
40
54
-5
0
0
0
0
-6
21
44-
-99-
-99-
-99-
11
12
13
14
15
16
17
18
19
20
21
22
23
-22-
-13-
-15
-9-
-34
3-
-22
12
6
7
6
-3-
-11
-29-
-43-
-24-
-10-
-18
0-
-14-
-17-
-31-
-20
-7
17
3
2
-8
0
4
4
11
11
3
-2
3
23
28
-2
6
0
-6
9
10
15
23
30
0
17
24
22
8
-9
10
11
26
7
3
13
22
16
25
25
33
28
17
-6
15
26
7
14
9
-4
10
3
17
52
23
86
38
15
99
10-
-18
99
99
99
99
99
0
0
11
12
13
14
15
16
17
18
19
20
21
22
23
28
36
35
3
9
20
32
38
38
46
41
35
30
35
34
25
25
49
38
30
34
46
42
47
36
32
29
25
24
22
22
35
38
28
48
30
32
22
24
12
8
11-
-13
13
17
14
18
38
25
35
30
17
-5
12
2-
-14
6
8
9
31
28
26
22
13
20
31
22
25
33
42
17
6
37
78
50
59
71
40
-89-
-99-
-99-
-98-
-99-
-99-
-99-
-99-
-54-
-54-
-54
0
0
10
5
14
17
7
9
7
77
10
50
27
39
14
29
43
99

TABLE 16
Corrections Applied to the Cape02 00
Right Ascension
dec\ra 0123456789
35 0 0-99 17 24 46 32 -9-40-99
30 16-99-39-68-59-76-80-99-99-99-
25 -76-62-74-73-80-89-85-99-91-99-
20 -55-37-55-54-88-87-83-95-91-99-
15 -58-47-62-55-78-69-75-99-99-99-
10 -61-48-68-67-87-68-73-99-99-99-
5 -45-46-50-51-54-65-99-99-99-98-
0 -38-68-66-99-77-99-28-57-44-99-
-5 -49-59-68-99-99-99-28-28 99-99-
Declination
dec\ra 0123456789
35 0 0 99 99 99 99 17-21-99-85
30 -99-12 73 99 99 95 31 15-38-20-
25 -59 -7 6 21 16 15 -2 2-13 -9
20 -17 8 12 27 19 11 3 13 26 7
15 10 15 29 33 40 45 60 40 36 8
10 14 2 27 9 27 6 93 11 16 11
5 13 18 34 31 41 -9-42 25 42 43
0 -1 12 6 24 12 43 12 16 95 25
-5 2 17 0 11 5 31 12 12 99 1
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-62
0
0
0
0
0
0
0
0
0
0
0
0
-99-
-99
0
0
0
0
0
0
0
0
0
0
99
-99-
-99-
-99
0
0
0
0
0
0
0
0
0-
â– 28
-95-
-83-
-99
84
0
0
0
0
0
0
0-
-99-
â– 38
-70-
-72-
-95-
-99-
â– 99
0
0
0
0
0
99-
-93-
-47
-79-
-81-
-85-
-90-
â– 80-
â– 99
0
0
0-
-99-
-29-
-40-
-42
-86-
-63-
-69-
-60-
-66-
•37
0
0
0
99-
-41-
-24-
-41
-65-
-44-
-77-
-42-
â– 59
93
0
0
0
99-
-52-
-43-
â– 63
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
99
0
0
0
0
0
0
0
0
0
0
0
0
20
99
0
0
0
0
0
0
0
0
0
0-
-99
31
75
99
0
0
0
0
0
0
0
0
0
7
14
24
16
42
0
0
0
0
0
0
0-
-63-
-10
10
9
-1
0
99
0
0
0
0
0-
-99
46
-8
31
15
8
-3
14
70
0
0
0
99-
-30
-1
1
2
3
-6
6
4
85
0
0
0-
-99-
-42-
-20
-4
-8
-3
-8
15
21
61
0
0
0-
-99-
-55-
-34
0
10
0
70
99
86
77
72
77
82
47
10
0
43
0
19
18
19
36
19
-1
cn
00

TABLE 17
Corrections Applied to the Nice 10
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
20
-99-
99
99
99
6-
-53-
-99-
-20
99
99-
-35-
-99
11-
-18-
-99-
-99
30-
-99-
-99-
-99-
-99-
-45-
-99
15
-55-
â– 46-
-67-
-89-
-59-
-19-
-90-
-97-
-94-
-82-
-81-
-84-
-68-
-85-
-60-
-18-
-99-
-80-
-88-
-78-
-32-
-53-
-68-
10
-99-
85-
-96-
-35-
-42-
-58-
-96-
-86-
-69-
-73-
-90-
-99-
-75-
-64-
-85-
-78-
-51-
-43-
-93-
-64-
-55-
-84-
-69-
5
-32-
85-
-64-
-68-
-10-
-56-
-88-
-79-
-97-
-99-
-99-
-86-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-98-
-50-
-90-
-78-
0
0
99
36-
-99-
-99-
-79-
-51-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-44
99-
-99-
-99-
-99-
-99-
-99-
-51-
-87-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
20
57
77
99
99-
-99-
-99-
-99-
-99
99
51-
-84
99
99
99-
-46-
-99-
-99-
-80
77
99
99
99
99
15
88
77
30-
-29
29
24
-2
15
28
85
35
48
34
99
96
74
98
49
41
78
-2
32
53
10
47
42
28
49
46
43
18
40
-9
3
37
45
44
90
93
54
44
13
33
46
35
51
10
5
99
79-
-59
29
42
82
28
41
46
69
5
49
51
41
90
79
46
42
14
40
57
87
43
0
0-
•99-
-99-
-19
99
99
99
-5-
-99-
-99-
-74
99
99
99
59-
-84
99
99
99-
-28
99
56-
-99-
23
30
25
75
50
99
23
99
53
19
18
99
on

TABLE 18
Corrections Applied to the Nice 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -99-99 -8 6-12-61-99-99-99-99-99-99-99-99-99-95-79-88-99 2 23-15-70 5
5 -50-52-60-51-56-63-80-99-88-86-82-82-99-48-54-98-76-75-99-53-27-51-85-40
0 -55-54-68-50-94-96-81-99-99-62-86-89-82-75-66-75-76-70-73-71-69-56-56-53
-5 -68 13-63-90-69-89-97-76-91-99-99-92-99-90-62-83-99-60-68-74-71-77-84-92
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 21 72 11 -6 47 99-16-99-64 99 99 99 99 99-99-95-99-56 99-99-99-98 56 -4
5 40 13 8 39 36 68 43 11 32 31 56 60 62 42 33 80 49 52 66 67 63 34 64 54
0 1 23 13 16 3 4 4 44 51 18 33 58 18 25 79 71 50 38 10 24 48 64 28 46
-5 -13 29 3 44 36 65 45 2 57 11 39 4 55 47 29 64 23 55 77 37 61 38 46 0
TABLE 19
Corrections Applied to the GCH Z 10
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
35 14 2-39-99 5 45-23-81 6 2-55-67-95-66 7 24-39-71-12-34-32 4-19-18
30 -63-41-39-58-58-59-34-74-67-84-84-46-47-91-99-99-79-94-73-83-72-76-82-48
25 -73-67-74-52-74-64-76-87-64-66-60-52-81-69-53-76-89-72-50-71-89-65-74-55
20 40-43-99-85-70-32-99-99-99-99-99-99-99-99-99-99-57-99-99-99-17 61 38 55
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
35 81 98 19-14 29 12 2 50 6 20 90 40 37 22 10-20 18 8-37-19-14-30-39 0
30 -32-17-15-31-38-22-39-18-18-20-21-27-18-15-23-39-12 1-29-40-32-32 -9-25
25 -13-19-18-28-16-30 -9-13 -7 -3 -1 -3-15-28-15-10-20-22-44-27-32-37 -4-17
20 24 -3 32 14 9-27 20 -6 23 5 9 6 76 18-19 8-11 28 7-21-74-74-69-45
cr>
o

TABLE 20
Corrections Applied to the Paris 90
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
60 -46-99 44-99-99-99-99 000000000000 0-99-99-99 99
55 -18 52 99 99 32 42 99-80-21 47 90 99-62-40 99-99 11 99 99 81 99 99 99 68
50 27 99 99 99-99-99 -5 8 23 48 99 65-99 11 40 84-26 6-10-27 99 19 8 31
45 54 83-68 99 28-99-99-94-99-74 14-19-71 15-16 68 -4 21-55 59 99 31 66 99
40 7 8-13-57-99-99-99-63 37-44-18 65-20-46-85-50-60-67-14-43-32-21-49-28
35 -99-28 -3 32-41-95-93-99-99-43-32-53-79 4-99-99-93-79-17-32 2 99 87-79
30 -9 5 -4-77-99-99-99-86-99-99-16 -5-99-99 2-67-99-69-57-45-31 46 30-97
25 59 99-13-53-99-99-99-99-99-99-92-99-99-99-99-99-99-60-24-25-47-80-41 11
20 -39-25-61 54-27-99-99-99-99-99-87-31-21 4-99-99-92-67-99-65-23-99-51 -9
15 -40-42-49-14-99-99-99-99-99-99-60-99-99-99-99-62-22 -8-55-99-99-89 40 -6
10 -83-15-23-99-32 -8-90-99-99-99-89-63-99-89-99-99-99-84-42 14-17-65 2-51
5 -6-38-86-92-99-99-99-99-88-22-26-77-41-99-24 8-14 33-37 72 37 76 83-99
0 7 99 12-52-99-99-99-97-99-99-99-99-77-99-29-99-99-17-64-64-17-99 21 87
-5 35 99 39 -6-68-69-99-99-99-99-57-72-16-10-77-99 20-88-99-29 27-49 -3 99
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
60
-99-
-99
47
99
99
99
99
0
0
0
0
0
0
0
0
0
0
0
0
0
99
99
99-
-99
55
-20-
-61
99
99-
-37
15-
-31-
-57
71
32
60
99
14-
•99
99
60
64
8
5
43
30-
-64-
-99-
-67
50
25
-9
14
58
-5
70
21-
-57
33
49
31
37-
-17-
â– 42
-4
42-
-39-
-92-
-77-
-70-
-46-
-33-
-20
-8
45
25
44
27
11
-1
96-
â– 32
8
66
99
27
-1
10
90
6
2
-7-
-40-
-46-
-90-
-70-
-59-
-34-
â– 12
40
57
51
7-
-62-
•70
-6-
â– 22
14
31
4
9
40
42
89
1-
-14-
-99-
-99-
-99-
-52-
-86-
-87-
-22-
-40
35
-44.
-49-
-44
33
39-
-14-
-40
43
31
20
35
33-
-12
-3
27-
-20-
-53-
-50-
-45-
-28
0-
-10-
-28-
-99
30
-57-
-35
79
14
19
55
35
49
32
55
15
31
57
-5
41
-7-
-42-
-43-
-28-
-27-
-21
11-
-32-
-24
25
24-
-36
19
29
84
37
33
30
62
47
14-
-67
8
99
58-
-15-
-29-
-32-
-34-
-71-
-40
-8-
-30
24
20
8
52
15
47
44
59
77
27
-1
52
65-
-20-
-21
85
55
-3
-8-
-41-
-99-
-22
37
54-
-26
-8
15
-31-
-27
-1
48
25
57
88
39
62
45
37
94
64
43
27-
•14
14
-3-
-48-
-59
3-
-28-
-54-
-21
10
-1
-4-
-14
30
-4
36
99
78
5
35
45
7
55
43
25
25-
-16-
-38-
-15-
-18-
-12-
-26-
-26
35
5
-22
25
45-
-45
27
73
66-
-15
33
46
51
53
29
68
44-
-37
-7
5
2-
-65
-6-
-51-
-99-
-93
0
26-
-43
49
-5
57
59
44
99
99
83
65
84
20
36
57-
-16
0-
-77-
-76
-8-
-56-
-18-
-38-
-22
-5
-59-
-11
99
19-
-34
19
93
99
51
32
69
18
-1
56
44
2-
-19-
-99-
-58-
-49-
-35
-2-
-16-
-99

TABLE 21
Corrections Applied to the Paris 00
Right Ascension
dec\ra 0123456789
30 2 75 57-14-99-90-47-12 4-68-
25 -62-48-57-83-99-99-99-99-99-99-
20 -81-94-82-99-99-99-99-99-99-99-
15 -88-99-72-92-99-99-99-99-99-99-
10 -85-99-93-99-99-99-97-99-99-99-
Dec 1ination
dec\ra 0123456789
30 -4-37 12 27 19 -4-17 18 31 22
25 28 4 32 31 18 3 -6 10 23 32
20 12 0 12 20 11 5-5-6 3 18
15 -25-34-38 -5-12-20-38-40-23 -6-
10 -72-99-99-99-96-99-99-83-25-14-
11 12 13 14 15 16 17 18 19 20 21 22 23
-99-96-99-99-99-51 30 55 0-71-99-99-54
-99-67-81-99-99-99-84-89-87-94-99-99-75
-99-88-99-99-99-99-99-99-99-87-82-82-81
-99-99-99-99-92-93-88-87-79-38-49-73-99
-99-99-99-63-43-33-28 19 11 72 30-23-99
11 12 13 14 15 16 17 18 19 20 21 22 23
17 -4 8 12 26 48 44 53 54 31 -2 15 3
6-13 3 -2 16 25 31 20 30 20 19 37 20
-4-10 0 1 12 6 13 -5 22 18 22 25 4
-27-30-27 -9-11-22-12-31 10 6 0 -7-27
-75-99-99-91-90-62-23-38-14-26-56-78-78
10
99
99
99
99
99
10
0
5
5
10
29
cr>
ro

TABLE 22
Corrections Applied to the GCH 2-25
Right Ascension
, dec\ra 0123456789
65 -4 -7 18 29-10 11 4 7 11 4-
60 -8-15-27 14 0 -9-17 0 -8 -5-
55 2-13-12-12-10-24-21-19-31-28
50 -33-23 0 -9-12-30 1 0-18-18-
45 -6 -8-15 -7-25 -9-23 -7 -2 5-
40 -22-28-27-31-20 -9-34-18 -4-21-
35 -33-28-15 -5-22-12-18-39-35 -8-
30 12-81-42-15-34-14 2-34-58-50-
Declination
dec\ra 0123456789
65 39 78 70 61 78 40 60 85 51 6
60 30 29 43 32 20 51 38 34 32 39
55 28 54 34 24 32 27 40 15 16 39
50 8 7-13 20 14 21 16 7 33 20
45 7 32 42 25 18 16 13 24 32 8
40 27 34 31 15 19 27 12 37 33 11
35 13 25 4 -4 10 12 -7 5 4 3
30 -5 24 46 6-13 -1 20 8 -8-19
11 12 13 14 15 16 17 18 19 20 21 22 23
13-17-33-38 -8 24-23-23-45-29 1 25 -5
-17-14 1 0-13-15-19-21-19-12-17 -4 -8
-19-21-24-16-18-14-26-10-27-41 4-13-21
-19-42-23-25-11 -8-46-23-20-20 -6 -5-11
-19-33-39-18-32-15-11-27-13-37-33-24-10
-8-33-27-28-20-29-30-31-24-27-24-13 -2
-23-31-13-20-24-43-39-38-21-29 -8-26-29
-18-44-16-15-33-54-36-24-41-67-48-46 45
11 12 13 14 15 16 17 18 19 20 21 22 23
11 5 3 -4 48 26 3 3 27 41 28 60 72
18 33 27 3 9 -3 -9-11-14 10 15 14 17
26 31 29 21 16 3 8 7-2 4 11 28 30
9 12 8-2 -7 15 0 -9-22 -8 14 11 5
-13 -8 -2 -7 5-13-18 -8-24 -5 -9 9 11
4 25 24 15 11 8 17-12 -1 -1 25 30 38
20 1 0-4 2-9 4-21-10 22 11 6 8
13-31-16 6 3-12 2-10-27 24 1 35 37
10
13
13
-8
19
18
28
22
28
10
30
11
40
0
-7
29
6
-7
cn
OJ

TABLE 23
Corrections Applied to the Berl 20
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 -84 99 79-99-99-78 71 20-99 63 84-82-88-88-38 99 99 37-19-99-99-99-99-99
40 -99-79-73-68-79-99-86-81-99-84-73-64-93-99-85-84-96-95-87-98-62-91-79-99
35 -99-99-99-92-84-99-99-99-99-99-99-99-94-99-99-99-99-99-99-86-99-99-99-99
30 -96-50-90-99-99-99-83-99-99-99-86-99-99-99-99-99-99-99-99-99-99-71-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 14-99-99 66 99 99 32 89-99-99-99 99 99-74-99-14 37-24 99 99 42 99 99 99
40 22-20-32-40-16-29-35 26-63-65-23 -4-12 5-31 20 18 0 9 6 27 28 17 47
35 -21-20 -3 13 -2-11-57-19-29 2 -3-11-24 5-13-25-12 21 0-16 -8 2 -4 -8
30 89 43 61 26 8 34 67 76 67 32-14 -9 25 47-25 42 35 81 85 35 52 6 75 89
TABLE 24
Corrections Applied to the GCH 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 99 10-13 83 58 71 94 54 50 54 69 99 46 35-32-34-28 4 18-12-62-65-27 26
85 12 -4-18 3-24 -9-14 16 13 6-24 11 -4-15-23-15 -1 43 2-64-50-45-32-45
80 -56-54-57-35-28 -7-40-61-31-20-40-55-26-13-52-45-50-42-53-54-65-29-72-76
75 -11-34-64-31 -9 -1-26-22-39-47-34-55-31-51-88-65-25-31-52-62-59-44-74-66
70 -48-38-32-41-60-49-20-35-39-33-51-46-61-85-63-64-51-72-48-54-73-78-66-38
65 -99-97-87-81-63-76-86-69-83-73-92-99-90-99-75-92-89-92-99-87-94-99-99-99
60 -27-99-99-89-99-99-99-99-99-99 56-55-99-99-64-99-99-99-99-99-99-99-99 -8
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 -7-15-44-28-37 12 30 58 21 12 7-42-10 34 28 26 20-19 21 -6 5 13 28 22
85 22-19-19 -1 12 21-15 1 9-25 -3-29-41 20 31 13-28 39-60 -9-20-12
80 5-14 -5-44-61-25 11 -3-19 -2-21 -9-13-23-26-23-24-43-24 3 0-34-27-20
75 44 5 -4 17 9 5 7-10 -4-11 3-33-13-14-57-33 3-12 1 27 12-14 10 40
70 14 38 43 29 40 28 41 16 -3-62-24-14 11 30 -2 16 21 -5 0 -6 30 74 41 23
65 10 11-18 6-13 7 18 -5 10 33 35-16-10 5 -1 15 23 2 1 3 29 54 28 -7
60 -35 63 99 52 26 45 25-40-15 21 32-61-54 20 48-31-47 40 3 -4 99 99 99 35
cn
-P>

TABLE 25
Corrections Applied to the Toul3 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
15 -42-71-97-99-99-99-99-99-99-99-54-99-99-83-93-99-88-99-99-99-98-90-65 -1
10 -69-82-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-74-82-74
5 -82-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-95
0 -99-59-69-61-87-99-99-99-99-99-99-84-99-99-57-41-99-99-99-99-99-99-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
15 -50 16-14-51-62 -2 25 0 6-51-31-28-67-23 6 8 10 11-34-20-34-28-55-74
10 -7 2 14 21 20 6 -2-21 2 -5 -7 -8-29 4 9 4 22 24 10 -1 -9 14 -1-11
5 7491 20 11 45 -5-12 -5-21 -4 -6-12 25 15 1 2-10-11 -6 -5 4
0 -39-28-23 -6 27 58 44 39 17 15 -6-27 -9 0-19 29 39 40 45 36 70 31 -6 8
cn
cn

TABLE 26
Corrections Applied to the Cape 2-25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0
65
1-
•94-
â– 99
0
0
30
0
0-
•99-
â– 18
-1
-7
6
44-
•36-
â– 99
25
0-
-99-
â– 52
-4
5
-9-
â– 17
13
0-
â– 13
20
99
83
19
19
10
-1-
•13
5
14
-9
15
41
17
-2
4
-8
20
26-
â– 21
10
-4
10
17
25
-2
0-
â– 35-
â– 99
99
80
-2
-4
5
-9
-7-
•32
-1
99
0
0
0-
â– 99-
•21
0
â– 16-
•10-
•28-
â– 77
0
0
0
0
0-
•99
-5
â– 30
52
99
0
0
0
0
0
0
0
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0-
â– 16
27
28
28
0
0
30
0
0
99
99
40-
â– 21
1
17-
13-
â– 41
25
0-
•99
-2
43
21
15
10
11
26
4
20
99
46
39
46
30
1
15
6
29
34
15
81
51
22
29
32
4
61
50
25
37
10
53
28
41
32
9-
â– 32
55
99
60
34
5
42
24
36
73
99
0
0
0-
â– 99
32
0
51
26
31
99
0
0
0
0
0
54
-5
33
83
99
0
0
0
0
0
0
0
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
99
0
0
0
0
0
0
0
0
0
0
0
0
48
29
0
0
0
0
0
0
0
0
0
0
0
-8-
-45
0
0
0
0
0
0
0
0
0
0
0
2-
-26-
-91
0
0
0
0
0
0
0
0
0-
-68
-21-
-12-
-45-
•99
0
0
0
0
0
0
0-
-99-
-45
-24-
-23-
-25
-6
99
0
0
0
0
0-
•83-
-54-
-33
15-
-28
-5
22
36
0
0
0
0
0-
â– 83-
â– 32
-7
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-72
0
0
0
0
0
0
0
0
0
0
0
0
99-
-99
0
0
0
0
0
0
0
0
0
0
0
24
29
0
0
0
0
0
0
0
0
0
0
0
47
18-
-88
0
0
0
0
0
0
0
0
0
99
43
45
26-
â– 33
0
0
0
0
0
0
0
23
53
58
45
32
31
92
0
0
0
0
0-
â– 29
20
39
46
47
49
41
25
0
0
0
0
0-
•29
44
44
10
0
0
6
11
6
11
10
48
99
10
0
0
44
71
28
50
50
67
45
cn
cr>

TABLE 27
Corrections Applied to the Cape 3-25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5 -54-18 0 -7 14 12 11-18-55-62-82-55-52-68-19-43-31-42-18-42-52-84-83-81
0 -25 -5 -3-20-17-29-17-22-26-19-25-14-19-29 0-27-29-42-49-55-46-52-55-42
-5 86 2-26-27-46-31-26-17 -4 -4 -1-22-17 -5-24-28-35-50-53-38-24-26 -1
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5 9 -3 58 84 68 15 0 3 -9 17 50 75 50 13 28 16 34 20 13 31 43 42 51 25
0 25 15 30 40 44 17 19 17 19 27 39 46 32 15 30 19 40 29 40 43 48 35 37 27
-5 35 26 19 22 34 25 30 26 31 32 32 28 22 21 33 21 42 33 57 55 60 38 38 38
CTl

TABLE
Corrections Appli
Right Ascension
dec\ra 0123456789 10
35 0 0-99-50 1 15 36 13-12-64-99
30 0 99-32-42-18-11 3-17-36-54-57
25 -24 99 22 19-17-14-18-20-12 3-11
20 -16 5-18-12-31-18-30-22-23-34-59
15 -10-25-26-45-55-30-37-28-55-52-47
10 8-31-41-56-73-53-66-38-54-40-42-
5 -25-40-44-50-31-39-43-79-65-63-42-
0 -38-41-36-35-25-32-28-50-38-40-31-
-5 -30-22-32-33-35-42-33-43-29-24-28-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
35
0
0
93
28
15
16
3
12-
-55-
â– 71-
â– 99
30
0-
-99
-1
-5
-4
-5-
•10-
-15-
-50-
â– 38-
-61
25
-99-
-99
9
15
20
-1
-6-
-17-
-10
11
7
20
-99-
-99-
â– 12
21
8
5
-2
-4
-3
1-
-11
15
-78-
-30
4
26
6
19
20
28
18
-8
-9
10
6
31
15
34
39
54
65
38
18
1
11
5
2
20
7
-7-
-27
0
44
39
-2
11
-6
0
7
13
3
-4-
-22-
•10
6
11
-4
7
12
-5
-1
1
13
26
1
-5
-7
7
2
12
15
to the W 40
12 13 14 15 16 17 18 19 20 21 22 23
000000000000
000000000000
95 99 00000000 0-24
49 99 00000000 0-33
26 93-40 0 0 0 0 0 0 0 0-82
31-23-39 79 0 0 0 0 0 99 99 99
33-29-24-29-24-81-36-37-16-12-18-14
33-30-29-38-35-57-29-40-41-39-44-47
46-35-42-44-39-42-28-47-60-52-51-43
12 13 14 15 16 17 18 19 20 21 22 23
000000000000
000000000000
99-99 00000000 0-99
74-99 00000000 0-99
12 28 88 0 0 0 0 0 0 0 0-99
6 12-49 99 0 0 0 0 0 97 4 37
18-21-20-29-21-40-49-61-16 025
-2-16 -9-15 1 0 2-22 1 -5 12 6
10 10 13 -7 7 14 33 18 34 10 24 -3
: 28
ed
11
0
47
15-
21
4
25-
31-
34-
30-
11
0
99
27-'
47-
-5
35
2-
-2
0
O'»
00

TABLE 29
Corrections Applied to the W 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 000000000000000 0-21-21-21-21-21 0 0 0
45 -54-76-67-19 4 12-99-91-99 99 0 0-99-99-47 24 27 24-23-43-72-46-37-29
40 -23-47-69-19 11 29-81-46-73 99 0 0-99-99-57-20 -6 -1-32-46-71-21-15 -9
35 -13-39-73-30-16-33-68-30 -7 99 0 0-99-99-73-60-51-51-58-58-50 511
30 -1 51 10 16-17 -6-23 1-25 2-51 96-99-99-98-99-97-99-99-99 99 99 30 8
25 -14 -2 -6 -7-18-26-41-39-52-37-51-28-99 00000000000
20 -15-42-52-55-35-44-53-68-61-59-67-53-59 99 000000000 99
15 -22-21-37-36-45-45-49-57-55-54-54-35-35 19-99 000000 0-39 3
10 -49-39-52-39-68-64-99 -7-40-33-52-46-37-25 32-99 0000 0-99-68-40
5 -36-33-37-26-28 34-99 99 -9-26-48-53-45-38-30-22-99 000 0-99-55-47
0 -41-50-34-41 19 43 0 99 36 5-39-45-71-55-70-37-99 000 91-65-46-54
-5 -39-70-69-99-99 0 0 0 99 73-14-17-48-40-52-39-70 000 91-49-34-56
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 000000000000000 0-42-42-42-42-42 0 0 0
45 -4-17-64-71-70-88-15-99-71-99 0 0 99 99 84-16-24 -4-27-32-56 -8 -1 50
40 -29-16-29-42-23-50-13-99-93-99 0 0 99 67 15-32-36 -3-17-2.2-69-17-41-41
35 -37-26 -5-16 8-36-21-60-47-99 0 0 99 18-17-36-51-32-41-35-85-24-61-72
30 -72-64 -7-17-17-32-31-51-18-25 43-45 12 10-13-40-74-92-99-99 99-99-99-99
25 40 -9 8-17-11-45-57-61-32-42-24-53 36 00000000000
20 -41-36-30-29-20-48-51-43-26-39-27-22 22 99 000000000 56
15 -15-19-46-50-39-57-53-63-57-60-56-41-36 6-99 000000 0-99 46
10 -43-33-51-65-58-77-51-95-57-51-48-55-65-70-93 99 0 0 0 0 0 99-99-33
5 -50-48-62-80-99-99 99-99-25-45-43-67-72-62-46 53 99 0 0 0 0-61-58-47
0 -51-37-35-24-29-99 0-99-27-59-66-77-78-75-67-58 15 0 0 0 99-32-44-47
-5 -67-65-68-38-35 000 99-62-44-60-54-84-80-99-84 0 0 0 99 -6-29-52
cr>
id

TABLE 30
Corrections Applied to the W ZOD 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0-
-99-
-12
5
33
53
68
94
99
30
-69-
36-
â– 22
2
6
16
10
5
-3-
-12-
25
-24-
â– 34-
-19-
-17
-5-
-12
-6
-4
-4
-3
20
15
2
1
-9-
-12
-9
-9
2-
-21-
-15
15
-9-
10-
-11-
-17-
-13
-9
-6
-1-
-19-
-18
10
-19-
17-
-24-
-13-
-10
4-
10
-5-
-11-
-10-
5
-37-
29-
-41-
-15-
-19
99-
99
94-
-33-
-21-
0
-34-
23-
-32-
-22-
-65
99
0
99-
-95-
-53-
-5
-21
-7
9
28-
-99
0
0
0
66-
-43-
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
99-
-22-
-11-
-25
5
14
63
54
30
-33
40
99
62
43
15
0
32
13
9-
25
19
13
34
19
12-
-15-
12
19
17
-4-
20
21
16
9
6
7
-8
-1
9
18
13
15
-8
-6
-7
-4
2
-8
-4
4
15
14
10
-21
-9
-6
-8
-6-
-30-
92-
â– 47
-6
16
5
-11
0
-9
-2-
-11
5-
99
99
-3
6
0
-18-
26-
-41-
-52-
â– 85
99
0
99-
-50-
-12
-5
-3-
37-
-51-
-99-
-99
0
0
0
99
99
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-90
0
0
0
0
0
0
0
0
0
0
0
0
-3
3
0
0
0
0
0
0
0
0
0
0
49
5
32-
-99
0
0
0
0
0
0
0
0
0
0
-18-
-18-
-51-
-23
0
0
0
0
0
0
0-
-99-
-10
-23-
-18-
-23
-3-
-99
0
0
0
0
0
44-
â– 24
-9
-17-
-15-
-14-
-19-
-40-
â– 34
0
0
0
0-
-19-
â– 31-
â– 29
-39-
-37-
â– 37-
-34-
-34
24
0
0
0-
99-
-58-
-47-
â– 37
-27-
-17-
-44-
-25-
•40
47
0
0
0-
â– 99-
-94-
-64-
â– 48
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
0
0
0
0
0
-99
0
0
0
0
0
0
0
0
0
0
0
0
-69-
-30
0
0
0
0
0
0
0
0
0
0
17
1
-9
99
0
0
0
0
0
0
0
0
0
83
-14-
-14-
-60
99
0
0
0
0
0
0
0-
â– 99
2
13
27
17
69-
â– 99
0
0
0
0
0
99-
-63-
-25
6
11-
-20-
-32-
â– 99
81
0
0
0
0
79
0
8
-3
-2-
-15-
-12-
â– 24
70
0
0
0-
â– 43-
-14-
â– 12-
-11
42
15
21
24
39
59
0
0
0-
â– 43-
-14
-1
-1
10
99
18
-7
-2
-9
20
31
48
11
10
62
76
29
1
9
19
-4
-8
50
o

TABLE 31
Corrections Applied to the Cape 1-50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35 29 27 2 2 5 48 81 13-54 33 66-46-72-27 1 23-37-18 28-25-48 12 9
30 -6 24-14 5 2-16-30-21 6 26 10 24 -8-28 -4 0-13 18 11-21-44-12-19-
25 -10 30-40-65 62 -6-10-16 -7 38-27-12 4-28 10 11-13 -9 -8 22-34-38 18
20 -25 -9-12-31 -1 -2 -1 12 0 11 8 2-24-33-26 4-24-49-30 19 35 3 1
15 -8-19 -4 48 17 12 19 -8-11 -5-26 33 66 22 0 5-21 -8 -3-19 1-63-21
10 -13 -6 1-1 0 26-17-28 10-27 13 -6-45-17-53-47-44 25 50-49-30 -7 -7
5 18 9 16 -4 -8-13-30-18-32 5 8 15 4-3-2 3 26 6 9 -4-23 35 18
0 -15 -4-32 -8 24-19-14-14-17-11-33-23-22-16 31-65-99-15-26 15 -7-47 17-
-5 19 10 23 3-33-41 10 10 27 19-22-19 -9 8 36 6-45 20 -5 33 60 5 50
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
35 -17-33-40-99-96-99-99-62-26-22-26 -9-13-47-18-46-51-13 24-12-35 72 55
30 18 32 45 21 10 5 11 17 8 1-11 2 0 2 41 12 18 0-10-12-10 98 30
25 9 27-13 11 65 32 0 8 34 23 20 39 53 46 54-30 -4 25 28-60 43 49 15
20 18-44-39 6 5 11 -8 12 14 9 10 6 -8 18 6-19 1 57 26-46-32 3 20
15 -7 17 53 80 21 9 36 3 28 35-33 13 33 55 44 40 21 8 3 8 -2 63 24
10 40 4 62 1-35 36 22 -9-28 3 7 43 41 23 35 10-14 5 43 63 10 -7 6
5 2 45 35 19 -5 41 83 -2 20 18 25 39 38 29 31 39 68 27 9 26 38 4 39
0 15 18-14 29 26 22 27 5 24 28 36 46 -4 11 -8-26 30 34 30 20 36 26 28
-5 32 22 41 36 12 10 35 32 36 51 77 26 11 47 21 43 41 25 31 48 44 9 31
23
6
35
25
-2
-5
-8
20
18
17
23
45
-5
-7
37
2
51
68
43
50

TABLE 32
Corrections Applied to the Bord 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
25 -16 41-91-99-99-61-64-99-99-99-99-99 99-20-99-99-99-99 27 99 60-71-99-15
20 -33-12-77-71-99-59-58-63-85-99-91-79-29-99-99-53-31-81-26 0-68-83-73-38
15 -54-52-71-68-44-47-60-59-89-98-73-56-53-89-86-49-51-59-70-62-77-73-74-58
10 -79-47-21-83-58-61-77-58-99-95-99-84-89-93-87-74-86-47-84-74-67-54-87-86
5 -96 22 99-99-99-99-99-77-99-99-99-99-99-99-94-77-66 -9-65-75-81-48-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
25 99 99 99 99 99 99 99 99 99 99 99 82 82 99 99 99 53-37-73 40 92 99 99 99
20 63 67 71 81 57 70 76 65 50 81 62 32 19 46 51 73 63 47 23 34 58 64 69 38
15 31 17 10 38 25 22 8 22 23 34 32 24 33 37 55 59 47 60 52 37 47 32 28 10
10 78 49 34 47 30-11 -5 28 33 4 12 26 56 50 80 82 75 93 76 52 60 52 48 48
5 99 99 99 81 36-52 35 64 44-44-29 12 52 65 99 99 99 99 99 69 68 99 99 99
TABLE 33
Corrections Applied to the ALB99 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -99-99-99-99 0000000000000000 0-99-99-99
5 -72-68-77-31-44 3-53-59-99-99-99-99-77-36 -5-20 -9-69-48-99-67-78-34-92
0 -63-11-47-14-44-16-70-60-87-53-83-75-61-31-25-49-48-81-58-99-77-69-33-45
-5 -83 23-27 -6-37-25-65-50-56-23-51-46-43-22-48-86-82-85-57-99-99-99-99-86
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 99 99-99-89 00000000000000000 99 99 99
5 30 29 1-39 -7 1 9 21 47 61 87 90 52 5 50-24-26 -6 27 99 99 99 85 59
0 -28 13 -8-39-23-11 0 19 32 33 33 57 26 8 45-30 -4 5 11 44 80 38-12-42
-5 -73 -5-18-40-38-18 -6 25 48 29 -4 12 -8 16 38-39 -1 7 7-25 -2-41-70-99
-^4
rv>

TABLE 34
Corrections Applied to the Mun97 OOii
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
55 0 12 12 12 00000000000000000000
50 -91-46-49-46-70-99-99-99-77-74-77-99-99-20-16 -6-99-99-99-44-40-59-85-58
45 -58-57-67-80-76-85-82-78-84-89-74-86-89-89-92-65-73-87-67-78-87-95-95-72
40 -79-87-84-97-79-87-98-90-78-80-82-84-95-99-99-99-99-99-96-93-92-73-88-98
35 15 15 4 -4-76-29-31-94-87-99-99-88-77-87-27-49-99-99-99-81-75-37 26 0
Declination
dec\ra
55
50
45
40
35
30
25
20
15
10
5
0
0
0
17
-14-
-32-
40
0
0
0
0
0
0
0
12 3
11 11 11
37-25-27
15-23-24
25-19-27
40 99 99
0 0
0
0
0
0
0
0
0
0
0
0
0
0
4 5
0 0
-65-99-
â– 20-44-
â– 25-17-
41 13-
0 0
6 7
0 0
63 99
37-26-
30-26-
17-38-
0 0
8 9
0 0
-5 -7-
24-27-
30-16-
24 12-
0 0
10 11
0 0
31-99-
47-47
35-31-
19-44-
0 0
12 13
0 0
99-99-
-3-16-
18-16-
38 34
0 0
14 15
0 0
99-99
51-39-
20-15-
23-77-
0 0
16 17
0 0
18 24-
44-35-
14-23-
51-25-
0 0
18 19
0 0
18 10
10 0-
24-33-
16-37-
0 0
20 21
0 0
22 -9-
15-24-
27 -8-
29 2
22 23
0 0
96-99
38-68
14-52
29 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 19
0 19
19 19
19 19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
^4
CO

TABLE 35
Corrections Applied to the Mun97 OOii
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
70 00000 99 99 99 99 99 00000000000000
65 -37-40-45-38-34-33-35-30-29-31-31-14-29-42-52-35-13-19-15-25-28-37-30-32
60 -34-40-45-37-30-32-46-43-44-44-48-40-52-48-52-50-31-32-30-38-37-47-38-32
55 -29-44-51-40-27-25-43-42-47-50-55-49-57-42-49-55-46-41-39-48-47-53-42-31
50 -16-37-58-49-30-16-40-45-50-57-60-53-54-29-44-61-74-62-57-58-56-55-39-24
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
65 23 32 9 4 26 45 26-18-40-43-19-15 20 20 6 2 -3-10 6 16 26 22 2 11
60 -7 12 -4 -5 7 15 1-10 -8-17-10-21 -1 0-14-15 -9-13 -3 10 16 18 -6 -9
55 -31 -5 -9-12-10-11-21-21 -7-16-14-26-10-15-37-46-27-24-21-12-11 3-23-28
50 -73-57-43-62-58-59-54-45-28-35-33-33-15-29-67-93-61-41-57-66-81-42-59-62
TABLE 36
Corrections Applied to the Kon 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0
0
99
48
31
-8-
-35-
-41-
-57-
â– 35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
-99-
-88-
-39-
-47-
-52-
-70-
-91-
-85-
-99-
-99-
-99-
-99
0
0
0-
-58-
-56-
-54-
-51-
-45
25-
-99-
-99-
-99
25
-69-
-52-
-62-
-65-
-82-
-93-
-99-
-98-
-99-
-90-
-99-
-99-
-99-
-99-
-64-
-77-
-80-
-85-
-99-
-99-
-99-
-97-
-99-
-82
20
-38-
-44-
-61-
-69-
-85-
-98-
-99-
-99-
-99-
-95-
-99-
-99-
-99-
-13-
-85-
-70-
-72-
-79-
-94-
-89-
-94-
-82-
-99-
-29
15
-51-
-60-
-70-
-77-
-81-
-94-
-99-
-99-
-99-
-90-
-96-
-86-
-90-
-61-
-75-
-49-
-50-
-59-
-71-
-74-
-82-
-64
-1-
-40
10
-67-
-77-
-83-
-75-
-65-
-50-
-75-
-83-
-88-
-92-
-96-
-90-
-87-
-82-
-46-
-26-
-25-
-36-
-52-
-63-
â– 73
16-
-21-
-58
5
-64-
-64-
-77-
-68-
-78
47
99-
-99-
-99-
-99-
-99-
-99-
-93-
-96-
-86-
-99
99
0
0
0
0-
-38-
-58-
-55
0
-63-
-55-
-64-
-66-
-99
0
0-
-99-
-86-
-99-
-99-
-99-
-89-
-85-
-78-
-75-
-70
0
0
0-
-68-
-99-
-80-
-70
-5
-66-
-72-
-71-
-96-
-12
0
0
0-
-99-
-99-
-99-
-94-
-75-
-63-
-67-
-65-
-99
0
0
0-
-68-
-99-
-88-
-77
-P*

TABLE 37
Corrections Applied to the Pulk99 00
Right Ascension
dec\ra 0123456789
20 -91-25-99-99-99-66 18-99-94-99-
15 -38 15 1-15-34 -5 -4-72-55-92-
10 -49-36-29-48-48-32-39-50-32-81-
5 -78-52-34-46-84-62-99-99-82-97-
0 -84-70-20-26-75-67-60-78-99-91-
-5 -19-46-31-77-75-87-55-61-85-44-
Declination
dec\ra 0123456789
20 99 -4 99 81 76 20 99 93 65 25-
15 59 -8 27 18 24 8 16 2 5 5-
10 22-14 17 26 49 45 16-28-16-18
5 38 13 23 22 39 49 40 -1 0-11
0 22 8 8-13 -1 9 26 12 -4 6
-5 -28-46-12-35 -5 0 11 11-45-36-
11 12 13 14 15 16 17 18 19 20 21 22 23
99 99 99 7 28 2-39-33-72-80-68-95-70
2-19-23-68-37-12-43-31-60-69-82-85-66
-84-90-70-60-39-37-63-64-65-11-50-31-74
-94-99-71-40-27-52-79-70-67-17-65-61-99
-81-99-81-57-33-53-76-81-99-63-72-67-99
-1-54-37-45-40-68-83-81-99-69-60-52-84
11 12 13 14 15 16 17 18 19 20 21 22 23
-55-71-28 -3 26 74 47 70 23 79 28 99 69
-19 -3 17 41 37 63 24 24 -1 35 21 62 25
-14 4 7 19 3 19 16 -9-11-24 13 14 0
8 2-3 9 25 44 57 39 23 22 30 35 34
-5-19 -9 7 29 26 13 1 -6 12 2 23 19
-32-25-22-21-14-19-23-37-15 -4-21 -9-34
10
26
73
67
54
86
44
10
41
22
-4
16
8
38
â– sj
cn

TABLE 38
Corrections Applied to the Madn 10
Right Ascension
dec\ra 0123456789
35 78 83 0 0 84 84 84-99-99-99
30 -41-63 3 56-13-28-26-67-56-48-
25 -19-41-31-88-92-19 29 7 -1-88
20 2-21-14 37 70-35-99-99 3-71-
15 8-38-47-52-22-15 22-80-85-67-
10 -1 48-55-27-21 28 41-99-82-22-
5 -38-99 -8 44 18-59-11-38-82-29-
0 19 8 3-22-57-16 -2-68-29-49-
-5 -34-48-31-12-52-99-74-99-99-14-
Dec lination
dec\ra 0123456789
35 -94-99 0 0 99 99 99 97 97 97
30 28 10-34 99 53-20 19 58 48-97-
25 35 8 15 17-79 18-52-99-90 58
20 31 10 13 49 93 70 4 99 99 83-
15 39-17 -2 4-23 0 37 7-55-63
10 -19 63 61 7 51 34 12-40 50 8
5 35-40-35 8 8 71 94 48 99 52
0 65-14-18-27-34 19-30-77-33 34
-5 10 59 36 77 27 26 10 -1-99-99
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 0-44-44-87-99-50 51
-28-18-50 13-16-22 19-56-41 -6 6-34-34
55 44-44-41-66-66-34-79-40-15-17-15-15
-72-40-67 27-18-54-60-50-18-51-18-78-54
-19 19-71-41-16-14 25 0-59-36 1 11 14
-53-99-13-14-70 -7 14 23 -6-24 19-24-54
40-49-27-22-24 2-53-88-47 14 65-41 -1
0-27 -3-25-10-46-28 14-19-42-54 12 24
-66-43-48 -8 -9-33 11-28-72-32 6-64-70
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 0-34-34 94 99 99-24
58 7 -5-11-61 26 31 21 11-28 49 -6 12
15 10 22 33 50 63 5 5 14 27 20 7 24
24 -5 14 81 56 78 53-12 55 44-51 58 1
78 27 15 17 50 33-16 43 47 29 28 -2-13
15 96 0 -9 94 74 32 58 35 -4 39 45-21
-79 27 46 15 73 32 15 20 31 15 74 35 11
-9-28-26-32 -6 62 36 6 48 11 41 39 8
56 54 64 97 99 45 38 33 56 20 68-33-26
10
0
83
17
53
67
25
13
48
40
10
0
59
27
38
99
35
11
20
99
CT>

TABLE 39
Corrections Applied to the Berg 1-25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
75
-99-
-56-
-16
22
22
22
22-
-99-
-99-
-99-
-99-
-59
58
1-
-53-
-53-
-53
0
0
0-
-99-
-99-
-99-
-99
70
-87-
-92-
-58-
-37-
-36-
-36
10
1-
-34-
-50-
-58
0
11
8-
-47-
-47-
-46
-7-
-77-
-53-
-54
-6-
-37-
-33
65
-81-
-85-
-68-
-50-
-38-
-32
16
99
17-
-21-
-73-
-43-
-19
7
0-
-27-
-49-
-69-
-67-
-51-
-54
-7-
-23-
-37
60
-66-
-86-
-74-
-62-
-49-
-33-
-26
3-
-34-
-43-
-80-
-62-
-20
3
5-
-94-
-96-
-84-
-37-
-52-
-73-
-65-
-47-
-53
55
-91-
-95-
-83-
-61-
-49-
-50-
-81-
-53-
-69-
-54-
-92-
-87-
-60-
-49-
-83-
-99-
-94-
-71-
-40-
-52-
-56-
-55-
-38-
-49
50
-59-
-48-
-50-
-41-
-48-
-70-
-81-
-41-
-54-
-46-
-75-
-67-
-38-
-63-
-96-
-81-
-82-
-59-
-51-
-45-
-59-
-65-
-67-
-59
45
-23
-5-
-64-
-59-
-74-
-68-
-89-
-83-
-81-
-82-
-94-
-92-
-54-
-66-
-72-
-66-
-75-
-72-
-73-
-39-
-74-
-90-
-99-
-49
40
-57-
-62-
-92-
-80-
-70-
-65-
-90-
-99-
-99-
-99-
-99-
-99-
-75-
-90-
-99-
-99-
-79-
-74-
-78-
-50-
-91-
-94-
-99-
-34
35
-56-
-72-
-61-
-79-
-71-
-85-
-99-
-99-
-99-
-99-
-99-
-99-
-92-
-80-
-99-
-99-
-99-
-86-
-77-
-66-
-99-
-99-
-89-
-82
30
-51-
-61-
-55-
-80-
-99-
-66-
-72-
-99-
-99-
-97-
-96-
-92-
-67-
-10-
-33-
.44.
-98-
-86-
-74-
-79-
-61-
-92-
-37-
-89
25
-90-
-77-
-38-
-68-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-94-
-88-
-81-
-98-
-99-
-97-
-99-
-99-
-84-
-71-
-85-
-99-
-99
20
-90-
-69-
-64-
-82-
-79-
-82-
-99-
-99-
-99-
-99-
-99-
-99-
-92-
-84-
-92-
-84-
-99-
-72-
-98-
-50-
-69-
-69-
-94-
-75
15
-94-
-59-
-65-
-71-
-84-
-75-
-93-
-99-
-99-
-99-
-96-
-94-
-92-
-85-
-92-
-77-
-99-
-63-
-64-
-35-
-71-
-79-
-91-
-60
10
-80-
-52-
-52-
-84-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-87-
-99-
-99-
-99-
-99-
-86-
-68-
-46-
-33-
-62-
-86-
-83-
-75
5
-78-
-60-
-43-
-55-
-70-
-49-
-67-
-13-
-99-
-99-
-99-
-99-
-99-
-97-
-93-
-70-
-54-
-99-
-81-
-77-
-31-
-49-
-69-
-59
0
-88-
-57-
-89-
-68-
-77
18-
-63-
-99-
-99-
-99-
-77-
-68-
-90-
-57-
-84-
-63-
-83-
-99-
-93-
-77-
-58-
-92-
-99-
-64
-5
-93-
-37-
-24
34
14
99-
-99-
-99-
-99-
-34-
-99-
-94-
-98-
-61-
-75-
-77-
-81-
-84-
-77-
-87-
-99-
-99-
-99-
-87

TABLE 39 CONTINUED
Declination
dec\ra 0123456789
75 -99-99-66 61 61 61 61-35-35-41-
70 -52-53-61-11 0 0 60 55 50 37-
65 -30-44-65-95-28 -2 28 85 42 48-
60 -9-22 27-37 2-11 24-27-34-28-
55 -28-55 -6-57 2-16-43-67 19 17
50 -2-20 -3-28 22 -5-78-99 -1 23-
45 72 79 99 99 99 57 3 64 18 26
40 74 28 62 64 99 98 53 34 24 32
35 4-66 14 38 19-24-40-15-12
30 -29 77 62 94 31 -2-11 12 52 27
25 -1 19 50 70 17-37 20 -5 70 50
20 20 -7 8 43 48 27 58 -8 22 -4-
15 47 56 51 64 42 60 85 62 51 41
10 4 13 18 26-46-33-87 -8 -9 5-
5 -5-18-16 17 31 87-71-78-45-69-
0 13 11-52-75-82 99 74 -7-10 17
-5 -57 -9 13 90 99-99-40-40-18 15-
11
12
13
14
15
16
17
18
19
20
21
22
23
-99-
-99-
â– 70
46
46
46
0
0
0-
-99-
-99-
-99-
-99
-76-
-97-
-48
38
27
37
75-
â– 16
-6-
-15
39
-8
9
-13-
-40-
-21
-3-
-13
9
24
28
6
0
57
23
32
11
36
11-
-13
17
30
9
48
-4
29
16
39
10
28
85
23-
-14
27
58
29
34
7
31-
-19
-1-
-44
-11
27
24
56
29
45
29
7
3
2-
-42-
-10
9
18
32
68
81
32
40
49
-4
0
-8-
-17
21
61
61
82
98
36
9
53
71
81
34
43
47
99
80
65
57
64
25
19
52
40
38
13
34
48
10
26
39
35
99
2-
-36
45
65
37
31-
-19
61-
-76
44
38
26
73
28
31
38
44
36
22-
-27-
-14
-9
61
30
5
35
23
44
44-
-24
3
30
43
35
55
78
66
44
40
48
68
86
39
23
59
67
69
75
66
27
26
30
59
99
99
99
91
99
81
91
32
-3
-14
-9
-6
-8
15
99
60
11
24
30
28
-9-
-12
-16-
-22
13
3-
-30-
-34-
-85-
-52
-3
25-
-17-
-14
6
-32-
-35
56
36
31-
-29-
-43-
-21
-1
13-
-42
-7
6
10
61
11
10
20
-4
27
-5
28
8
12
35
12
22
26
42
-6
99
^*4
00

TABLE 40
Corrections Applied to the ABB-6 00
Right i
Ascension
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
0
-58-70-99-99-
99-
99-
99-
97-
92-
-63-
82-
99-
94-99-
99-
99-
-99-
86-
-80-
99-
99-99-
-99-
80
-5
-99-82-99-99-
99-
99-
99-
99-
99-
-99-
70-
99-
99-99-
85-
83-
-99-
93-
-73-
99-
•98-89-
-99-
99
Declination
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
0
5-58-15-64
22
74
15
12
2
-5
9
58
91 80
84
75
85
86
84
99
0 51
32-
53
-5
7-17 9-27
34
50
27
12
28
2-
17
23
27 1
11
38
59
76
31
80
18 48
83
0
TABLE
: 41
Corrections
Applied to the
Buch 50
Right .
Ascension
dec\ra
0 12 3
4
5
6
7
8
9
10
li
12 13
14
15
16
17
18
19
20 21
22
23
15
-38 8-15-42
9-
â– 77-
â– 66
18
32
35
29
41-
17-36-
•19
40
25
3'
-11
12-
•40-30
31-
•25
10
-5 14 11 13
11
22
18
24
9
16
22
12
25 7
16
26
15
18
12
15
24 15
35
15
5
10 11 6 9
12
5
7
29
25
11
19
14
24 17
28
29
5
13
10
28
11 26
17
2
0
8 -1 -7 -7
5
0
2
9-
â– 15
11
25
5
16 3
10
14
4
8
9
14
3 5
13
13
-5
1 4 9-21
-7
9
11
20
18
2
15
4
13 8
5
4
-2
-7'
-20
17
1-12
-5
3
Declination
dec\ra
0 12 3
4
5
6
7
8
9
10
11
12 13
14
15
16
17
18
19
20 21
22
23
15
-99-57 53 20-
-17-
â– 14
66
24
23
99
50-
â– 29-
â– 41-17
12
6
-11-
â– 12
29
1-
â– 52-99
-13
58
10
-13-20-16-17
-5
-6
-8
14-
â– 14'
-10
-8
21
5 -9
-9-
â– 11
6
-9
-32-
â– 19
13 0
7
10
5
-9-17-20 9
2
-9-
•16
-9
-7'
-13-
â– 12
-3
4-10-
â– 17
-8
-11
-2
-22-
-21-
-27-45
-34
-3
0
-2-15-15 1-
-10-
-28-
-26-
-14-
•19'
-13
-8-
â– 23-
•17-12-
-30-
â– 17
-20
-5
-11
5
-1-17
12-
â– 11
-5
-21 -4-23 -6-
â– 12
0
-4
6
19
6
-6
-9
15 2
5
10
7-
â– 22
10
20
11 -9
-11-
â– 32
LD

TABLE 42
Corrections Applied to the Bonn09 00
Right Ascension
dec\ra 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
55
7
8
0-
â– 99-
â– 99
51
79
99-
-22-
•34-
â– 99-
-99-
-66-
-46-
-99-
â– 99-
-99-
-99-
â– 90-
-95-
-99-
-76-
•30
-1
50
-28-
29
-2-
â– 50-
-50-
-99-
-99-
-73-
-80-
-22-
•54-
-98-
-62-
-92-
-99-
-99-
-99-
-99-
-67-
-36-
-85-
-85-
-88-
-80
45
-37-
72-
-69-
-72-
-26-
-99-
-97-
-90-
-97-
-42-
-57-
-66-
-72-
-88-
-76-
-74-
-99-
-62-
-95-
-48-
-81-
-99-
-87-
â– 99
40
-12-
71-
•78-
-90-
-45-
-99-
-59-
-28-
-99-
-49-
-84-
-59-
-68-
â– 75-
-58-
-53-
-91-
-51-
-96-
-31-
-37-
-73-
-38-
-79
35
7-
73-
-85-
-89-
-59-
-79-
-75-
-25-
-99-
-39-
-99-
-53-
-65-
-76-
-71-
â– 73-
-94-
-58-
-70
35
58
37
45
12
30
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
0
0-
-27-
-27-
-27-
-27-
-27
0
0
0
0
25
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Decli
mation
dec\ra 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
60
10
10
10
10
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
-31
-9
-2
-5-
-15-
-10-
-43-
-30-
-90-
-48-
-67-
-44
2
-7-
-15
-7
20
90
62-
-12-
-99-
-99-
-69
32
50
15
3
-4
-1
4
31
28
37-
-20
1-
-15
9
30
13
12
30
-6
5-
-11-
-30-
-60-
-12
15
49
45
48
21
18
0
-6
6
21
42
-1
2
-4
21
19
14
18
39
6
16
14
22
22
60
45
41
40
15
-5
17
15
10
6
6
34
-1
11
-5
27
11
51
28
41
14
41
39
17-
-21
27
3
13
35
-38-
•34
15
50
65
54
38
38
18
36
24
62
45
99
68
51
-6
-6
21-
-41-
-99-
-83-
-95-
-38
30
0
0
0
0
63
63
63
63
63
0
0
0
0
0
0-
-99-
-99-
-99-
-99-
-99
0
0
0
0
25
0
0
0
0
63
63
63
63
63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
TABLE 43
Corrections Applied to the ABB+20 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
30 -48-85-99-30-99-99-72-18-13-67-99-99-99-99-99-99-99-75-99-84-99-99-99-99
25 -66-65-64-87-92-92-98-99-99-99-99-99-99-91-99-99-99-87-74-70-98-86-86-93
20 -53-55-52-83-99-99-99-99-99-99-92-99-99-99-99-99-99-80-65-76-81-82-83-71
15 -99-99-99-96-99-99-99-99-99-99-99-94-99-99-99-99-99-99-99-74-28-39-45-98
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
30 51 12-16 22 39 75-40-86 49 44 59-70-99-64-99-59-25 8 37 47 79 99 67 50
25 11 5 -8 23 13 7 -6-21 -2 9 11-15-11 1 24 7 19 16 8-9-8 2 0 20
20 27 21 13 23 37 23 15 19 11 32 31 11 30 24 34 21 35 42 28 39 46 19 19 46
15 36 14 43 45 77 10 -6 37 20 55 35-17 38 35 55 68 68 70 21 23 56 74 54 71

TABLE 44
Corrections Applied to the ABBO 00
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 -76-99-89-46-99-99-35-99-99-99-72-35-71-99-99 5-81-99-84 50-61-99-99-99
5 -53-78-99-80-99-99-98-99-99-99-99-99-99-99-99-99-99-99-96-91-75-86-99-83
0 -71-58-67-85-99-99-99-99-78-94-99-99-99-99-99-93-77-98-99-99-98-99-99-98
-5 -99-99-98-85-92-99-99-99-92-99-99-99-99-73-99-99-70-84-99-99-99-99-97-93
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
10 99 99 -5 75 99 99 99 99-26 99 99 96 99 99 99 99 99 99 99 99 99 99 99 99
5 -5 -6-39-36-30 -9-40 1-36-15-57-28-24-21-54-23 -4 4 -4 -6-22-33 9-21
0 25 19 8-20-22 -2-18 -1-26 -4 7 0-9 25 27 28 3 14 34 24 30 30 19 -1
-5 -11-67-66-72-29-38-60-11-15-24-33-10-21-17-35 6-17-32-11 -8-15 -4 14 1

TABLE 45
Corrections Applied to the Lund44 50
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 -46-22 77 24 -7-47-60 111 0-98-98-98 0000000000
45 -13-52-23 4-99 16 12-88 36-65-73-21 66 99-60-99-99-99-99-99 57 99 73 24
40 -1-17-42 15-47 13-21 18 -5-57 49-26-24-29-15 -1 99-20-17 26 3-36-48-34
35 -23-10 -8-20-20-13-40-18-17-17 -8-26 -8-44-39 88-77 14-14-29-20 -8 -8-24
30 -7-12 6 -4-11 -3-22 20-10-40-29 0-45 -3-13 -6 4 -6 13 1 7-10 5 -1
25 -36 6 10-17-10 20-14-32-21 10 -7 15-19-52 14 86 62 43 8 20-14 -1 6-14
20 -55 -1-71-15-24-10 28-38-30-46-39-11 17-68-56 30-50-14 25-18-20-32 -2-21
15 -76-87 15-30-67 -9 58 -9-53-44-83 -1-99-99 1 10 3-2 1-7 53 46 -4-25
10 39-60 16-64-57-35-99-98 19-35-30-41-13 40 31-63-96-14-19 21-26 44 59 99
5 99-99-92-41-92-43-36-14-13-66 -2 -9-52-34-24 14 36 51-77-77 9 14 5 99
0 -43-99-97 37-34 54 25-99 80 29 -7 28-52-99-99-88 99-40-50-62-71-99-50 30
-5 -99-99 0 0 0 0 0 17 17-37-54-31 99-41-99-99 0-87-28 18-69-28 21-80
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 -99-99-72 99 99 99-99-99-99-99 0-99-99-99 0000000000
45 -18 25 43-18-54-62 29-62-47 65-55-42-39 88 99 71 99 99-99-99-82 35 85 31
40 -41 75 38 22-26 -2 5 46 16 37 84 -8 41 30 -2 18 5-52 2 4 61 -4 9-4
35 -32-20-20-12-37-25 -3-26 20 24-16-10-29-20-61 69-30-76-11-20-21-24 -6-46
30 -7-42 24-15 -264 -5-36 16 4-36 -8-44 21 -6 18 21 9-30 -4 -6 -8-15
25 -64-74 -4-52-36-89-66 17-44-39-14-34-30-59-30 70-37 5-32-72 6 2-15-13
20 22 3 53 33 -2-20 19-32 -4-50-48-16 5-45-31-12-21 26-10-28-11 35-29-29
15 -41-52 30-53 22-74 94 85 29 16 41 39 34 31 17 24 55 35-49-28 8 -1-49-20
10 99 99 21 0 -7-39-17 -2 0 20-23 -6 99 18 9 26 4-22 35 21-78 49-95-89
5 21-97 34 70 41 20 34-11 14 11 51 26 43-53 -1 52 71-99-74 75 21 73 27 -2
0 15-26-73-92 33 22 89 27-27 36 40-63-99-99-28 25 88 22 19 7 5 4 13 47
-5 -99-86 0000 0-99-99-87-67-85-99-99-12 30 0-99-74 4 26 29 66-99
oo
ro

TABLE 46
Corrections Applied to the Stras 30
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
90
0
0-
-12-
-16-
-22
7
38
0
0
0
0
0
0
0
0
18
18
18
0
0
0
0
0
85
25
12
47
6
8
7
38
-8
-8
-7
23-
-13-
-20-
-20
0
15
15
19
39
16
32
6
15
80
28
12
39
24
20
35
52
6
3-
-30-
-27-
-43
-6
19
20
13
-1
-4
11-
-24
17
47
35
75
55
66
30-
-14
7
51
35
10
46
31
14
3
15
4
19
-9-
-15
-1
56
86
90
51
22
70
70
65
-2
5
27
2
-3
10
40
-6
24
58
15-
-11
46
24
10
5
30
12
39
29
51
65
57
81
44
17
25
67
52
-1
51
41
42
22
16
29
35
24
-2
29-
-27
12
62
45-
-10-
60
41
-9-
-53-
-59-
-64
-4
99
99
26
52-
-23-
-50-
-55-
-82-
-99-
-14
5
35
34
68
23
1
74
55
67
30
5-
-21-
•17
1
-7
-8
-5
-9-
-37-
-65-
-24-
-14-
-84-
-46-
-55
51
46
-9
21
57-
-10
50
6-
-37-
-38
20
35
35-
-13-
-59-
-17
22-
-18-
â– 33
49
19-
-15
22
1
35
39-
-34-
â– 52
-5-
â– 10
45
26
41-
-70-
â– 52
13
27
-1
8
24
35
35
95
24-
â– 79-
-31
0
25
-5
0
0
0
99
4
40
55
18-
-99-
â– 68
14
14
2
21
35
20
32
15
56
57-
-17
28
99-
-75
8
50
39
15
15
35
51
25
-4
-2
41
5
-4
32-
-11-
-13
10
8-
-10-
â– 35
-2
9-
-21
25
14-
-20-
•21
46
-8
30
-9
33
63
50
70
76
37
11
4
9
30
70
20
8
-2
-7-
â– 24
14
17
31
37
84
39
25
â– 10
23
27
2
-3
45
3-
â– 70
55
60
23
83
62
-4
37
21
-7-
-11-
-12
12
49
55
-9
20
65
39
11
55
66
28
32-
-36-
-23-
-40-
-61
-3-
-34-
-37
-2
12-
-41
42
27
50
5-
-17-
-26
15
5
93
17-
-35-
-12-
-14-
-16-
-28-
-27
31
55
40
-9
5
13
6-
-52-
-48
37
53
32
99
99
10
0
-5
54-
-12-
â– 51
43-
â– 30
-2
-1
-2
14-
-14-
-20
12
13
42
22
80
99-
-24
2
9-
-19
5
19
40
21
8
5
13
8
2
-3-
-34
8
64-
-47
4
17
0-
-35
34
6-
-14
23-
-13
26
0
60-
-43-
-39
13
18
70
16-
-37-
-15
15-
-19-
-21
4-
-15-
-30
5-
-12
9
40
21
10
11
20-
-5
13
15
1-
-14-
-11
5
35
30
12
41
51
53
59
7
31
-7
20-
-13-
-15-
-20
3
16
7
23
0
23
27
27
18
10
99
39
0
-4
62
-2
55
24
11
99
-8
-7
12
16

TABLE 46 CONTINUED
Declination
dec\ra 0123456789 10 11
90 0 0 31 24 -1 -2 22 0 0 0 0 0
85 13 -2 37 13 -5 -2 22 2 2 32 85 34-
80 -52 -2 46 25-51-80-59 41 38 5-44-54
75 -53-58-16 99 57-31-46-31-75-60-69-99-
70 -74-47 9 -4-14 -8-56 51 43-48-67-34
65 -2-40 78 85 38 14 32 44 17 60-21-70-
60 3-97-99-99 86 84 37 -9-42-55-31 23
55 8 45 17 0 28 10 53 -5-14-16-57-72-
50 -27 7 -1 57 39 -5 53-88 -9 15 -7 -6-
45 53 88-21-26-21 -1 7 58 38 -7 -7-99-
40 -52-24 32-23 5 35 59-11-50-17-25-92-
35 -46-38 89 99 26-18 -5-99-66-48-63-62-
30 3-11-11 14 9 18 75 33-14 12-47-20
25 -19 -5-26 12 27-12 10 25 -7 22 38-70-
20 -60-78-38 73-99-96-99-88-99-79-81-47-
15 5 39 14-54-66 99 99-13-86-84-62-33-
10 53 13 1 99 25 24 50 18 30 2 7-27-
5 -13 16 37-51 34 7-24 16 2-32-31 -8
0 32-31 -2 2-66 8 52 6-66-86-38-83-
-5 -52-41-26 -2 37-20-28-38 -3 45-69-99-
13 14 15 16 17 18 19 20 21 22 23
00111000000
-84 0-41-41-40-55-50-68-44 44 40
99-29-99-86 5-21-13-21-39-48-54
-66-37 5 14 23-86-99-26-77-96-54
-99-99-99-38-48-84-91-45-40 1-29
-88-29 28-19-99-31 36 46 97 65 27
99 -3-70-87-99-99-31 16 53-78-99
-12-85 27 9-46-11 -1 -6 4 53 14
-52-45-13 99 99 62 89 95 23 23 9
-3 26-33-99 99 0 0 0 15 -1 10
-58-31-56-99 99 43-99-99-99-99-61
-64 1-45-26 65 46-32-58 80 74 16
-28-55 25-16-29 -2 70 6-86-32 -1
-33-53-38 20-70 31 4-99 9 36-18
-93-54-84 46-99-99-87-99-99-93-52
67-68-99 11 30-83-41-19-99-24-49
-55 25 7-10-41-41 47-63-56 12-49
33 55 -5 1 74 37-99-21 22-34 19
-7 1 61-77-99-19-37 49-14 -8 52
-32-95-18 12 30 99 25 -6 49 69-45
oo
12
0
84
52
23
59
51
70
21
13
92
96
53
0
99
99
49
56
1
82
71

TABLE 47
Corrections Applied to the Cin 00
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
80
0
0
0
0
99
79
79
7
49
73
75
35
-8-
-24-
-67
30
-8
25-
-35-
-14
11-
70
-38-
-21-
-49-
-64-
-24-
-24
21-
-47-
-28-
-22-
65
-98-
-73-
-78-
-24
27
23-
-27-
-77-
-48-
-13-
60
-99-
-99-
-90-
-41
53
9-
-39-
-14
0-
-34-
55
-71-
-99-
-99-
-97-
-40-
-91-
-99-
-66-
-37-
-99-
50
-95-
-11-
-97-
-99-
-99-
-81-
-99-
-99-
-82-
-99-
45
-99-
-85-
-99-
-99-
-99-
-99-
-77-
-54-
-41-
-99-
40
-99-
-99-
-83-
-49
3-
-47-
-67-
-86-
-78-
-99-
35
-83-
-46-
-80-
-71-
-68-
-52-
-99-
-58-
-99-
-72-
30
-61-
-35-
-99-
-58-
-51-
-25-
-88-
-93-
-92
9
25
-99-
-30-
-98-
-71-
-65-
-70-
-99-
-99-
-99-
-99-
20
-87-
-44-
-41-
-59-
-99-
-99-
-99-
-97-
-95-
-99-
15
-99-
-67-
-99-
-66-
-82-
-99-
-99-
-99-
-99-
-99-
10
-98-
-47-
-99-
-72-
-76-
-74-
-79-
-99-
-99-
-99-
5
-99-
-99-
-82-
-59-
-82-
-80-
-99-
-99-
-99-
-98-
0
-99-
-90-
-93-
-99-
-99-
-99-
-99-
-99-
-99-
-55-
-5
-99-
-55-
-63-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
11 12 13 14 15 16 17 18 19 20 21 22 23
-3-99-99-99 76 76 76 76 76 0 0 0 0
-11-19 33 9 99 25 41-99-99-99-91-11-17
-8 -5-15-78 3-38 -7-73 2 -9 9-63-48
-33-99-99-98-57-99-99-99-65-56-40-54-42
-61-45-99-78-99-99-99-83-49-20-42-69-99
-99-28-31 41-88-99-74-19 53 18 18-25 -6
-99 -3-78-60-99-99-99-99-99-99-99-99-74
-99-64-99-99-99-99-99-42-51-88-99-99-99
-95-99-99-82-84-72-92-69 21 -3-65-58-76
-59-47-84-48-39-61-97-99-49-34-25-99-90
-82-59-99-86-99-90-92-83-67-92-49-99 8
-99-99-99-90-99-99-99-99-99-99-26-99-79
-99-99-63-71-75-99-34-87-71-92-60-74-99
-99-99-99-99-99-99-61-99-74-99-99-99-99
-77-99-99-99-99-99-99-63-77-99-99-97-85
-89-99-99-99-99-99-99-80-99-99-73-29-67
-99-99-99-99-91-39-85-64-99-99-99-99-75
-95-96-94-99-94-89-99-99-64-59-99-99-99
10
18
46
60
13
32
93
97
99
65
43
-9
79
99
99
99
99
90
99
00
cn

TABLE 47 CONTINUED
Declination
dec\ra 0123456789
80 0000 0-37-37 59 99 99
75 -99-83 42 89 99 99 95 57 99 74
70 -69-27 11 31-15 15-29 28 73 66
65 64 37-36-19-99-23-78 26 63 67
60 9 26-69 -1-99 16-20 2 44 32
55 11 0-51-86 4-92-55-61 17-17
50 -17-99 -9-12 99-99 -7 4 42-41
45 -27 0-64-55-82 99 82 99 -7 12-
40 -15 92-19 28-99 76 9 88-23 59
35 -1-13 36 77 59 -1-23 -9 55 60
30 33 3 66 78 99 87 99 46 20 7
25 50-11 50 88 51 1 83 53 5 40
20 78 97 54 99 95 90 31 15 51 78
15 80 99 51 66 79 63 37 -7 10-26
10 41 4-12-37 -5-21 25 22 10-25-
5 -36 7 -1 52 6-53-29 4 10-15
0 -27 43 -9 97 29-39 -9 50 85 0
-5 -53-32-99 55 99 68 59 18 13-63-
11 12 13 14 15 16 17 18 19 20 21 22 23
-99 43 39 99-83-83-83-83-83 0000
-54 99 34 99-99 44 81 99 76 99-99-99-99
11 99-64 50-62 14 26 14-37-53-76-79-70
47-17-38 59 47 65 44-27 44 4 86 99 98
20-69-33 -4 1 5 90 27 99-20-14-99 32
-54-68-15 99 29-28-32-99 11-99-86-78-38
-3 42 5 97 6 88-17-53-93-84 0 71-21
-48-77-92-57-99-10-29 53 7 24 21 54 -8
-24-30 61 73 12 21 -4 -6-55-28 -2 99 69
23-61 49-17 79 -5 11 4 16-73-69 18 34
48 25 50 14 62 9 72 21 29-48-43 26 44
54 61 30 9 39 59 21-55-14 38 5 88 78
65 41 7-14 81 44 52 9 71 99 75 51 96
18 35 68 16 99 42 84 8 9-12 32 20 54
17 29 86 44 48-26-24 15 70 61 21 10-32
-5 1-62 2 39 65-36 52 19 47 2-16-52
-15 -2-25 -9-33 41-47 30-29 8 33 20 33
-33-49 20 22 29 44 45 62 8 17 17 15 30
10
1
23
60
72
37
-1
2
18
22
6
46
32
85
17
52
-2
14
68

TABLE 48
Corrections Applied to the PFKSZ
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
41
10
24
19
31
20
9
4
3
4
-8-
-12-
-29
15
44
60
54
55
40
34
15-
â– 33
-2
1
85
32
5
6
-6
-9-
-26-
-26-
-17
-2
-1-
-11-
-18-
-18
0
25
20
22
3
-8-
-24-
-16-
â– 13
22
8
80
4
16
5-
-12
-9-
-28
12
7
38
20
4
5
-4
-5
12-
-14-
-19-
-32-
14-
-24-
-12
16
6
27
75
8
25
2
11
30
15
58
36
19
2-
-12
13-
â– 11
-7
7
19
19
2
8
6
-1
11-
-15
33
70
30
31
5
16
28
37
38
29
18
15
1
18-
-13-
â– 10
-5
10
-1
4
-5
17
-3
0
-5
16
65
4
7
3
17
16
15
18
43
48
59
34
28
3
-2
11
-4-
â– 14
-9-
26
-4-
-18
10
16
6
60
29
12
9
24
18
29
16
48
27
25
20
26
19
-8
1-
-24-
â– 11
0
-4
10-
â– 12
7
14
26
55
24
20
8
24
7
5
7
8
9-
â– 18
4
-8
4-
â– 12
19-
â– 14
-5-
â– 18
0-
-15
-5
8
2
14
50
-19
-4-
•13
ii-
â– 17
9
21
2
11
-7
16
24
-2
1
12
0
-9
-1
6
1
-1
-5-
â– 12
-7
45
-13
12
2
ss
-8
22-
-15-
-18
-1
7
12
25-
-23-
-15-
â– 24
2-
â– 25
5
-6
10
-9
-4
0
11
40
7
10
4
8
-9
4
5
13
14
3
6
8
3
8
-4
3
-5
-5
-1
-6
15
9
5
14
35
9-
â– 12
11
7
11
-3
7
10
13
-3
8
-2-
â– 11
-9
-5
-9-
â– 11-
â– 39
-9
0
46
-2-
â– 10
-1
30
31
4
2
7
4
1-
-11-
-10
16
5
26
22
-3-
-16-
-20-
â– 16
-5-
•21
1
10
16-
-17
-2
2
25
39
21
4
-9-
â– 18
6
12
-1
18
-6
25
29
11-
-16-
-23-
â– 20
-9
-8
9
15
24-
-12
11
2
20
-2
11
9
7-
â– 24
0
-3
-3
14
5
13
-2-
-19-
â– 23
-6
10
-8
2
5
17
7
-5
-9-
â– 18
15
14
22
0
32-
â– 21
-6-
-42-
â– 11
38
13
35
-1
-7-
â– 17
10
27
3
17
3
19-
â– 10
-2
-7
19
10
6
22
6
32-
-11-
-42-
•16
6
38-
â– 22
27
9
10-
â– 13
8
-4
4
-7
-2
5-
â– 22
-1
-4
21
5
-12
0
10-
â– 10
2-
-13
4-
-10-
-15-
-28-
-13
5
-3-
â– 11
17
13
11-
-13-
11
3
-5
29
6
-6
0
7
0
20-
â– 19
-5-
-19
6-
-33-
-15
7
12
10-
-13-
-21-
-11
8
-6-
•16
-7
27
9
22
-2-
-20
-5
-16-
â– 20
-1-
•14
15
3
31-
-39-
-13
2
13
4-
â– 20-
-15-
-17
6
0
0
17
10-
-72-
-63-
-37-
-46
oo

TABLE 48 CONTINUED
iec\ra
0
1
2
3 4
5
6
90
-38-
â– 20
18
60 79
-2-
â– 67
85
0
21
24
19 1-
•36-
â– 55
80
-3
-4-
•23-
â– 18-43-
â– 18
13
75
-70-
â– 45-
•21
22 -9-
â– 14
8
70
-46-
â– 14
-1
22 16
11
33
65
-15
11
-8
-8-23
9
45
60
-14
10
6
39-20
6
-1
55
-35-
â– 11
1
25 -9-
10-
â– 14
50
-16
3
5-
•26-25
-2
18
45
-14
27
40
1-41
28
' 8
40
6
18
15-
â– 24-50-
12-
20
35
29
-6
12-
•11 26
4
12
30
4
-5
8
-8 18
1
-6
25
8
13
6
-9-11
4
15
20
-11
-4
-4
5 26
0
3
15
-5
2-
13
-5 5
18
24
10
11
3
1
-4 9
73
43
5
-12
9
29
2 -7
-1-
34
0
-2
17
17
9 9
17-
10
-5
-27-
22-
â– 13
8 37
35
19
8 9
-27 -7
-17 -8
-9-27-
-16 -6
23 21
25 23
14 34
-6 0
10 0
-15-26
1 4
11 10
•12 -4
-5-21-
8 10
16-12
58 19
-12 18
-38 -2-
14 49
10 11 12
8 5 5-
2-17 0-
11-24-15
12 2-54
35 39 11
19 16 -9-
51 19-33-
3 11 -6
-4 16 7
10 3 10
17-15-16
18 9 9
24 10
5 2
12-18
15 14 -5
30 6 -4
-8 18 20
18 -7 5-
23-21-71-
7
19
1
13 14
â– 40-18-
â– 14 13-
3 22-
18 11
-3-17
•24-17
â– 16 -5
0 8-
0 1-
14 12-
-1 13-
-9 6
6 20
12 48
5 18-
5 -2
63 30
39 19
36 -7
99-30
1-
-8
2-
15 16 17
15 28 7
25 23
28-12 -1
16-17 2
21-17
32 -3
15 21 27
13 27 25
24 54 50
24-23 3
17-24-21
13 24 3
17 -2-37
-8-14-27
10 14 -3
6 35 8
32-11 6
4-21 5
-4 8 3
18 19
14 -3
13-49
-9-33
3-15
-6-31
-15 -6'
20 14
29 5
31 35
-2 8
â– 15 4
â– 17 -1'
•29 -9
13 5
20 -3
20
12
6
2
6
-1
18 45 25
18 24
1 11
20 21
-12-50-
-30-27
-12-21
7 -8-
1 14
-24-12-
4 5
12-13-
11-29
-1-21
2 4
-24-20
-5 3
14 4
10-23-
32 0-
-7 -9
1-13
37 20
6 13-
22 23
64-68
22-18
36 27
19
14
15
12
-6
-9
-7
9
24-20
-9-31
25-22
11 2
-4-18
-2 -7
12 0
23-25
18 12
-9 21
-4-14
6 21
22 6
ex»
CXI

TABLE 49
Corrections Applied to the Lund42 50
Right Ascens
dec\ra 0 1
75
-46-10
70
-21-24
65
-3-16
60
-15 -8
55
-26-22
50
-64-37
45
-53 29
40
-44 6
35
17 53
30
-2 33
25
-42-41
20
25-76
15
-11-96
10
-62-96
5
-76 0
0
0 0
-5
0 0
ion
2 3
16 37
3 12
-6 -5
-23 4
-53-27-
-51-71-
35 12
-13-87-
99-76-
87 19
6 41
-13 99
0 99
0 99
0 99
0-99-
0-99-
4 5
37 37
28 13
7-11
4 28
â– 43 -8-
â– 88-85-
14 6
•44-58-
â– 84-99-
3-73-
63-26-
99 79-
91 67-
99 90-
72-10-
85-86-
99-99-
6 7
0 0
0 0
0 0
99 99
11 99
91 99
13-51
10-51
99-99
61-60
21-32
81-99-
61-93-
17-87-
60-99-
27 -7
99-66
8 9
0 0
0-99-
0-31-
0 51
0 63
0 29
0 29-
0 80-
o go-
99 99
-3-13
98-46-
85-13
42-17
59-59-
99 48
99 98
10 11
0 0
•99-99-
•31-31-
51 51
63 63
29 29
â– 20-20-
58-58-
14-14-
69 69
-5 1
33-33-
25 33
3-24-
37-99-
37-99-
94-99-
12 13
0 0
â– 99-99
â– 31-31
51 51
63 63
29 29
•25-25-
69-69-
â– 46-46-
53 53-
3 3
33-33
48 38
â– 24-74
99-99
99-99
99-99
14 15
0 0
0
0
0
0
0
70
70
70
70
0
0
0
0
0
0
0
16 17
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0-67'
0-67
0-67
0 99
0-45-
0-85
0-92-
0-99-
0-99'
0-88-
0-88-
18 19
0 24
0 -6-
0 57
0 87
0 -6-
0 55
67 47
-6 13
2-19
10 21-
46-26-
-1-14
65-46
91-55
57-27
78-46
88-88-
20 21
24 24
40-27
7 35
39 62
19 0
-5 1
25 25
33 20
7-51'
45 8'
14 37
58 21
13 36
22 37
39 10
4 35
88-88
22 23
17 1
•69
0
2
68
26 51
-6 17
•54-28
â– 31-27
•43-46
â– 55-39
â– 10 26
28 61
66 22
33 9
27 11
6-22
59 56
0 0

TABLE 49 CONTINUED
Declination
dec\ra 0123456789
75 99 99 99 99 99 99 0 0 0 0
70 99 99 26 94 91 99 0 0 0-46-
65 66-20-88-99-99-71 0 0 0-25-
60 3-66 7 1 47 62 99 99 0 -3
55 46-36-42-21 32 99 99 99 0 -8
50 92 45-85-99-34 32 99 99 0-29-
45 2-12 99 81 59 5 13-48 0-29
40 -45-99-99-31 3-21-10-48 0 99
35 61-74-99-41-94 4 -7 71 0 81
30 79 99 53 11-51 37 35 99 91 7-
25 -84 99 99 99 8-18 6 57 74-21-
20 -75 99 99 88 39 11 48 43 25 4
15 91 99 0-99-52-42 6 23 29 15
10 -99 99-99 27 -2 99 33 28 41 42
5 -99 0-99-27-99 99-50 11-18 33
0 0 0-99-31-99 22-43 99 94 88
-5 0 0 0 99 99 99 99 99 99 99
11
12
13
14
15
16
17
18
19
20
21
22
23
0
0
0
0
0
0
0
0
99
99
99
99
99
-46-
-46-
-46
0
0
0
0
0-
-99-
-63-
-71
48
57
-25-
-25-
-25
0
0
0
0
0-
-99-
-99-
-99
3-
-23
-3
-3
-3
0
0
0
0
0-
-99
38
7
86-
-19
-8
-8
-8
0
0
0
0
0-
-99-
-93-
-44
23
73
-29-
-29-
-29
0
0
0
0
0-
-50-
-99-
-86-
-90
58
8
8
8
4
0
0
99
99
44
19
17
-5-
-17
43
16
16
4
0
0
99
98
23-
-53-
-78
13-
-13
88
51
51
4
0
0
99
85
54-
-51-
-94-
-57
99
-24-
-21-
-21
4
0
0
99
99
99
99
58-
-34
32
-99-
-99-
•99
0
0
0-
â– 33-
-38-
-23-
-20
6-
-60
11
-20-
-27-
-27
0
0
0
99
74
87
22
85
53
99
35
47
50
0
0
0
99
99
99
36
33
37
67
-4
-4-
-99
0
0
0-
â– 99-
-78-
-52
5
5-
-24-
-45
74
74
99
0
0
0
49
99
99
99
66
66
35
-15-
-15-
-34
0
0
0
79
99
98
99
91
99
53
-31-
-31-
-99
0
0
0
18
18
18
18
18
0
0
10
0
46
25
-3
-8
29
8
43
88
24
96
-8
26
48
28
27
99

TABLE 50
Corrections Applied to the Cin 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
75
-99-
-99
99
99
99
0
0
0
0
0
70
-33-
-34
45
7-
-39-
-69-
-82
0
32
32
65
-46-
-56
9
30-
-22-
-49-
-48-
-14
45
22
60
-75-
-92-
â– 34
11-
-60-
-79-
-43-
-38-
-28-
-37-
55
-68-
-99-
-99-
-68-
-99-
-83-
-49-
-56-
-87-
-68-
50
-83-
-99-
-68-
-35-
-88-
-68-
-66-
-12-
•32
20-
45
-44-
-88-
-21-
-97-
-79-
-99-
-99-
-68-
-99-
-75-
40
-61-
-96-
-11-
-99-
-60-
-99-
-56-
-57-
-99-
-44-
35
-80-
-25
57
-7-
-21-
-21
40
24-
-50-
-62-
30
-99-
-99-
-99-
-99-
â– 56-
-67-
-21-
-79
-1-
-80-
25
-66-
-99-
-78-
-60-
-58-
-78-
-99-
-99-
-99-
-99-
20
-8
-3
99
98
7-
-84-
-99-
-62-
-99-
-80-
15
-35-
-53-
-47-
-56-
-63-
-65-
-99-
-76-
-51-
-77-
10
-86-
-99-
-99-
-99-
-99-
-92-
-95-
-99-
-84-
-99-
5
-63-
-89-
-40-
-64
90-
-24-
-99-
-99-
-99-
-99-
0
-43-
-99-
-57-
-46
34
8-
-99-
-99-
-99-
-99-
-5
-69-
-99-
-36-
â– 56
-6-
-33-
-74-
-99-
-99-
-99-
11 12 13 14 15 16 17 18 19 20 21 22 23
13 13 13 13 13 0 0 0-68-68-94-99-99
2 -3-21-67-99-99-99-99-91-62-58-46-40
-12-15-29-42-99-99-99-70-63-42-54-38-40
-99-65 6 26-20-84-88-37-31-99-91-87-56
-99-99-40-41-71-99 16-23-12-85-39-20 1
-61-96-99-99-99-99-40-22 -1-40-13 14-10
-73-99-99-75-65-23-99-99-99-99-99-48-40
-27-99-61-42-73-60-99-99-99-99-99-70-97
34 56 70-38-99-99-99-49-77-28 -6-44-50
-34-40 70-38-63-50-62 38 38 33-35-57-34
19-24 -9-83-99-78-71 2-10-48-30-56-80
-28-99-85-99-99-99-76-14-45-67-62-66-85
-99-99-99-71-53-46-14-42-27-51 -4-37-49
-99-99-91-37-26-99-99-99-76-61-13-62-54
-83-52-35-99-99-99-94-99-21 -7-35-75-99
-99-99-99-99-99 -1 48 51-41-99-99-83-99
-99-99-99-99 -9 22-15 20 45-50-63 31-75
10
0
11
14
52
99
72
99
99
99
80
99
99
40
97
99
99
62

TABLE 50 CONTINUED
Declination
dec\ra 0123456789
75 99 99 99 99 99 0 0 0 0 0
70 43-26 99 44-87-99-99 0 89 89
65 -17-42 94-50 -1-98 11 17 99 53
60 -13 58 47-65 99-10 99 4-19-43
55 46 64 32-13-26 20 56-15-59-24
50 -4-89-43 26-53-28-15-48-53 -9-
45 18 61 72 29-38-99-39-97 30 -2
40 61 25 76 13 8-77 10-46 99-13
35 6-64-41-57 51 5 52 -2-26-92
30 -48-14 32 30 35-85-21 33 98 49
25 -42-99 2 52 47 13-33 32-18 18-
20 31 2 53 99 99 77-21-27-52 33
15 90-31 70 52 99 6 55-26 99 79
10 11-99-14 -6 99-96-73-99-51-99
5 -39 44 81 99 99 58-13 -4-53-99
0 -55 0 -1 17 99 99 25-11 -8-99-
-5 13 6-22-62 48 68 99-99 99 99
11 12 13 14 15 16 17 18 19 20 21 22 23
-39-39-39-39-39 0 0 0-99-99 15 99 99
27 20 -6 -4 9 36 63 -6-66-99 -9 53 55
4 23 7 29 41 33 37-42-25-69 45 47 30
-24-15-57 10 28 20 52-12 33-47 28-30 38
99 45-51-93-62-60 94 5 43-61 72 81 99
34 99 52 28 28 -7 91 43 99 99 99 99 98
-5 22 20 51 39 83 84 -8 15 50 56 9-19
7 23 45 69-10 46 99 73 89 62 19-44-96
32 28-23 11-99 12-17-16 8 99 99 87 79
-16 1 1-8-4 34-52-94-99-45 57 9 43
1 35 99 87 6-19-61-68-99-93-14-10-57
56-48 14 12-32-49-42 16 66 44 99 60 -4
-67-39 15 49 99 99 99 61 62 5 38 31 7
-23 75 -5 28 3 41 50 62 68 1 28 6 -4
-23 62-80 -9 19 59 8 45 41 36 18 45 99
-99 10-13-28-44-13-71 -7-36-21-59-75-27
-1 9 21-69 86 91 99 4-26-99-99-99-27
10
0
62
49
4
10
35
26
89
12
38
41
-4
72
99
85
85
99

TABLE 51
Corrections Applied to the Moscow40 50
Right Ascension
dec\ra 0123456789
90 45 -4 40 36 99 99 73 49-32-99-
85 29 -2 -5-16 1-16 10 24 1-46-
80 46 23 -9-40-69-13 20 42 28-13
75 28 36 15-15-31 42 66 63 59 20
70 -5 43 9-11-31 1 14 -5 29 21
65 -47 2-24-25-27 33 46 37 76 65
60 7 42 8-12-26-20 41 59 70 80
55 -3 44 21 54-20-67 25 18-47-40-
50 -51-11 11 21-10-32 12 61 -5-80-
45 -10 3 19-20-81-99-86 13-14 1
40 17 22 54-17-50-28-37 48 22 30
35 -43-11 14 33 19-13-63-11 33-30-
30 18-19-40-60-48-26 -6 0 15-13
25 97 84-18-60-92 5-12 20 18 1-
20 31 38 -1 28 12 99-44 23-24 70-
15 10 3 4-15-54 8-99 0-85 65
10 16 29 40 46 -4 67-42 45-99-55-
5 -65 -2-63 -9-25 45 -8 42-65-99-
0 26 24 46 52 54 44 -5 23-56-99-
-5 99 47 90 79 85 2-59-66-86-99-
11 12 13 14 15 16 17 18 19 20 21 22 23
-99-58 27 54 69 40 -2-87-88-53-99-99-99
-57-42 -1 11 18 25 13-32-52-19-24-44-87
16 -3-27-28-38-16-13-19-29 22 6-27 16
45-13-34-34 0 -8 0-15 11 25-10-59 8
45-17 8-32 50 20 68 11-18-43-21-39 13
40-16 15-55 12-63 10-68-56-39 -4 15 6
59 26 5-49-77-95 6-15-48-70-31 2 23
-55-57-33 -8 7 10 -1-45-35-47 -1-38 -3
-56-16-37 -5-22-63-82-73 27 14 36 1 37
-35 -7-50 6-44-17-63-39-50-14 -7 43 82
-21 10 10 59 10 -1-34 3 12 35 -2 49 88
-47 15-32 29 2-27-39-14 1 39 6-30 1
21 8-14 -804 -9-28-50-36-13 7 25
4-17-18 8-46-57-13 35 22 5 21 47 64
40 13 32 31 -6-71-21 58 17-18-29-24 20
-11 -2-24 12 47 21 97 -2 6-21 2-24 -6
-37 3-26 24 16 21 72-50-19-48 28 -3 46
-40 -8 10 55 29 9 11-30 -8-35 34-12 64
-99-81-42-29 6 3 10-21 13 -4 59 38 82
0-99-55-55 1 1 26-40 14 17 80 92 99
10
99
74
-7
11
1
10
39
99
99
2
-1
43
16
15
10
15
33
58
99
99

TABLE
Declination
dec\ra 0123456789
90 -25-33 43 99 99 99 30-99-38-19
85 24 76 64 80 91 42 36 4-8 5
80 13 61 17 25 -7 1 20 76 11 21
75 -63-26-10 26 -5-27-31-14-33 -8
70 -3 65 13 39 19 14 42 33 5 -9
65 -22 89 57 72 16 12 2 45 77 26
60 -5 52 45 57 9 2-35 33 60 45
55 -15-14-40 -7-58 8 42 96 31 30
50 -37 5 -2 -5-73-79-14 13 36 34
45 -38 41 77 17-33-75 49 61 99 84
40 -29-16-82-19-99-12-31 10 -4 29
35 15-10 -8-21 -1 44-13-29-41-28
30 27 8 0-50 80 11 6-53-20 6
25 -8 46-67 12 7 -7-29 7 41 77
20 -99-17-61 67 29 25 -4 39 92 64
15 -52 18-25-10-18-14-18 4 53 17
10 -48 -6-41-18 -2 28 59 57 53 43
5 -59 15-57-73-70-91-58-99-54-41
0 -7 47-20-53-11-66-10-99-32 12
-5 99 99 45-39 25 64 99 99 99 99
CONTINUED
11 12 13 14 15 16 17 18 19 20 21 22 23
1-57-74 5 36 12-15-18-13 9-17-41-13
12-16-10 24-16 2 -1 -7 -9-30-87-69 5
500 32-51-23 1-57-16-22-10-25 14
-87-99-89 -7-24-32 8-23 4 19 9 6-5
9-11 41 31 36-29-14-26-53-36-18 56 39
14-22 -6-25 33 -5 0-63-70-29-11 4-11
24-17-60-54-16 23 28 0-10 23-12-31-32
22 13-16-10 2 24 41 38 28 -4 11 10-19
36 2 13 1 6-52-25-16-50 -9-15 19 -9
-9-75 -2-30-19-20-24 -4-72 16 7 44 -6
-22-49 -1-23 15 26 34 19 9 16 9 28-21
7 4 33-42-41-20-13-33-28-16 -6 -4-27
13 -3 88 30 24-11-62-35-30-19 17-21 11
2 -2 60 22 59 78 38 30 7-14 34 14 78
-17-24-40 -3-16 43-30-32-17 34 25 3 -2
-19-43-19 52 1 57-19 29 12 40 17 -8 16
11-49-11 4 20 -2-24-12-44-13 -2 -9 -8
17 8 24 6-33-25-18 27-21 4-42 14-26
22 32 9 14-43-47-79 15 -2 55 0 62 21
99 99 15 15-43-43-69 39 35 85 99 99 99
51 '
10
34
10
-14
-22
1
31
25
-20
18
21
-5
-10
8
44
82
31
-53
-61
62
99
UD

TABLE 52
Corrections Applied to the Tri 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0
0
0
0
0
0
0
30
56
56
56
0
0
0
0
0
0
0
25
70
42
-6-
-23
67
99
99
99
84
99
20
-59
49
54-
â– 21
53
37
-7-
•16
-4-
-32-
15
-25
31
26-
-23-
-19-
-21-
-22
-9
50
10-
10
-63-
15
38
-9-
-53-
-22
8
6
-9-
-38-
5
-18
9
13-
-41
-9
20-
-39-
-25-
-17
-1-
0
48-
â– 99
-1-
-19
17-
-39-
-67-
-60-
-37-
-37-
-5
0
0
0
0
99
99
99
99
0
0
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
35
0
0
0
0
0
0
0
0
0
0
30
99
99
99
0
0
0
0
0
0
0
25
7
99
13-
-70
99-
-77-
-93
99
77
12-
20
-20-
18-
-38-
â– 39
60-
-11-
-36-
•32
-2-
-54-
15
-10-
99
35-
-46
58
27
57-
â– 31
10
25-
10
57-
14
73-
-52
63
68
10-
â– 10
52
16-
5
34
-2
95
12
93
99
86
48
87
37
0
99-
85-
-68-
â– 45
86-
-56
21
80
32
15
-5
0
0
0
0-
-23
70
99
99
0
0
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 43 43 43 0000
0 0 0 0 0 0 43 43 43 0-68-68-68
-99-99-99 64 99 57 99 99 99 -7 99 99 99
20 42-54 10-36 4 -4 -6 35 -1-46 15-18
-24 49 -9-25-12-18 23-42-18 33 -8-21 9
15 -3-99 -4-34-23 15-27-65 -4-17 -9 20
49-36-52-17 4-99-22 20 42 15-29-32-35
-17-35 32 -7-17 61 -5-99-33-99 7-35-13
99 99 34 99 99 99 99 99 99 99 99 99 99
11 12 13 14 15 16 17 18 19 20 21 22 23
000000 96 96 96 0000
0 0 0 0 0 0 96 96 96 0-99-99-99
-99 99 99-99 99 99-37 99 99 99 99 5-99
-30-54 9 30 -5-34-73-80 59 39-99-80-17
-52 3 16 97-17-21 22 26-27-19-38-60 25
58 75 -8 -2 83 29-36-19 62 99-50-39 62
12 83 29 75 99 21 99 53 32 99 57 1 99
15 33 99 99 39 -2 99 5 99 99 26 0 99
-99-99-99 59 99-99-99-99-99-99-99-99-99
10
0
0
-3
61
68
71
59
99
0
10
0
0
99
53
44
89
55
56
0
to
cn

TABLE 53
Corrections Applied to the Bruss 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
90
0
0
0
16
16
-1-
-20
18
42
52
55
55
0-
-32-
-32-
-32-
-32-
â– 36-
-99-
-13
-7
-5
-5
-5
85
-44-
-99
0
16
16
-3-
-18
-4
21
38
39
39-
-38-
-66-
-27-
â– 40
21-
-62-
-40-
-45-
-18-
-13-
â– 14-
•15
80
-61-
-99
-9
0
-9-
-17-
-22
-9
6
26
4
5-
-35-
-99-
-10-
â– 99
22-
-99-
-43-
-83-
-56-
-84-
-63-
â– 76
75
-81-
-99-
-45-
-41-
-16-
-20-
-19
2
6
13
-2
11
6
41
14
-1-
-24-
-42-
-22-
-44-
-56-
.99-
â– 12-
â– 98
70
-99-
-99-
-80-
-56-
-27-
-21
-5
31
2
-7
7
22
34
25
-2
-2-
-17
25
96
61
61-
-20-
-44-
-99
65
-67-
-54-
-34-
-21
7-
-29-
-20-
-18
12
7
13
0
18
-7-
-28-
-61-
-62-
-89-
-83-
-78
-7-
-35-
-40-
â– 49
60
-29-
-26-
-47-
-40-
-24-
-40-
•21-
â– 29
13-
-14
-4-
-67-
-40-
-48-
-34-
-19-
-34-
-59-
-99-
-99-
â– 99-
-90-
-42-
-42
55
-45-
-53-
-99-
-60-
-99-
-28-
-42-
-26-
-24-
-19-
-31-
-69-
-23-
-37-
-50-
-54-
-61-
-35-
-37-
-56-
-69-
-79-
-26-
-57
50
-45
-8-
-51-
-34-
-99-
-13-
-57
-8-
-62-
-23-
-40-
•77
7-
-87-
-57-
-95-
-70-
-52-
-52-
-53-
-51-
-54-
-49-
-55
45
-61
2-
-26-
-44-
-94-
-69-
-85
3-
-80-
-99-
-77-
-99-
-32-
-99-
-57-
-99-
-15-
-42-
-42-
-71-
-70-
-66-
-67-
•58
40
-61-
-19-
-27-
-34-
-39-
-77-
-97-
-41-
-35-
-98-
-99-
-99-
-70-
-85-
-70-
-84-
-32-
-96-
-24-
-95-
-91-
-95-
-81-
•62
35
-61-
-40-
-54-
-33-
-58-
-60-
-85-
-91-
-66-
-98-
-99-
-91-
-97-
-82-
-99-
-88-
-91-
-99-
-41-
-99-
-59-
-84-
-66-
-67
30
-36-
-37-
-54-
-26-
-99-
-71-
-85-
-85-
-38-
-45-
-59-
-62-
-99-
-97-
-99-
-72-
-78-
-86-
-64-
-98-
-78-
-93-
-74-
-82
25
-61-
-68-
-65-
-75-
-99-
-99-
-88-
-99-
-55-
-99-
-99-
-99-
-90-
-91-
-99-
-99-
-99-
-61-
-61-
-24-
-76-
-80-
-73-
-68
20
-99-
-99-
-51-
-99-
-77-
-99-
-97-
-96-
-83-
-91-
-99-
-96-
-79-
-79-
-99-
-99-
-99-
-72-
-94-
-48-
-94-
-76-
-89-
-85
15
-68-
-99-
-58-
-61-
-24-
-76-
-82-
-96-
-44-
-59-
-44-
-91-
-98-
-59-
-65-
-41-
-75-
-45-
-70-
-95-
-83-
-60-
-55-
-57
10
-67-
-91-
-70-
-70-
-32-
-61-
-72-
-99-
-73-
-99-
-62-
-99-
-93-
-73-
-70-
-73-
-89-
-55-
-31-
-99-
-29-
-59-
-58-
-99
5
-77-
-82-
-43-
-50-
-71-
-71-
-74-
-59-
-51-
-85-
-74-
-94-
-90-
-90-
-84-
-87-
-75-
-91-
-62-
-78-
-25-
-41-
-58-
-99
0
-59-
-68-
-64-
-79-
-99-
-99-
-99
0-
-99-
-93-
-93-
-76-
-71-
-66-
-57-
-62-
-37-
-95-
-78-
-99-
-52-
-53-
-46-
-87
-5
-99-
-99-
-99-
-99-
-99-
-99-
-99
0
0-
-69-
-69-
-99-
-99-
-99-
-99-
-99
99-
-99-
-99-
-99-
-99-
-99
29-
-99
to
cr>

TABLE 53 CONTINUED
Declination
dec\ra 0123456789
90 00 0-50-50-37-19-24-34-40-
85 5-75 0-50-50-36-22 3 18 25
80 0-99 99 36 3-22-28 6 7 15-
75 -38-99 1 8 60 -3-46-44-29 -7-
70 -59-99-49-53 57 33-31-77-22 24-
65 90 11-43-74 18 34 37 18 16-22-
60 68 -7-70-60 18 21 27 12 45 30
55 -57-62-73-39 14 25 -1-17-12 9
50 -81-10 9 23 50 25 19 3 60 38
45 -65-72-15 36 58 32 75 69 92 -5-
40 -99-99-48 24-18 14 41 50-41-48-
35 -98-97-42 63-41 8 5 53 34 28
30 71 12-18 31-10 26 12 5 43 33
25 -6 37 17 -8 -9 8 32-16 62 89-
20 -95-44-32-57-18-18 1-20-23-28-
15 2 15-27-80-75-61-52-39-11-73-
10 -76-25 18 22 13 -4-25-54-31-88-
5 -23-47 18-16 9 3-24-99-94-55-
0 50 15-15-78-55-55-39 0 99-33-
-5 93 93-27-67-87-87-87 0 0-50-
11 12 13 14 15 16 17 18 19 20 21 22 23
-43 0 34 34 34 34 38 99-45-54-56-57-57
17-99 24 25 27 31 36 22 -7-34-45-45-45
-37-99-86-50-15 10 32 5 30 33 57 36 28
-61-99-25-47-20-63 34 1 48 43 95 44 6
-57-53-30-53-61-84-30-99-32-49 42-43-99
6 50 85 22-20 -5 14 5 -8-24 59 51 37
44 81 99 99 74 77 28 31 20 37 64 62 96
-1 52 27 52-38 18-18 6 8 55 61 27 34
-17 46 39 53-18 11-33-18-16 56 53 25-14
-31 2-25-21 -4 4 29 13 5 54 45 33-18
9 67-25 -7 2 -6 31-43 20 58 57 38-32
62 76 11-21 27 -6 31-24 29 14 19 17-14
48 -9 32-61 19 3 32 7 32 29 66 94 89
-17-86 -4-67 -7-13 11-10-25-13-10-41-70
-3-37 -1-55-15-25 17-14-56-50-37-49-98
34 20 -6-40 0-11 4-12-25-29 11 12 25
55 9-46-85-69-67 -7 19-12-52-34-34-70
2-27-46-55-95-99 16 27 -7-50 2 12-58
-17 11 33 16-11-99 28 7 25-24 28 47 22
23 99 99 99 99-77 99 99 99 87 87-65 93
10
43
17
35
42
55
59
-7
-6
14
27
40
3
-6
20
45
35
41
35
33
50
to

TABLE 54
Corrections Applied to the Leid21 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
55
-86
99
99
25-
-33-
-71-
â– 28
0
0
0
0
0
0
0
0
0
0-
-28-
-45-
-92-
-83
82-
-19-
-96
50
5-
•51-
-58-
-42-
-67-
-85-
-99
-1
99
0
99
99
17-
-99-
-99-
-83
13-
-55-
-50-
-37-
-37-
-74-
-98-
-50
45
-48
-9-
-53-
-92-
-55-
-71-
-99-
-76-
â– 18-
-17-
99-
-99-
-99-
-92-
-75-
-79-
-72-
-99-
-61-
-30-
-62-
-69-
-78-
-99
40
-75-
38-
-88-
-70-
-83-
-70-
-48-
-99-
-99-
-99-
98
32-
-23-
-90-
-46-
-72-
-36-
-43-
-92-
-34-
-99-
-40-
-25-
-88
35
-80-
•75-
-86-
-96-
-99-
-68-
-99-
-99-
-82-
-50-
34-
-95-
-93-
-75-
-84-
-99-
-99-
-99-
-99-
-73-
-97-
-68-
-78-
-91
30
-71-
•46-
-37-
-62-
-63-
-37-
-95-
-99-
-99-
-99-
52-
-52-
-31
41
1-
-99-
-99-
-99-
-54-
-61-
-51-
-53-
-12-
-56
25
-99-
•99-
-71-
-91-
-90-
-99-
-16-
-91-
-80
-2-
52-
-52-
-86-
-99-
-99-
-94-
-38-
-99-
-99-
-99-
-44-
-44-
-96-
-99
20
11
-6-
-77-
-99-
-60-
-83-
-99-
-99-
-80
0
0
0-
-99-
-10-
-99-
-87-
-90-
-99-
-97-
-99-
-99-
-73
11
-8
15
-15
99-
-18-
-70-
-77-
-63-
-87-
-99-
-92-
-99-
72-
-52-
-45-
-93-
-99-
-99-
-86-
-71-
-21-
-26
0-
-68-
-24-
-34
10
-34-
•33-
-55-
-83-
-63-
•68-
-78-
-61-
-99-
-99-
84-
-58-
-66-
-99-
-59-
-61-
-82-
-40-
-23-
-61-
-85-
-93-
-99-
-42
5
-84-
65-
-57-
-52-
-57-
-70-
-99-
-47-
-99-
-99-
56-
-72-
-99-
-99-
-98-
-99-
-99-
-99-
-99-
-68
-2-
-52-
-37-
-90
0
-18-
28-
-99-
-81-
-99-
-99-
-99-
-81-
-81-
-94-
99-
-99-
-96-
-99-
-87-
-37-
-25-
-53-
-92-
-99-
-99-
-99-
-99
16
-5
0
0-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
â– 99
0
0
11-
-99-
-99-
-99-
-82-
-79-
-87-
-99-
-99-
-71-
-41-
-24
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
55
99
99
25-
-15
99
80-
-99
0
0
0
0
0
0
0
0
0
0
35
62
99
99
34
-5
99
50
-6
73
20
1
77
99
99
99
99
0
0
0-
-66
77
99
78-
-26
27
55
94
20
6
43-
-10
45
47
79
65
46
59
70
36
99
99
19
87
71
45
40
99
99
82
48
34
49
-4
41
99
51
40
45
38
58
27
26
55
39
84
98-
-17
79
99
99
93
8
99
99
42
-1
43
46
71
51
61
35
-18
48
46
-2
-6
47
-6-
-21
31
55
66
44
36
70
73
74-
-44
4
32
32
40
47
96
48
30
-4-
â– 35
66
62
72
99
-2
4
38
62
2
2
-1-
-27-
-80
11
22
13
25
20
31
54
5
30
25
16-
â– 28-
-87
99
96
14
20
99
31-
-99
2
2
36
84
99
99
48
10
99
99
24
20
94
13
20
72
86
60
99
67
40-
-26-
-38-
-26
0
0
0
85
17
57
27-
-33-
-25
42
79
84
44
27
20
15
49
1
23
25
50
99
44
18
99
99
99
99
99
99
99
70
67
71
50
51
83
48
43
69
10
29
12
28
36
27-
-14
45
43
27
41
92
99
55
20
12
20
24
82
90
51
26
72
99
40
5
83
64
45
51
93
99-
-26
29
67-
â– 33
45
-3
2
21
13
93
65-
-75-
-15
78
19
45
14
52
0
-13-
â– 16-
-24-
â– 18
23
19
16
99
99
99
0-
-49-
-58
31
56
27-
-24-
-30
77
48
32
35
22-
â– 32
-5
0
0-
-99-
â– 99
-2
16
16-
-99-
-99-
-99
0
0-
-45
10
9-
-47-
-99-
-11-
-16-
-36
51
90-
-14-
-99
<£>
oo

TABLE 55
Corrections Applied to the Leid24 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
50
-65-
â– 62-
â– 62-
â– 68-
â– 77-
-85-
â– 68-
-80-
-80-
â– 82-
•67-
â– 62-
â– 82-
-87-
â– 99-
â– 94-
â– 85-
â– 59-
â– 59-
-63-
â– 13-
â– 74-
â– 76-
â– 69
45
-70-
â– 71-
-70-
•73-
-77-
â– 85-
â– 68-
-83-
-87-
-87-
â– 72-
â– 67-
â– 81-
-81-
â– 97-
•89-
-86-
â– 59-
â– 59-
â– 65-
â– 71-
•74-
•75-
â– 72
40
-76-
â– 77-
â– 77-
â– 75-
â– 77-
•85-
â– 68-
-90-
â– 93-
-93-
-80-
-70-
â– 80-
â– 76-
•91-
-84-
-83-
-58-
â– 59-
â– 65-
â– 70-
â– 75-
â– 75-
â– 77
35
-86-
â– 71-
-70-
•72-
-90-
•97-
-17-
-99-
â– 93-
â– 91-
â– 93-
•89-
-93-
-93-
â– 96-
â– 91-
•99-
â– 99-
â– 99-
â– 91-
-99-
â– 94-
-15-
â– 21
30
-86-
â– 71-
•71-
â– 74-
â– 94-
-99-
-19-
-99-
-93-
â– 91-
-93-
•86-
â– 94-
-94-
â– 91-
â– 92-
â– 99-
-98-
â– 99-
â– 88-
•96-
â– 93-
-14-
â– 21
25
-85-
•71-
-71-
•76-
-98-
•99-
-20-
-99-
â– 93-
â– 91-
â– 93-
â– 83-
-95-
-94-
-94-
â– 89-
-93-
-92-
â– 99-
â– 84-
-93-
â– 91-
•13-
â– 20
20
-69-
â– 46-
-40-
-33-
-35-
•39-
-99-
-99-
-99-
â– 90-
-86-
â– 89-
-80-
-81-
â– 85-
â– 84-
-85-
â– 66-
-50-
-32-
-49-
•59-
â– 99-
â– 33
15
-76-
•49-
-41-
-33-
â– 33-
â– 35-
-99-
-99-
-99-
-85-
-80-
•84-
-69-
-74-
-80-
-87-
â– 85-
-66-
â– 55-
-40-
-62-
â– 61-
-99-
â– 40
10
-80-
â– 53-
â– 41-
-33-
-34-
â– 38-
-99-
-99-
-99-
-77-
-72-
â– 74-
-55-
-65-
â– 16-
-90-
-86-
â– 61-
-58-
-45-
â– 72-
â– 14-
-99-
â– 46
5
-79-
â– 58-
-76-
-45-
â– 81-
â– 81-
-76-
-99-
-99-
-99-
-99-
-99-
-83-
-76-
-86-
•79-
-89-
-74-
-73-
-75-
â– 21-
â– 31-
-99-
â– 81
0
-70-
-46-
-68-
-48-
•81-
-83-
â– 11-
-99-
-99-
-99-
-99-
â– 99-
-83-
-75-
-85-
-76-
-83-
-70-
-71-
-67-
-18-
-22-
-99-
-74
-5
-61-
•38-
â– 62-
â– 50-
-80-
-80-
â– 72-
-99-
-98-
-99-
-99-
-99-
-82-
-74-
-83-
-71-
-79-
-68-
-69-
-62-
-13-
â– 14-
-99-
-68
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
50
17
0
8
32
61
60
39
47
55
90
64
53
45
58
91
65
64
41
47
47
49
51
59
36
45
27
15
20
43
62
61
39
46
54
87
63
50
42
50
83
58
60
39
43
40
44
48
61
46
40
34
28
31
50
63
62
38
46
52
82
62
48
38
40
70
45
55
35
39
36
39
46
63
52
35
31
41
34
50
47
67
8
32
13
19
17
36
35
37
48
54
32
7
8
6
11
7
19
9
30
33
43
36
52
51
73
14
32
15
23
23
40
39
36
50
60
35
5
-2
-3
4
5
18
13
25
34
43
36
54
56
79
19
34
17
25
32
44
42
35
53
66
45
8-
-11-
-11
0
2
17
18
20
-2
32
51
69
64
36
91
90
99
85
69
65
42
46
50
38
33
34
33
37
23
41
49
12
15
-4
30
51
73
70
42
94
87
99
77
63
59
37
41
48
42
38
40
36
42
31
55
68
19
10
-7
28
52
73
70
44
91
77
87
69
55
50
27
36
45
48
45
47
40
47
38
64
80
25
5
-1
-1
11
20
22
8
7
-5
14
8
34
22
21
29
46
50
25
6
4
7
16
21
26
0
0
20
16
23
26
25
10
9
0
21
13
34
24
21
26
38
43
18
5
5
7
14
18
30
12
-5
31
28
32
30
26
8
11
7
29
19
35
25
22
22
29
30
9
3
5
7
12
15
35
20
<£>

TABLE 56
Corrections Applied to the Lund 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 -12-21-83-61 18-71-99-99-90-99-99-88-99-99 99-99-99-99-99-99-99-99-51-37
40 -91-85-72-94-93-99-99-99-99-99-99-99-81-99-88-99-99-99-99-90-99-84-89-77
35 -88-98-63-60-95-95-95-99-99-99-99-99-99-97-86-99-99-99-99-99-71-48-99-94
30 -99-99 99 -8 70 71-68-99-99-99-99-53-99-73-99-99-99-99-99-54-65 18-99-99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
45 70 99-36-23-16-55-26 81 35-68 92 99 99 99 99 99 99 99-99-99-66 22 99 11
40 27 8-17 7-19-22-21 2 12 1 8 1 -5 -8 51 22 4 44 -5-35 11 8 27 27
35 17-33-12 8 17-30-28-32-16-14-13-13-22-37-20-34-23 -9-41-32 -2-18-34 9
30 39-99-99-87 99 -4 78 32-99-61 30 99-43-99-15 99 25-99-99 -1 71-23-93 99
TABLE 57
Corrections Applied to the Leid27 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
65 -79-38 3-47-64-82-99-98-77-58-41-30-15-42-30-37 -8-65-45 -8 54 -3-99-97
60 -57-48-29-62-83-94-90-77-54-63-55-54-43-60-55-65-47-95-71-32 1 -2-67-60
55 -44-50-53-67-87-97-72-62-46-72-66-63-56-64-64-77-78-99-94-62-52-28-53-39
50 -42-34-45-37-62-72-40-36-41-80-84-70-69-65-71-84-99-99-99-99-99-95-71-41
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
65 40 30-86-90-87-40 32 67 59 2-61-10 36 97 52 40 98 36 44 21-12 5 -8 77
60 43 6 -6 8-44-13 -6 12 17 9-34 1 26 53 30 17 53 0 21 -4 9 25 35 85
55 41-17 34 61 -9 4-35-29-11 18 0 16 21 39 35 29 38 -7 8-27 22 30 74 83
50 37-92 43 99 40 2-90-99-45 30 37 31 14 32 49 54 38 3 -7-74 33 26 99 81
100

TABLE 58
Corrections Applied to the Berl Z 10
Right .
Ascension
dec\ra
0 12
3
4
5
6
7
8
9 10 11
12
13
14
15
16
17
18
19
20 21 22
23
90
-23-10 29
49
21-
37-
39-
25-
35-
79-66-36
34
18
32
34
31
40
24
18
0-13 -3
9
85
-15 -5 3
2
-2
-7
0
13
4
11 21 20
53
53
38
24
22
16
10
-1-
16-29-12
-5
80
-11 -5-11-
11
-2
3
13
4
-9
20 24 14
18
32
12
1
6
-6
3
12
15 -6 -1-
13
75
-30-36-27
-7
7
3
12-
42-
51
-2 3-18-
31
-9
-6
-6
10
-5
28
54
73 30 3-
28
70
0 0 0
0
0
0
0
0
0
0 15 15
15
15
15
0
0
0
0
0
0 0 0
0
Declination
dec\ra
0 12
3
4
5
6
7
8
9 10 11
12
13
14
15
16
17
18
19
20 21 22
23
90
-66-79-24
-8
57
59
63
34
58
17 13-20
53
22
-7-
33'
-39
14
-8
43-
â– 23 -8-41-
•53
85
-55-17-20-
35-
23-
19
-4-
•25-
13-
49-23-12
0-
•28'
-32-
38'
-27-
40'
-31-
14-
â– 40-35-65-
•48
80
-29 -1-31-
39-
60-
33
8
28
8-
66-54 0
-5
-9-
-25-
22
-3-
•75-
-10-
17
-1-10-40
-4
75
-3 7-22
14-
25
25
99
99
84-
78-99-15-
22
9-
-35-
â– 18
1-
â– 64
38
-1
23 1-36
44
70
0 0 0
0
0
0
0
0
0
0 99 99
99
99
99
0
0
0
0
0
0 0 0
0
TABLE 59
Corrections Applied tc
i the Konl9 ;
25
Right
Ascension
dec\ra
0 12
3
4
5
6
7
8
9 10 11
12
13
14
15
16
17
18
19
20 21 22
23
60
-99 -6 -6-
â– 99-
â– 99-
•99-
•49-
â– 31
0
0 0 0
0
0
0
0
0-
•99-
-99-
â– 99-
â– 99-99-99-
â– 99
55
-23-42-78-
â– 40-
â– 96-
•46-
â– 72-
-68-
•93-
•69-99-21-
•91-
â– 87'
-86-
â– 71
-77-
•89'
-92-
•99-
â– 99-41-99-
â– 99
50
29-42-75-
â– 99-
•66
13-
•28
10
11
-7-45 32-
•61-
â– 99
-97-
â– 99
-83-
•21'
-61-
•88-
â– 62 -4-64-
•38
45
0 0 0
0
0-
â– 83-
•83-
â– 83
0
0 0 66
66
66
0
33
62
99
38
12
0 0 0
0
Declination
dec\ra
0 12
3
4
5
6
7
8
9 10 11
12
13
14
15
16
17
18
19
20 21 22
23
60
99-99-99
10
-7
15
99
99
0
0 0 0
0
0
0
0
0-
â– 25
2
-1-
-99-99-99
99
55
53-33 53
85
40
33
28
40
13-
â– 36-93-28
15
17
29
-7
-31
11
42
33
25-19-41
48
50
22 -3 25
39
41
81
80
39
14
84 67-13
45
34
38
65
99
82
46
96
71 23 42
31
45
0 0 0
0
0
99
99
99
0
0 0-1
-1
-1
0
99
99
99
-99-
â– 99
0 0 0
0

TABLE 60
Corrections Applied to the Toul3 00-II
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
20
-55-
65-
-49-
-49-
•17
41
41-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-71
33-
-61-
-93-
-40
99-
-99-
-99-
-99
15
-41-
36-
-15-
-79-
-59-
-80-
-87-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-69-
â– 99-
-99-
-76-
-73-
-99-
-99-
-99
10
-84-
99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-87-
-99-
-99-
-60-
-73-
-99-
-99-
-99
5
-75-
99-
-99-
•99-
-99-
•99-
•99-
-99-
-99-
-99-
-99-
•99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-66-
-99-
-99
0
-10
22
10-
-23-
-96-
-99-
-99-
-99-
-99-
-99-
-70-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-99-
-42-
-85-
-72
-5
-18
-4-
-19
68-
-39-
-99-
-99-
-72
56
12-
-55-
-99-
-99-
-99-
-99
6
40
39-
-99-
-99-
-99-
-99-
-99
47
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
20
22-
99-
-25-
-25
58
41
41
41
81
99-
-99
99
99
99
48-
-75-
-99-
-33
37
80
84
99
99
99
15
28-
53-
-20
21
45
89
5
16-
-88-
-27-
-99-
-37-
-52
15-
-20
47
36
72
40
64
12
16
-9
58
10
22-
26
18
9
18
8-
-16
15-
-13
44
4
-3-
-22
-6-
-12
33
12
20-
-38-
-24-
-29-
-13-
-13
2
5
46
4
23-
-21
-3
28
15
38
16
20
16-
-16
6-
-20
15
7
8
-6-
-53-
-24
11-
-13
5-
-27
0
76
21-
-27-
-47-
-25
70
86
99-
-21-
-74-
-93-
-86-
-18-
-37
50
29
60
24-
-12
32
61
-2
29-
-20
-5
-99-
•99-
-88-
-23
11
99
99
99-
-99-
-99-
-99-
-13
99
99
99
99
99
99-
-69
49
99
99-
-10-
-99
TABLE 61
Corrections Applied to the Pulk 10
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 -68-99-49-38-11 -2-47-81-99-99-99-99-99-27 58 59 5-99-99-16 -9 41 -5-44
45 -61-58-62-77-80-55-99-95-66-65-99-68-99-87-74-70-59-73-61-68-84-54-58-75
40 -37-42-75-59-84-85-77-69-87-84-85-89-88-65-47-82-99-99-97-74-68-73-65-29
35 -99-99-34 80 50 3-99-99-99-74-51-63-37-59-99-99-99-99-99 23 79 49 99 99
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
50 87 75 19 9 73 71 77 40-22 18 15 9-11-73 7 20 20 56 96 58 -3-17-38 12
45 19 47 33 11 18 38 -7 9 20 33 11 5 31 17 22 12 15 32 8 17 22 42 22 21
40 54 45 27 44 35 36 50 28 19 54 36 39 54 56 51 54 33 6 2 48 35 5 34 63
35 99 63-13-87-99-13 99-13-74 20 28 23-64-52 50 99 99 39 0 30 99 99 66 93
ZO L

TABLE 62
Corrections Applied to the Lick 17
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
60 -67-62-44-15 -5-27-47-89-45-53 -7-20-16 -9-32-64-64-53-72-24-30-37-80-51
55 -65-73-57-35-26-52-60-89-50-51-15-30-38-34-56-64-56-43-62-32-42-51-73-53
50 -60-77-59-43-30-60-67-84-56-49-32-37-47-43-73-66-52-45-67-70-74-78-59-56
45 -47-65-44-24 -6-51-64-77-54-43-47-39-43-36-75-61-50-53-83-99-99-99-37-50
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
60
64
47
29
33
29
12-
-30-
-44-
-39-
-31-
-14
3
29-
-17-
-42-
-40-
-35-
-39-
-54
-6
22
49
80
59
55
45
32
22
24
24
21
7
-8
-7-
-13
2
20
24
-2
-6-
â– 10
-5-
-17-
-33-
-15
3
16
40
39
50
25
15
11
12
14
27
40
21
17
6
20
25
15
9
28
21
23
1-
-14-
-36-
-27-
-33
-8
11
45
-8-
-26-
-11
-5
2
30
60
36
31
23
26
13
5
10
44
39
38
7
-8-
-52-
-46-
-70-
-52-
-36
TABLE 63
Corrections Applied to the Lick 28
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
20
8
5
17
28
36
15
-5
40
44
50
42
99
91
39
-4-
-28
-9-
-21-
-25-
-70-
-46-
â– 13
13
30
19
2
-4
4
21
28
32
21
36
42
40
33
57
58
35
22
-1
29
19
36-
-10
-9
12
23
25
11
4
-5
-1
8
19
25
21
13
10
12
4
24
25
24
32
20
51
46
58
43
7
23
11
20
-1
3
2
11
2
24
5
13
3-
-18-
•10
-5
15
15
19
22
18
12
0
7
35-
-11
12-
-15
15
-38-
•22
-4
20
3
30-
-22
-7
-3-
-21
-6
20
33
24
31
13
4-
-37-
-44-
-17
37
-6
-3-
-51
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
13
57
42
96
53
47
20
99
99
74
53
13
29
96
99
70
76
43
19
57
97
58
20
27
30
-13
17-
-15
14-
19-
-11-
-32
22-
-19-
-29
-9-
-27-
-17
13
18
8
20
6-
-22-
-10
13
-7-
-21-
-10
25
-28-
•29-
-47-
-32-
33-
-42-
-46-
-25-
-45-
-17
1-
-23-
-24
-9-
-18-
-18-
-12-
-25-
-47-
-45-
-34-
-35-
-22-
-38
20
9
-9
7
24
45-
-13
18
6
2
29
8-
-15
-2
40
41
21
20-
-15
8
19
20
14
20
-1
15
83
77
99
99
92
12
67
55
44
46
0
1
22
97
99
74
72
6
60
78
66
52
49
83
1 03

TABLE 64
Corrections Applied to the Turin 10
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
55 -99-64-99-85-99-75-30-13 66 27 9-19-41-27 39 99 99 99 79 99 99 48-45-54
50 -99-71-99-48-99-71-41-80-51-88-97-77-99-99-99-83-96-47-99-59-68-28-95-99
45 -99-82-92-19-81-65-43-96-74-99-99-90-99-99-99-99-99-89-99-99-99-66-99-99
40 -99-71-22 39-42-69-55-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99-99
TABLE. 65
Corrections Applied to the Bord 00-11
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
20 -36-16-97-75-97-99-94-71-42-31-55-99-99-99-99-74-70-31-62-99-64-90-99-75
15 -70-33-37-63-33-52-77-86-99-93-75-50-80-62-81-31-14-60-11-62-68-53-35-42
10 -46-25-17 -7-57-62-66-50-73-62-52-83-59-77-37-49-29-38-28-42-32-65-52-31
5 99-99-99-99 12-99-92-99-99 79 99-45-99-28-25-99-95-52-63-99-99-99-99 99
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
20
23
46
34
25
65
39
46
60
43
4
55
52
35
5
3-
-22
67
99
90
-1
-7
-5
39
70
15
57
47
23
45
47
31
27
20
39
26
35
19
42
44
63
85
56
27
29
47
42
38
69
52
10
56
45
45
93
57
36
44
47
61
21
52
69
44
48
35
91
99
48
99
33
-1
46-
-14
5
5
99
99
32-
-24
14
79
99
99-
-71-
-99-
-37
32
99
99
43
99
60-
-85
50
99
99
99
99
99
1 04

TABLE 66
Corrections Applied to the Ottw28 25
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
90
0
0
0-
-51-
-51-
-17
37
41
32
28
27
26
-6
12
12
12
12
11-
-90
-7
-1
-1
0
85
-6
0
-5-
-26-
-41-
-26
0
24
27
25
20
14-
-10
2
5
6
7
6-
-42-
-21
-9
-2
-2
80
-3-
-11-
-27-
-28-
-31-
-17
-7
-9
-5
-2-
-11
-8-
-13-
-45-
-46-
-30
2
16-
-26-
-16-
-22
-4-
-12
75
-3
1-
-24
-6-
-29
-9
4
21
38
48
26
27
10-
-36-
-35-
-24
24
20
-9-
-10-
-14
0-
-11
70
-14
14
33
24
-8-
-12-
-14
10
34
44
14
34
56
54
39
26
35
25
64
52
62
13
2
65
44
55
86
47
87
31
31
4
22
-3
4
27
70
57
35
29
22
7-
-18
8
26
11
5
60
21
45
32
44
99
34
26
7
53
81
64
34
41
9
-5-
-23-
-19-
-23-
-28-
-17-
-24-
-23-
-27
55
-24-
-46-
-72-
â– 37
35-
-48
1
6
49
33
36
28
14
-1
-2-
-18
30
14
26
7
44
4
17
50
7-
-13-
-40-
-35-
-70-
-99-
-33-
â– 20
39-
-47
2
6
0
-6-
â– 16
11
44
25
40
50
99
67
34
45
15
4
5
10
-7-
-19
0-
-14
64
23
40
26
40
41
19
11
12
-1
20
31
52
31
7
40
-8-
-21-
-13-
-11
-5
4
19-
-17
8
13
42
37
28
50
35
31
33
4
25-
â– 11
6
2
-5
35
-5
8
-6
-1
3
18
33
29
1
-5
19
38
31
33
52
59
59
37
56-
-18
5
8
15
30
-12
26-
-18
-9
16
39
69
82
49
14
19
-2
57
20
40
36
21
39
55
25
24
72
80
25
-74
39
8
4-
â– 28
-5
6
27
4-
-37
54
3
61
28-
-19-
-29-
-38
11
21
35
36
43-
-20
20 -35 12 43 28 59 13-32-42-18-21 33 5 6-4-8 3-5 9 -8 -9-11 17-14-
15 22 10 47-74 -3-26 -3 16 33 36 6-20 4 -5 17 19 41 2-17 16 -8-19-43-
10 -1-40-16-44 13 14 5 -3 41 45 -4-48 3-14 37 23 36 -5-11 86 71 4-21-
5 36-47-32 15 7 20-43-99-56-30-29-37-32-62 -8-22-12-19 4-11 -5-51 -7-
0 97-10 -6-33-89-89-99 0-99 43 43 27-22-59-20-25 21 40 25 -6-38-63 -7-
-5 -99-99-99-99-99-99-99 0 0 97 97 38-20-50-95-95-99 76 40 40-54-54-99-
23
0
0
11
15
12
35
2
43
20
4
18
5
97
14
39
25
55
72
31
99
105

TABLE 66 CONTINUED
Declination
dec\ra 0123456789
90 0 0 0 27 27 58 99 41 7 -3
85 -59-85-91-34 2 20 8 4 6 6
80 1-25-38-25 -5 4-13 -141
75 24 8 16 20 42 37 32 75 28 -8
70 -47-43 5 -1 19 6 5 16 16 14
65 -10 26 48 51-74-60-56 -5 24 18
60 -14 3 35 48-47-78-63-22 14 3-
55 -43-31 37-14 31-97-21 -8 38-13-
50 -79-26-33-71-39-99-20-35-11-56
45 -51 17 -3-19 32 15 -1-51 -8 18
40 -36-11-38-58-18-31-50-15 28 53
35 -63-58-19 -4-36 10 11 74-35-20-
30 -75-44 2 16 6 36 35 40 -7 -5-
25 31 3 -2-46 -4 13 40 2 -7-30-
20 -9 19 -5-24 95 90 94 21-14-11-
15 -27 29-69-33-18-34 1-15 4 18
10 8-26-77-10-26-68-34 -5 -2 9
5 -84-91-35 49 41 24 33 99-20 1-
0 -31-23 -2 12-37-37-67 0-99 -1
-5 -40-40-98-99-99-99-99 0 0 89
11 12 13 14 15 16 17 18 19 20 21 22 23
-8-87 12 13 13 13 10-70 13 18 20 20 20
-7-51 24 17 18 -9 2-47-19 4 16 20 21
-9 -7 99 31 60-61 38 -8-40-34 2 20 41
-1 19-12-99-64-86 21 17 19 0 25 19 34
2-21 6 26 41 16 17-71 -3 -5 30 -5-30
10-29 2 16 31 22 0-68 -6-13 24 -4 6
4-1 9 -5-81-69-41-13 19-39-17-52 26
-2 46 28 0-95-12 77 99 91-53 -4-51 42
22-25-31-91-99-84-53-41-21-70-13-34 -6
-26-56 -9 32 -6 1 40 57 48-12 17 1-18
13 16 42 34-36-36-38-15-18-16 18 16 1
-55-56-19-37-77 22-23 27-51-13 8 28-22
-25-26 49 41 9 52-13 1-44 -1 -3-66-99
-5 -3 3 31-24-39 -6-19 -1 18 39 24 -1
3-5 7 25 12-16 24 -8-37-54-38-30-11
-37-89-46 16 40 15 -1 -7-38-55-65-53-12
-1-67-34-38-12-70-75-76-45-16-47-33-22
52 -3-13 -4-32-83-96-14-26 19-47-39-99
28 -1-23 20 2 67-13 28-55 -5-55-21-92
50 13-16 17 17 99-99-99-99-99-99 -8-40
10
-8
6
19
-2
7
-8
53
26
-2
7
30
51
12
27
45
-5
1
17
-1
89
1 06

TABLE 67
Corrections Applied to the 0ttw42 50
Right Ascension
dec\ra
0
1
2
3
4
5
6
7
8
9
90
0
0
0
99
99
65
-4
-4
15
26
85
22
27
28
60
96
77
29
18
29
42
80
11
13
15
15
7
16
3
12-
-11-
-23-
75
7
0
-4
-8-
-13-
-18-
-36-
-28-
-19
-5
70
42
25
3
-7
0
7
-7
0
27
52
65
24
33
58
24
12
-5
4
9
31
5
60
-8
16
31
21
0-
-27-
-12-
-22
17-
-29
55
0-
-11
-8
15
-5-
-29
-2
-9
13-
-35
50
7
43
19
13
4
5-
-20
4-
-52
19-
45
-10
21
3
-7-
-23-
-12-
-40-
-48-
-99
15
40
-27-
-25-
-13
2-
-17-
-15-
-31
4-
-11
20
35
27
28
2
25-
â– 29
1-
-10
24
-5
-6-
30
-31
33
1
44-
-44
20
13
21
14
13
25
-29
22
0
25-
-23
-4
47
28
22
10
20
56
37
25-
-12-
-29-
-84
15
-4
3
-4
15
18-
-21-
-41-
-15
14-
-16
24-
-11
-1
-2
10
-1-
-40-
â– 38
-1
2-
-22
11
21
4-
-14-
5
67
4
5-
-14-
-24-
-22
23
99
56
12
0
20
5
4-
-27-
-25-
â– 31-
-22
15
11-
-21-
-5
-4
56
34
21-
-23-
-31-
-55-
-28-
-17-
-45-
11
12
13
14
15
16
17
18
19
20
21
22
23
29
29
7
7
7
7
7
10
4
1
1
1
1
36
21
15
8
10
-2
9
-7
1
-2
-1
1
1
0
10
44
16
24-
-10
15-
-14
-8-
-15-
-11
2
0
2
3
71
64
54
8
-7-
-31-
-26-
-11-
-14
1
0
14
6
7
0
-6-
-10-
â– 28
10
20
32-
-14
-1
3
-21
6
-2
0-
-19-
-23-
-27-
-10
5
14-
-25-
-27-
-22
-18
2-
-11
3
47
34
20-
-17-
-12-
-11-
-33
-7-
-38
-8-
-16-
-65-
-98-
-34
-8
5
4-
-29
5
-3
70
-2
-4-
-29-
-16-
-27-
-10
-8
-5
11
40
-4
6
16
10
55
11
-4
7
33
57
67
68
84
13
31
25
18
39
42
-3
19
37
63
50
18
14-
-15-
-10
4
12
-19
28-
-12
9
2
25
7
2
21
-2-
-11
-1
43
12
74
20
27-
-34
-3
5
29
48
34
43
32
55
48
38
-7
27-
-22
-3-
-38
-5
18
48
54
37
45
14
5-
-15
-6
5
37
10
27
35
14
11
18
45
19
67
47
9-
-29-
-35
18-
-16
35
-9-
-24-
-44-
-11
-26-
-17-
-23-
-11-
-23-
-31
7
-9
78
15
31
-2
8
-34-
-28-
-32
25
26
48
-3-
-17-
-25-
-21
18
9
22
-34-
-21-
-36
6-
-24-
-21-
-19-
-27-
-18-
-37-
-41-
-50-
-46
-6
28
24
18-
-41
-9
53
82
76
-9-
-88-
-87-
-48
10
31
40
19
-6
14
0
35
4
16
34
21
26
32
31
-9
16
13
-4
37
40
1 07

TABLE 67 CONTINUED
Declination
dec\ra
0
1
2
3
4
5
6
7
8
9
90
0
0
0
99
99
99
51
2-
-19-
-27-
85
-17
2
1
53
99
86
23-
-17-
-30-
-32-
80
-30-
-22-
-30-
-21
9
57
54
16
42
61
75
-34
5-
-14
27
-5
34
77
54
44
22
70
-30
35
79
90
-1-
-15
4
6-
-18-
-21
65
-5
1
9
23
8-
-29-
-53-
-70-
-56-
-18
60
11
-4
-4
9
9-
-19
2
4
36-
-10
55
-32-
-16-
-17
35
26
53
46
10
7-
-36
50
-60-
-53-
-17
17
-7
24
9
19-
-17
5
45
-8
2
21
34
66
65
64
28
-2-
-33-
40
76
99
71
49
87
86
96-
-14
21
15
35
37
-2
26
18
57
4-
-13-
-73-
-38-
-27
30
9
-2
41
38
40-
-26
9-
-19-
-16-
-25
25
4
18
39
37
85
67
99
30-
-40-
-11-
20
40
42
60
17
60-
-17
26
61
52
75-
15
1-
â– 22
1-
-20
47-
-29-
-23
47
82
0-
10
-30
43-
-14
32
63
45
77
88
92-
-26-
5
-68
38-
•36
25
99
99
99
62
50
36
0
-13
15-
-70-
-99-
-44-
-29
46
7
6
12
-5
94
99
49
51-
â– 75-
-48-
-31
44
21
32
11 12 13 14 15 16 17 18 19 20 21 22 23
-33-82 22 23 23 23 1-99-72 10 38 50 50
-48-67 32 5 11-54-38-99-99-51 22 48 47
-5-47 97-42 8-99 39 -9-12 13 96 42 37
20 18-17-45-48-27-35 -6 46 99 99 34 27
44 68 42 52 42 53-25 50 22 53-14 -5 -2
-5 30 8 19 28 50 47 71-57 5-19 19 34
-92-31-71-41-99-87-99-27-99-76-19 3 41
27 52 -1 22-92-28-99-99-99-22 -1-35 -4
50 -9-70-79-26 25-35-12 11 19 27 10-24
-55-18-54-18 89 46 72 31 61 40 51 47 21
34 43-27 15 20-16 0 10 45 27 8 28 68
7 63-17 63 -5 -1 -7 13 30 -4-49-20 39
-10 45 -9 64 13 26-55 22 24 55.12 24 19
-22-37-93-39-36 5-67 -8 20 83 56 29 13
27 43 52 99 44 33 30 7 52 50 28 21 16
-20 42-13 17-67-14 0-21 22 3 -7-10-13
-21 22 30-34-51 -7 29 13 48 -5 39 4 35
50 66 81 26 27 -8 4 -5 26 16 61-13 31
-33-16-70 0-26-38 1 24 40 1 19-28 29
25 46-40 40 8-22 -9 3 43-15 -8 35 86
10
32
37
21
13
49
42
17
17
21
19
64
22
-7
46
17
44
34
41
44
86
108

TABLE 68
Corrections Applied to the Konl7 25
Right Ascension
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
60 -40-99-99 71 99 99-99-99-99-95-47-61-99-21 6-99-99-23-24-99-99 99 81-64
55 -48-49-58-53-42-84-55-58-18-60-35-32-95-59-41-40-54-82-54-73-25-86-60-61
50 -35-15-50-43-39-38-63-74-63-80-59-76-58-78-68-71-43-90-34-68-46-18-16-54
45 99 99-99 20 59-17-77-99-99-99-99-99-85-99-99-99-41-99-99-99-99 0-99 35
Declination
dec\ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
60 59 99 99-76-93-53 99 99 99 12 33-27-99-99-99 99 99 99 -8 17-99-99 99 99
55 -5-32 30 -4 1 28-68-45 33 37 6 6 39 30-72 8 35 35 9 43 14-42-13 62
50 49 24 39 31 35 42 68 38 26 14 49 47 67 43 61 99-15 44 46 32 54 54 19 69
45 46 45 99 0-99-99 6 99 36 64 99 22 45-94 3 99-17 2-58-99-99 0 99 99
109

CHAPTER IV
RESULTS
Residuals Between the Two Versions of the NIRS
After I compiled my version of the NIRS, I compared my
positions and proper motions to those in the original
version compiled by Corbin. I computed position and proper
motion residuals in the sense Corbin minus Cole. Figures 1
through 4 give the distributions of these position and
proper motion residuals. The one sigma dispersions of these
residuals are .02 and .03 arcseconds for right ascension and
declination respectively and 0.16 arcseconds per century for
both proper motions.
The absolute value of all of the position residuals were
less than 0.35 arcseconds with 95 percent of them being less
than 0.05 arcseconds. One "pathological" case arose with
the proper motions in right ascension, however. AGK3R
number 10314 indicated a difference in proper motion in
right ascension between the two versions of the NIRS of 166
arcseconds per century. This was rather alarming since the
next largest difference was only four arcseconds per
century. Referring to the original independent catalogue
data, I noted that this proper motion was computed on the
basis of two observations, those of the AGK3R and the Buch
110

of Stars No. of Stars
1 1 1
Figure 1: Distribution of Right Ascension Residuals,
Corbin minus Cole in arcseconds
Figure 2: Distribution of Declination Residuals,
Corbin minus Cole in arcseconds
.2

No. of Stars No. of Stars
112
Figure 3: Distribution of Proper Motion in Right
Ascension Residuals, Corbin minus Cole
in arcseconds per century
Figure 4: Distribution of Proper Motion in
Declination Residuals, Corbin minus
Cole in arcseconds per century
2

113
50, whose epochs were separated by only 0.028 years! With
this separation in epochs a position difference of 0.05
arcseconds between the two ICs would result in a proper
motion difference of 178 arcseconds per century. By the
criterion that two position proper motions should have
epochs seperated by at least 28 years, this proper motion
should not have been included in any NIRS catalogue. Thus,
for the purposes of comparing the two versions of the NIRS,
this proper motion in right ascension was not included.
Tables 69 through 72 give mean values of the residuals in
position and proper motion, in the sense Corbin minus Cole
as a function of right ascension and declination. These
were averaged over blocks one hour of right ascension by
five degrees of declination and the units are hundredths of
arcseconds. The last column on the right of each table
gives mean residuals averaged over zones of declination five
degrees wide while the last row for each table gives mean
residuals averaged over bands of right ascension one hour
wide. The final number on the bottom of the right hand
column of each table gives the overall mean of the
residuals. The right ascensions as well as the proper
motions in right ascention in figure 1 and 3 and table 69
and 71, as with all figures and tables involving right
ascension, have been multiplied by the cosine of the
declination.

TABLE 69
Mean Right Ascension Residuals, Corbin minus Cole
units
dec/ra
of "
0
.01
1
2
3
4
5
6
7
8
9
10
90
-4
-3
0
2
0
-5
0
3
0-
â– 12
0
85
0
-1
0
1
2
-2
-1
-2
-1
-2
2
80
2
3
4
2
-1
-4
1
0
2
1
3
75
-1
1
4
-1
-3
-5
-1
0
2
2
1
70
0
-2
0
-2
-2
-4
-3
-2
0
-2
-1
65
4
5
6
2
0
-2
0
-1
-1
-3
0
60
0
2
1
-4
-2
-1
0
-1
-1
0
1
55
-2
0
0
-1
0
1
1
0
1
2
0
50
-1
-1
-1
0
3
1
-2
-1
0
-1
-1
45
-1
-2
-1
2
0
-2
-2
-2
-4
-2
0
40
-3
0
1
2
0
3
1
-1
-3
0
2
35
-2
0
1
2
3
4
2
4
2
1
-1
30
-2
-5
-1
2
1
-1
-2
2
1
1
-1
25
-1
-2
1
2
2
1
2
2
0
-1
-1
20
1
0
0
-1
0
1
2
1
0
-1
-1
15
0
-1
-2
-3
0
1
1
0
-1
-2
-1
10
-1
-1
0
0
1
1
-2
-2
-4
-2
-1
5
3
2
1
0
2
3
0
-1
-2
-3
-2
0
2
1
-1
0
3
4
2
2
0
-2
-1
-5
1
-3
-3
-1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
12
13
14
15
16
17
18
19
20
21
22
23
21
0-
10
0
-2
0
-5
0
3
6
0
-4
0
3
-2
-4
-4
-3
-5
-7
-6
2
5
4
3
1
6
-1
0
1
1
1
-1
0
0
0
-2
3
5
1
-2
0
2
1
-2
0
1
2
-1
-4
1
3
-4
-1
2
0
0
-1
0
2
-1
-2
-2
-1
0
-1
2
4
0
1
-1
1
5
2
1
0
-1
1
-4
-3
1
1
2
-1
1
2
1
1
0
-1
-1
-1
-1
-2
0
2
1
1
0
1
-1
-2
0
0
-1
1
-1
0
-1
0
0
0
-1
3
-1
2
0
-1
-1
-1
0
-2
-1
-3
-1
-3
0
-1
1
0
1
1
0
1
-1
0
-2
-1
-1
1
1
2
-1
1
1
0
2
3
6
5
2
2
1
2
2
1
-1
-1
1
2
1
0
-1
-7
-3
-2
4
0
-1
-1
0
-1
-2
-1
0
-3
-8
-5
-2
2
2
1
1
2
3
1
0
0
-2
0
0
0
1
2
3
-2
-1
1
0
-2
-3
-2
-1
0
-2
-1
-1
-1
1
1
1
-3
-2
-2
-1
0
2
-1
-1
-4
-2
-2
1
0
-2
-2
0
2
1
-2
-3
-3
-2
1
-1
1
-1
-2
-2
1
1
2
0
-1
-2
1
2
-1
-1
-2
0
3
5
2
0
0
1
3
4
2
0
0
0
0
0
0
0
-1
0
0
0
0
0
-2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
114

TABLE 70
Mean Declination Residuals
units of ".01
dec/ra
0
1
2
3
4
90
-3
5
6
0
0
85
-9
-3
3
-3
-5
80
10
4
5
3
5
75
10
5
2
-2
0
70
2
-3
-5
-3
-2
65
1
-1
0
2
-1
60
4
-1
2
3
-1
55
2
1
1
0
1
50
5
2
1
0
3
45
1
-1
-1
0
0
40
-1
-1
0
0
0
35
2
1
0
-1
0
30
0
-4
-6
-2
-1
25
-1
-1
-2
-2
-3
20
-1
1
1
0
-2
15
1
2
1
0
0
10
1
4
2
1
-1
5
1
3
1
1
-1
0
-1
3
0
0
2
-5
2
9
7
5
1
0
0
0
0
0
6
7
8
9
10
11
12
0-
â– 39
0
3
1
9
0
-7
-1
-8
1
-2
2
1
-3
-1
-2
-1
-4
-3
-3
2
2
1
2
2
5
2
-1
0
-2
2
0
2
-1
-4
-1
-6-
10
-9
1
1
0
3
-1
-3
-1
1
-3
0
4
2
-1
-1
-1
-1
-2
-1
2
3
4
0
-3
-1
-3
0
0
2
4
0
1
-1
-2
-2
-1
2
-1
4
5
1
0
-1
1
1
5
2
-1
1
-1
2
0
2
-2
-2
-3
-3
-1
2
4
2
1
1
2
5
3
1
0
-1
0
-1
1
2
0
1
-2
-3
-4
-4
-2
1
2
0
0
-1
-1
-2
2
0
0
-3
-4
-3
1
-3
-3
0
-2
0
1
1
0
0
0
0
0
0
0
5
9
3
2
4
1
3
2
1
2
3
0
0
2
1
3
1
2
1
2
2
0
Corbin minus Cole
13
14
15
16
17
18
19
20
21
22
23
-9
0-
12
0
-4
0
1
-3
0
13
0
2
-4
-2
-3
-5
-5
-2
5
3
1
4
-5
0
-1
2
5
5
5
4
3
0
2
7
6
0
0
2
3
2
2
-2
-4
-1
3
0
0
0
-3
0
-1
1
0
-1
1
-2
-5
-6
-3
0
-1
0
1
1
1
1
0
0
-6
-2
1
0
-5
-1
3
1
0
-1
0
1
-2
3
3
0
-4
-1
3
0
0
-2
0
3
2
5
0
0
-2
-2
-1
-3
-3
0
0
3
3
2
3
0
-1
-2
-2
2
0
2
1
1
1
0
1
0
-3
-3
-1
1
-2
2
5
2
-1
-2
-2
0
1
0
2
3
0
0
2
1
3
3
3
0
1
1
0
-4
-5
-3
5
1
2
1
2
0
2
1
1
-1
-2
-1
2
2
1
-1
-1
0
2
1
2
1
1
2
0
2
2
2
-1
0
1
1
0
-1
1
3
0
1
1
0
3
0
-3
-2
-4
-6
-4
-1
-1
-1
0
1
4
0
0
2
-1
-3
-1
2
1
0
1
-1
2
0
3
3
3
2
2
-1
-5
-7
-6
-9
-3
0
0
0
1
-1
0
-6
-8
-2
-3
-8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 1 5

TABLE 71
Mean Proper Motion in Right Ascension Residuals, Corbin minus Cole
units of ".01 / century
dec/ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 29 0 -1 22 0 13 0-3 0 38 21174 0 49 0-30 0 37 0-10-57 0-75 0 -12
85 2 4-13 9-4 4 5 13 13 3-15 0 19 21 5 1 16 44 35 4-29-31-35 -9 0
80 1 -6-21 -2 10 23-2 2 5 3-20-16 4 14 -6 -6-11 9 2 -5-14 -8-28-24 0
75 30 11-13 14 21 24 2 2-11-21-14-19 4 -4-18 -3 22 16 4 -7 -7 0-21 -8 1
70 6 13 20 14-10-18 -8 -6-11 -1 -3 7 5-19 -1 8 9-1 3 4-17-29-12 5 0
65 -21 -797 6-14-27-32-24-12-11-12 -5-9 7 1 -8-19-21 -7-19-36-24-14 -1
60 -7 -6 6 10 10 -9-11-19 5 -7 -7 -4 8 12 19 11 10-18-17-10-14-14-11 -2 0
55 1 -4 -4 -1 16-17 -5 3 15 -2 0-7 0 9 10 0 1-11 -3-20-12 93-1 0
50 -15 2 3 6 7 3 8 9 14 -4 -6 -5-18 -4 -6 -3 0-32 -2 1 17 5 -1-10 -1
45 -11 10-25-14-17 -8-17 -2 2 -3-19 -6-15 -6709 -9-14 -6 -8-21-16-18 0
40 -10 -6-21 -9 -6 13-3 4 1 12 -5 19 6 9 22 2 -4-16 -9-10-15 -293 0
35 -19-19 0 17 -1 6 3 -7-25 -4-2 6 6 21 25 -7-4-6 0 8 2 17 -8-11 -1
30 -13 -4 6 -8 -2 16 28 -1 -6 -9-10 3 3 -5-10-11-12-25-24-16-11 4-40 -1
25 -6 0-1 0-7 0 -4 -9 -3 -3 -4 -2 -3 13 14 -4-21 -6 5 -2-12 -3-16-10 0
20 -4 -2 4 4-11 -1-7 5-7-5 1 2 2 19 2 -8 -4 11 15 -2 -5 -5-11 -8 0
15 -9 -6 -2 -9 -2 18 1 0-24-32-11 5 -1 -6-13 5936 -4-21 -9 -5 -6 0
10 3 -8 -8-11 -4 20 -3-17-14-13 -8 -3 -7 -7-14 -6 4 3 9 14 11 6 1 6 0
5 0-4-1 10-12 9 -2 -8 -2 -4 1 -4-12 -5 -2 -1 -7-7 0 4 20 4-11 -3 0
0 -4 12 15 19 8 7 9 -5 11 3 -8 -2 -7 -5 0-8 3 0-17-21 9 8 -2-13 0
"5 08233-4-3-9 -3-11 2701 -6-17 3 13 14-21 5 14 20 1 0
-1-1-1 1-1 02-1 000 1-1 0-1 00-1-2 02 0-1-1 0
CTi

TABLE 72
Mean Proper Motion in Declination Residuals, Corbin minus Cole
units of ".01 / Century
dec/ra 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
90 -7 24-4 1 0 66 0131 0 20 13 17 0 20 0 34 0 -4 0 66 69 0 54 0 9
85 -3 3 4 2 2 46 3 13 11-11-26-28-46 26 62 37 -4-12 13 36 31 8-10-19 0
80 56 18 9-36-43 -3 16 4-17-18-32 -8-14 13 8 10 1-16 2 27 6-35-31 10 2
75 79 31 9 10 18 19 28 7-5 6 17 -6 2 4-36-10 16 5 -1 23 9-16 -4 38 4
70 -13 7 0 12 23 22 24 7-17-42-17-17 8 15-15 -2 8-19-35-31 -2 30 -5-16 -1
65 -16-12-27-23-14-13 1-7 0 2 10 -1 4 1 -3 10 7-13-15-10 21 32 16-11 -1
60 10 13 9 -2 0-12 64-2 -9-29 5 12-18-25 -6 -3-30-14-16 225-4 0
55 17 11 10 13 4 -1 0-28-16 4 8 15 10 2-6 2 1-11-19-13 8 12 23 32 1
50 41 -7-14 0 1 -9-29 -3 31 14 25 14 6 -7 -9 1-25-29-31-11 11 10 8 0
45 8 25 12-12 -1 4-13-19 -6 9-11-14 02 2 9 1-6 -3-21-25-11 -40 0
40 13 16 7 5 9 15 -1 2-17-11 -4 9 15 24 26 17 -6 -8 -6 10 3 8 11 18 0
35 -24-16 -905 3-23 -4 -2 5 -7 7-13 -9-11-12-16 -9-13 -6 9 1-8 -4 -1
30 1 14 1 -9 9 34 14 27 9 7 0 4 10 7 -1 -9 8 7-19-22-10 -7 15 11 0
25 1-3-8-5-22-3-2343-4002 -2 -3 -4-23-20-20-22 93 0
20 4 -5-10-10 1-10-15-11 -9 12 15 -1 -5 -1 -3 -7 -1 -1-11-13 -7-13 -1 12 0
15 20 19 10 10 4-2 7 -3 -5 -2 -6 -4 1 19 23 18 11 -4 -6 7 21 19 19 10 1
10 9 10 2 5-12-13-21-15-18-25-16-16 -7 1 7-1 7 7-1 -6-17 0 -5-12 0
5 1 5-12-14 -5 16-3 8-6 4 6 -7 -3-10-13 -2 -8 -7 3-13 2330 0
0 5 1-10-22-17 -2 -3 6-6 7 16 7-14 -7 4 17 -7-20-18-21 -4 -5 -3 -7 0
-5 -12-27-12-40-16-10 -8 -5 -7-13-17-27-27-37-34 -6 2 -6-24-31-36 -5 -1-20 0
2 -1 100010000100200 -1 -1 -1 0010 0

118
Overall, the systematic differences between the two
versions of the NIRS are not significant in the sense that
these differences are not larger than the uncertainties
associated with each catalogue. That is, the dispersions of
the residuals are smaller than the mean rms errors of the
associated quantities. But there are significant
differences when one considers the precision and accuracy of
the positions and proper motions of the two catalogues.
Internal Errors
The qualitative concept of the precision of a parameter
is generally associated with the variance of that parameter.
The rms error is the accepted least squares estimate of the
square root of the variance of a parmeter. The rms errors
for the positions and proper motions of a star are given by
the square roots of the quantities in equation (21) of the
previous chapter. In my compilation of the NIRS, 17433
stars had three or more independent right ascention
positions and 17467 stars had three or more independent
declination positions, enabling rms errors to be calculated
for these positions and proper motions. For comparison,
Corbin had 17682 stars with three or more right ascension
and/or declination observations. Table 73 gives the mean of
my rms errors as compared to those of Corbin. The
uncertainties of these means are .00035 and .00037
arcseconds for right ascension and declination, respectively

119
and .0022 and .0023 arcseconds per century for proper motion
in right ascension and declination, respectively. The
reduction of mean rms errors is shown to be between 5 and 7
percent.
TABLE 73
Mean RMS errors
Right
Ascension
!!
Declination
M
RA
Proper
Motion
"/century
Dec
Proper
Motion
"/century
Corbin
NIRS
0.075
0.087
0.45
0.46
Cole
NIRS
0.072
0.082
0.42
0.44
The distributions of these rms errors are given, for both
versions of the NIRS, in figures 5 through 8.
It is well known (cf. Firneis and Firneis 1975) that the
formal, internal errors of a process of data reduction are
very dependent on the model, the assumptions of that model
and the method of solution used. Thus one typically
encounters discrepancies between the internal and external
errors of various derived sets of statistical parameters.
Consider for example the decades-long controversy over the
value of the Hubble constant. Two sets of investigators
using different methods have arrived at two estimates for

No. of Stars No. of Stars
1 20
Figure 5: Distribution of Right Ascension RMS
Errors in arcseconds
Figure 6: Distribution of Declination RMS Errors
in arcseconds

No. of Stars No. of Stars
1 21
Ascension RMS Errors in arcseconds per
century
Figure 8: Distribution of Proper Motion in
Declination RMS Errors in arcseconds
per century
t

122
this parameter, but the difference in their estimates is
almost an order of magnitude larger than the rms error of
either estimate.
But when one compares two investigations which use the
same model, the same assumptions concerning that model and
the same method of obtaining estimates, the rms errors
become a valid basis for that comparison. The NIRS which I
have compiled does have rms errors which are significantly
smaller than those of Corbin.
Perth 70 Residuals
The real test of my research comes in the form of
predicting future observations. The Perth 70: A Catalogue
of Positions of 24900 Stars (Perth 70) (H$g and von der
Heide 1976) is a catalogue with a mean epoch of 1970, 26
years later than the mean epoch of the NIRS. I was able to
match 3324 stars of the Perth 70 with the NIRS. I then
predicted the Perth 70 positions and computed residuals with
the two version of the NIRS. It should be noted that the
portion of the Perth 70 which I was able to match has a
density of about one star per square degree from -5 degrees
to +5 degrees, but only about one star per fifteen squares
degrees north of +5 degrees.
Table 74 gives the one sigma dispersion of the position
residuals between the Perth 70 and the two versions of the
NIRS.

123
TABLE 74
Position Residuals, Perth 70 minus NIRS
Mean
residuals
Dispersion
RA
DEC
RA
DEC
Corbin NIRS
" .057
".084
" .215
" .300
Cole NIRS
" . 058
" .064
" .211
" .302
Significance level
of difference
43%
0.3%
14%
35%
First iteration
of 6317 stars
" . 045
" .048
" . 196
" .304
Under the assumption that the residuals are independent
and normally distributed random variables, certain
conclusions can be drawn. The differences of the mean
residuals in each coordinate, divided by the square root of
the sum of their estimated variances, form t statistics with
which the significance of these differences can be
determined. The decrease I have achieved in the mean
declination residual is quite significant while the increase
in right ascension residual is not.
At this point it might be asked if these mean residuals
are due to the system of the NIRS or that of the Perth 70.
An indication of how much of the mean residual is due to
each of the systems can be found using the first iteration
of my NIRS which included only those ICs which could be
directly compared to the FK4. The first iteration catalogue

124
of 6317 stars was compared to the Perth 70 and it is seen
that my mean declination residuals are closer than Corbin's
to this first iteration system which more accurately
represents the system of the FK4.
Another test of significance can be preformed if it is
also assumed that the residuals have a zero mean. In this
case, the ratios of the squares of the dispersions in each
coordinate form F statistics. While the increase in
dispersion of the declination residuals is not significant
at the 35 percent level, it is not quite as clear that the
decrease in dispersion of the right ascension residuals is
significant at the 14 percent level.
The distribution of position residuals between the Perth
70 and the two versions of the NIRS are given in figures 9
and 10. The most apparent feature of these figures is the
reduction of mean declination residuals which I have
achieved.
Mean position residuals between between the Perth 70 and
the two versions of the NIRS as a function of right
ascension and declination are given in tables 75 and 76.
These were averaged over blocks one hour of right ascension
by five degrees of declination and the units are hundredths
of arcseconds. The last column on the right of each table
gives mean residuals averaged over zones of declination five
degrees wide while the last row for each table gives mean
residuals averaged over bands of right ascension one hour

No. of Stars No. of Stars
125
Perth 70 minus NlRS in arcseconds
-2 -1.5 -1 -.5 0 .5 1 1.5 2
Figure 10: Distribution of Declination Residuals,
Perth 70 minus NIRS in arcseconds

126
wide.
The
final
number on
the bottom of
the
right
hand
column
of
each
table gives
the overall
mean
of the
residuals.
When
examining
these tables
it
must
be
remembered that the blocks north of +5 degrees have at most
two or three stars and often none. Therefore these means
north of +5 degrees are often based on one or two positions.

TABLE 75
Mean Right Ascension Residuals, Perth 70 minus NIRS
Perth
70 minus Corbin,
units
of
• It
01
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0
-3
0
0
0
-6-
21
0
14
3
0
0
0-
-11
0-
-34-
â– 38
0
0
-7
0
0
0
0
-12
30
0
0
0
-8
-7
0
0
4
15
5
-1
-6-
â– 11
15
-6
44
4
0
0
0
0-
â– 32
0
0
-2
25
-10
2
3
-4-
â– 44
13-
12-
14
-1
0
0
-4
-2
0
42-
â– 32
0
0
0
-1
0-
â– 38
0
0
-9
20
0-
17
0
11
0
-4
0
0-
19
-9
0-
â– 11
30-
-22
-5-
-30-
•28
14
0-
â– 31
12
6
0
0
-5
15
-16-
24
0
37
20
0-
21
-2
14
-1
3
0
0
0-
•11
0
13
-1
0
2-
â– 21
5
4
0
-1
10
-21
1
26
0
0
3
0
-8
0
0
8
1
9
-8
0
0
8-
20
0
13
18
11
-4-
26
1
5
-1
0
9
8
12
5
5
2
11
6
6
11
-3
0
-5
0
-3
2
-2
4
12
0
6
1
4
0
-1
3
5
11
5
8
3
12
10
8
16
6
8
-1
3
4
0
8
2
5
7
4
2
2
5
-5
1
5
5
9
14
13
10
15
15
24
22
14
12
13
8
10
-1
13
8
14
5
1
2
-2
10
-1
2
6
9
8
8
4
9
12
11
14
8
6
3
2
4
-1
7
2
6
8
2
3
0
6
Perth
70 minus Cole
!, units of "
.01
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0-
11
0
0
0
-6-
20
0
5
11
0
0
0-
-18
0-
-37-
â– 37
0
0
-8
0
0
0
0
-14
30
0
0
3
-7
-3
0
0
5
10
2
-7
-1
-6
18
-4
33-
â– 14
0
0
0
0-
•34
0
0
-3
25
-4
-3
5
-4-
â– 48
12-
16-
13
-5
0
0
-9
9
0
26-
â– 35
0
0
0
-2
0-
â– 44
0
0
-10
20
0-
17
0
11
0
2
0
0-
20-
13
-1
-9
32-
-23
-9-
-31-
â– 20
11
0-
•34
15
2
0
0
-5
15
-20-
21
-3
30
14
0-
21
4
10
-4
-3
0
0
0
-9
0
11
3
0
5-
â– 22
2
-1
0
-3
10
-24
2
24
0
0
6
0-
14
0
0
8
4
16-
-10
0
0
8-
â– 21
1
21
24
14
-9-
•25
2
5
1
1
11
12
14
10
6
1
10
3
4
6
-5
-2
-8
-3
-4
1
0
1
14
-2
3
1
3
0
-1
5
8
15
10
14
8
12
12
6
13
3
7
-4
1
0
1
9
-1
-1
8
6
3
1
6
-5
2
4
3
9
18
14
11
13
13
22
22
14
11
10
8
10
5
18
10
10
7
7
10
-1
11
0
3
8
12
12
13
7
8
11
9
12
6
5
0
0
1
0
9
2
2
9
2
4
0
6
127

TABLE 76
Mean Declination Residuals, Perth 70 minus NIRS
Perth 70 minus Corbin, units of ".01
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0-
11
0
0
0-
11
7
0
49
-2
0
0
0
18
0-
30
14
0
0-
â– 20
0
0
0
0
30
0
0
2-
38
-5
0
0
33-
â– 38
48
11-
•24
0
15-
â– 17-
13
0
0
0
0
0
14
0
0
25
-21-
53-
â– 10
14-
21-
67
-9
4
17
0
0-
â– 25
7
0
-4-
51
0
0
0-
â– 46
0
-8
0
0
20
0-
99
0
-6
0-
12
0
0
15-
â– 15
23
24
0
22
47-
16
9-
49
0-
â– 18
18
22
0
0
15
44
18
36
42
22
0
36
-3
-3
77
68
0
0
0
30
0-
16
59
0
38-
â– 39
42-
32
0
10
-19
56-
â– 27
0
0-
46
0
12
0
0-
â– 16
-6
13
14
0
0
9
-5-
34-
â– 23-
â– 35
15
38-
18
5
-12
-8
-1
-3-
10
9
2
2
7
2
13
19
16
8
6
6
5
-4
17
7
2
-6-
â– 12-
13
0
14
19
21
12
13
19
15
11
9
18
20
12
8
9
1
-1
7
5
7
4
11
5
9
11
-5
13
24
8
-8
5
16
19
-8
22
13
22
14
12
16
7
13
13
9
6
17
12
-1
8
11
6
11
12
2
5
14
13
5
12
13
19
13
11
11
4
3
7
3
9
7
8
1
3
4
Perth
70 minus Cole
¡, units of .
.01
dec/ra
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
35
0-
â– 11
0
0
0-
15
18
0
48
7
0
0
0
27
0-
•42
8
0
0-
-18
0
0
0
0
30
0
0-
-11-
â– 33
16
0
0
34-
-40
52
15-
-11-
â– 16
14-
â– 18-
16
-7
0
0
0
0
21
0
0
25
-20-
â– 58-
-15
11-
29-
â– 71-
-15
-2
25
0
0-
-14
13
0
7-
â– 47
0
0
0-
-61
0-
-11
0
0
20
0-
â– 99
0
-8
0
-6
0
0
21
-9
33
26
-2
18
59-
â– 15
5-
â– 48
0-
-15
14
20
0
0
15
47
27
31
42
21
0
39
-1-
-11
78
73
0
0
0
35
0-
â– 16
65
0
46-
-38
48-
â– 22
0
10
-12
63-
-30
0
0-
â– 52
0
9
0
0-
-20-
-13
9
12
0
0
12
-5-
â– 41-
-26-
â– 38
15
34-
•16
5
-11
-4
-5
-7-
â– 13
14
2
7
6
3
15
18
14
5
4
4
0
-7
18
4
2
-5-
â– 12-
â– 12
0
13
22
19
7
10
20
17
12
8
17
21
11
6
10
6
6
6
1
0
-6
3
-2
-1
7
-5
12
28
11-
â– 10
2
12
15'
-12
21
8
18
9
5
7
-1
13
12
6
-7
2
0
-7
0
6
6
15
10
-2
3
15
13
6
11
12
19
11
8
8
4
7
5
0
3
-2
2
-3
-4
1
2
-2
19
3
28
-5
2
11
11
8
4
0
â– 20
5
31
-7
2
9
7
6
128

CHAPTER V
CONCLUSIONS
In investigating the traditional procedures used in the
compilation of star catalogues, it has been seen that the
procedures which were used in the past result in very good
star catalogues. But it has also been shown that the
tabular method does have its shortcomings. The foremost of
these are that not all available model constraints are used
in estimating the model parameters and that the parameter
estimates are biased.
When I first started researching the methods used in
catalogue compilation, I saw what I thought to be oversights
in the data reduction procedures. Now that I have worked
with these large quantites of data and their myriad
idiosyncrasies, I have come to appreciate the difficulties
and compromises involved. What I have referred to as
subjectiveness and craftsmanship is actually a long process
of trial and error. This tedious work of examining results
and subtly modifying procedures produces a catalogue which I
have slightly improved upon with my analytical approach to
catalogue compilation. I have not examined my results at
each stage of the reduction process and modified my
procedures accordingly. Rather, I have started with a
129

130
clear-cut procedure and seen it through without any "mid¬
course corrections." What I have shown is that my
"production line" method is slightly superior to the "hand
crafted" results of the past. With the use of a
simultaneous reduction, one can not only have the a
catalogue which is better than traditional catalogues, but
also the principles and underlying assumptions of the data
reduction process are clearly stated.
The catalogue which I have compiled, like most
astrometric data, is generally most useful in machine
readable form. Therefore, this catalogue is available from
the author on magnetic tape. It must also be noted that the
original version of the NIRS has been available to and has
been used by the the astrometric community for several
years. If one wishes to maintain consistency in astrometric
research, the original version of the NIRS should be
considered for use.

REFERENCES
Bien, R., Fricke, W., Lederle, T., and Schwan, H., 1978,
Methods for the Comparison of Systems of Star Positions
to be applied in the Construction of the FK5,
Veroffentlichungen Astronomisches Rechen-Institut,
Heidelberg, No. 29, Verlag G. Braun, Karlsruhe
Brosche, P., 1966, Representation of Systematic Differences
in Positions and Proper Motions of Stars by Spherical
Harmonics, Veroffentlichungen Astronomisches Rechen-
Institut, Heidelberg, No. 17, Verlag G. Braun, Karlsruhe
Corbin, T., 1974, Base System of Proper Motions for the
AGK3R, Astronomical Journal, 79, 885-899
Corbin, T., 1977, The Proper Motion System of the AGK3R,
Univerity Microfilms, Ann Arbor
Corbin, T., 1982, A Catalog of Mean Positions and Proper
Motions of 20194 AGK3R Stars, Unpublished Manuscript,
U.S. Naval Observatory, Washington
Corbin, T., 1985, Computation of Compilation Catalogs, in
the procedings of IAU Symposium No. 109, Astrometric
Techniques, H. Eichhorn and R. Leacock, Eds., Reidel,
Dordrecht, Holland
Eichhorn, H., 1974, Astronomy of Star Positions, F. Ungar,
New York
Eichhorn, H., 1980, On the Construction of a Comprehensive
General Catalogue of Star Positions, Celestial Mechanics,
22, 127-134
Eichhorn, H., 1982, On Systems of Standards, in Automated
Data Retrieval in Astronomy, C. Janchek and W. Heintz
Eds., D. Reidel, Dordrecht, Holland
Eichhorn, H., 1983, Compilation of Complete Star Catalogues,
Unpublished Proposal to the National Science Foundation
Eichhorn, H., and Cole, C.S., 1985, Problems in Data
Compilation, Celestial Mechanics, 37, 263-275
131

132
Faddeeva, V. N. , 1959, Computational Methods of Linear
Algebra, translated by C. D. Benster, Dover Publications,
New York
Firneis, M. G., and Firneis, F. J., 1975, An Attempted
Explanation for the Discrepancy between Internal and
External Errors in Stastical Adjustments, Astron. Nachr.,
Bd. 296, H. 2
Fricke, W., and Kopff, A. in collaboration with W. Gliese,
P. Gondolatsch, T. Lederle, H. Nowacki, W. Strobel and
P. Stumpff, 1963, Fourth Fundamental Catalogue (FK4),
Veroffentlichungen Astronomisches Rechen-Institut,
Heidelberg, No. 10, Verlag G. Braun, Karlsruhe
H0g, E., and von der Heide, J. in collaboration with von
Fischer-Treuenfeld, J., Holst, G., Loibl, B., Ziegler,
U., Nikoloff, I., and Helmer, L., 1976, Perth 70: A
Catalogue of Positions of 24,900 Stars, Abhandlungen der
Hamburger Sternwarte, Band IX, Hamburg Observatory,
Hamburg
Khrutskaya, E. V. , 1980, On the Evaluation of Material in
Compiling a General Catalog of Stellar Positions, Soviet
Astronomy, 24, 115-118
Lawson, C., and Hanson, R., 1974, Solving Least Squares
Problems, Prentice-Hall, Englewood Cliffs, New Jersey
Schwan, H., 1977, Development and Testing of a Method to
Derive an Instrumental System of Positions and Proper
Motions of Stars, Veroffentlichungen Astronomisches
Rechen-Institut, Heidelberg, No. 27, Verlag G. Braun,
Karlsruhe
Schwan, H., 1985, A New Technique for Analytical
Determination of a Fundamental System of Positions and
Proper Motions, in the procedings of IAU Symposium 109,
Astrometric Techniques, H. Eichhorn and R. Leacock Eds.,
D. Reidel, Dordrecht, Holland
Scott, F.P., 1967, International Reference Star Program
Progress Report, Report from IAU Commission 8, Positional
Astronomy
Scott, F. P., and Schombert, J. L., 1970, The International
Reference Star Program, in IAU Colloquium no. 48, W. J.
Luyten Ed., D. Reidel, Dordrecht, Holland
Smith, C., 1979, The International Reference Star Programs,
Sonderdruck aus Mitteilungen der Astronomischen
Gesellschaft Nr. 48, Astronomisches Rechen-Institut,
Heidelberg

BIOGRAPHICAL SKETCH
I was born in Columbus, Ohio, on September 9th, 1954, to
Lyman and Stella Cole. I was their fourth and last child
having three older sisters. When I was three, my family
moved to rural Pensylvania and, when I was five, we moved to
Rockford, Illinois. I attended St. Peter's Roman Catholic
grade school and graduated from Rockford West high school in
1972.
I began my college education at the University of
Illinois where I was enrolled in a professional
pilot/aircraft maintenance curriculum. I transfered to the
College of Engineering and earned a Bachelor of Science
degree in aeronautical and astronautical engineering in
1978.
I next moved to West Palm Beach, Florida, were I was
employed as a test engineer for Pratt & Whitney Aircraft.
While working for Pratt & Whitney, I was responsible for
full scale engine tests of the TF30, the engine used in F-14
and F-lll aircraft.
I entered graduate school at the University of Florida in
1980 and earned a Master of Science degree in 1983. I had
various outside activities before becoming a graduate
student and I may resume my interest in scuba diving,
motorcycle racing or skydiving after I graduate.
133

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Heinrich Eichhorn, Chairman
Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree gf Doctor of Philosophy.
Howard L. Cohen
Associate Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Frank Martin
Professor of Statistics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of JJogtor of Philosophy.
, \
\
A
i \
/ /KV A
\ John P. Oliver
Associate Professor of Astronomy

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
This dissertation was submitted to the Graduate Faculty of
the Department of Astronomy in the College of Liberal Arts
and Sciences and to the Graduate School and was accepted as
partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
December 1986
Dean, Graduate School

UNIVERSITY no OI n.r-x.
1 -I Oft*» T 1111 1,11 "I II
J 1262 08554 1422



UNIVERSITY no OI n.r-x.
O A Oco Aa'- "" 1111 "I I*
J 1262 08554 1422



PAGE 1

5,*25286 &203,/$7,21 2) 7+( 1257+(51 ,17(51$7,21$/ 5()(5(1&( 67$56 %< &$5/ 67(3+(1 &2/( $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

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nV DGYLFH DQG IRU WKH NQRZOHGJH ZKLFK KH KDV LPSDUWHG WR PH )LQDOO\ RZH PDQ\ WKDQNV WR /HVOLH *LOEHUW IRU KHU SDWLHQFH DQG WKH HPRWLRQDO VXSSRUW ZKLFK VKH KDV JLYHQ PH WKURXJKRXW P\ WHQXUH DV D JUDGXDWH VWXGHQW

PAGE 3

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

PAGE 4

5()(5(1&(6 %,2*5$3+,&$/ 6.(7&+ LY

PAGE 5

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

PAGE 6

&RUUHFWLRQV $SSOLHG WR WKH 3DULV &RUUHFWLRQV $SSOLHG WR WKH *&+ &RUUHFWLRQV $SSOLHG WR WKH %HUO &RUUHFWLRQV $SSOLHG WR WKH *&+ &RUUHFWLRQV $SSOLHG WR WKH 7RXO &RUUHFWLRQV $SSOLHG WR WKH &DSH &RUUHFWLRQV $SSOLHG WR WKH &DSH &RUUHFWLRQV $SSOLHG WR WKH : &RUUHFWLRQV $SSOLHG WR WKH : &RUUHFWLRQV $SSOLHG WR WKH : =2' &RUUHFWLRQV $SSOLHG WR WKH &DSH &RUUHFWLRQV $SSOLHG WR WKH %RUG &RUUHFWLRQV $SSOLHG WR WKH $/% &RUUHFWLRQV $SSOLHG WR WKH 0XQ 22L &RUUHFWLRQV $SSOLHG WR WKH 0XQ 22LL &RUUHFWLRQV $SSOLHG WR WKH .RQ &RUUHFWLRQV $SSOLHG WR WKH 3XON &RUUHFWLRQV $SSOLHG WR WKH 0DGQ &RUUHFWLRQV $SSOLHG WR WKH %HUJ &RUUHFWLRQV $SSOLHG WR WKH $%% &RUUHFWLRQV $SSOLHG WR WKH %XFK &RUUHFWLRQV $SSOLHG WR WKH %RQQ &RUUHFWLRQV $SSOLHG WR WKH $%% &RUUHFWLRQV $SSOLHG WR WKH $%% &RUUHFWLRQV $SSOLHG WR WKH /XQG &RUUHFWLRQV $SSOLHG WR WKH 6WUDV &RUUHFWLRQV $SSOLHG WR WKH &LQ YL

PAGE 7

&RUUHFWLRQV $SSOLHG WR WKH 3).6= &RUUHFWLRQV $SSOLHG WR WKH /XQG &RUUHFWLRQV $SSOLHG WR WKH &LQ &RUUHFWLRQV $SSOLHG WR WKH 0RVFRZ &RUUHFWLRQV $SSOLHG WR WKH 7UL &RUUHFWLRQV $SSOLHG WR WKH %UXVV &RUUHFWLRQV $SSOLHG WR WKH /HLG &RUUHFWLRQV $SSOLHG WR WKH /HLG &RUUHFWLRQV $SSOLHG WR WKH /XQG &RUUHFWLRQV $SSOLHG WR WKH /HLG &RUUHFWLRQV $SSOLHG WR WKH %HUO = &RUUHFWLRQV $SSOLHG WR WKH .RQO &RUUHFWLRQV $SSOLHG WR WKH 7RXO ,, &RUUHFWLRQV $SSOLHG WR WKH 3XON &RUUHFWLRQV $SSOLHG WR WKH /LFN &RUUHFWLRQV $SSOLHG WR WKH /LFN &RUUHFWLRQV $SSOLHG WR WKH 7XULQ &RUUHFWLRQV $SSOLHG WR WKH %RUG &RUUHFWLRQV $SSOLHG WR WKH WWZ &RUUHFWLRQV $SSOLHG WR WKH 2WWZ &RUUHFWLRQV $SSOLHG WR WKH .RQO 0HDQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH 0HDQ 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH 0HDQ 3URSHU 0RWLRQ LQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH 0HDQ 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH YLL

PAGE 8

0HDQ 506 HUURUV 3RVLWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 0HDQ 5LJKW $VFHQVLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 0HDQ 'HFOLQDWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 YLLL

PAGE 9

/,67 2) ),*85(6 ),*85( 3$*( 'LVWULEXWLRQ RI 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH ,OO 'LVWULEXWLRQ RI 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH ,OO 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH 'LVWULEXWLRQ RI 5LJKW $VFHQVLRQ 506 (UURUV 'LVWULEXWLRQ RI 'HFOLQDWLRQ 506 (UURUV 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 5LJKW $VFHQVLRQ 506 (UURUV 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 506 (UURUV 'LVWULEXWLRQ RI 5LJKW $VFHQVLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 'LVWULEXWLRQ RI 'HFOLQDWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 L[

PAGE 10

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

PAGE 11

RI WKH 1RUWKHUQ ,QWHUQDWLRQDO 5HIHUHQFH 6WDUV 1,56f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

PAGE 12

&+$37(5 ,1752'8&7,21 7KH (VWDEOLVKPHQW RI DQ ,QHUWLDO 5HIHUHQFH )UDPH 2QH RI WKH JRDOV RI NLQHPDWLF DVWURQRP\ LV WKH HPSLULFDO HVWDEOLVKPHQW RI D IUDPH RI UHIHUHQFH LQ ZKLFK 1HZWRQnV ILUVW DQG WKLUG SRVWXODWHV RI PRWLRQ DUH YDOLG 7R WKRVH LQYROYHG LQ WKLV HQGHDYRU WZR LPSRUWDQW IDFWV EHFRPH UHDGLO\ DSSDUHQW )LUVW LQ DOO DUHDV RI VFLHQFH ZKLFK LQYROYH G\QDPLFV VXFK DV OXQDU DQG SODQHWDU\ WKHRU\ JDODFWLF G\QDPLFV DVWURQDXWLFV DPRQJ RWKHUV WKH GHWHUPLQDWLRQ RI DQ LQHUWLDO UHIHUHQFH IUDPH WR VRPH UHTXLUHG DFFXUDF\ LV HVVHQWLDO 6HFRQG WKH FRPSOH[LWLHV RI WKH GHWHUPLQDWLRQ RI WKLV LQHUWLDO UHIHUHQFH IUDPH DUH RIWHQ FRPSOHWHO\ LJQRUHG 7KH IDFW WKDW WKH GHWHUPLQDWLRQ RI DQ LQHUWLDO UHIHUHQFH IUDPH KDV EHHQ WDNHQ IRU JUDQWHG LV D WULEXWH WR DOO WKH DVWURQRPHUV ZKR KDYH RYHU WKH FHQWXULHV SHUIRUPHG WKLV LQGLVSHQVDEOH VHUYLFH IRU WKHLU IHOORZ VFLHQWLVWV 7KLV ZRUN KRZHYHU LV QHYHU ILQLVKHG $V VFLHQFH SURJUHVVHV VR GRHV WKH SUHFLVLRQ RI PHDVXUHPHQWV LQFUHDVH ZKLFK LQ WXUQ UHTXLUHV DQ LQFUHDVHG DFFXUDF\ RI WKH VWDQGDUG 'XH WR WKH URWDWLRQDO DQG UHYROXWLRQDU\ PRWLRQ RI WKH (DUWK LW KDV ORQJ EHHQ UHDOL]HG WKDW VWDUV FDQ EH XVHG WR

PAGE 13

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f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f LQ FRQQHFWLRQ ZLWK D VWDU FDWDORJXH LV QRW QHFHVVDULO\ LQHUWLDO UDWKHU HVWLPDWHV IRU WKH SDUDPHWHUV QHHGHG WR WUDQVIRUP WKH V\VWHP WR DQ LQHUWLDO UHIHUHQFH IUDPH DUH DVVXPHG NQRZQ ,I HVWLPDWHV IRU WKH GLVWDQFHV DQG UDGLDO YHORFLWLHV RI VRPH RI WKH VWDUV LQ D FDWDORJXH DUH NQRZQ WKLV LQIRUPDWLRQ FDQ EH FRPELQHG ZLWK WKH SRVLWLRQV DQG SURSHU PRWLRQV LQ RUGHU WR

PAGE 14

HVWLPDWH 2RUWnV FRQVWDQWV RI JDODFWLF VKHDU DQG JDODFWLF URWDWLRQ DV ZHOO DV WKH VRODU PRWLRQ 7KXV WKH NLQHPDWLFV RI RXU 0LON\ :D\ JDOD[\ DUH GHVFULEHG DQG DQ LQHUWLDO UHIHUHQFH IUDPH LV HVWDEOLVKHG $ IXQGDPHQWDO VWDU FDWDORJXH FRQWDLQV WKH SRVLWLRQV DQG SURSHU PRWLRQV RI DW OHDVW VHYHUDO KXQGUHG VWDUV DQG WKHUHIRUH RYHUGHWHUPLQHV LQ D VHQVH WKH V\VWHP ZKLFK LV GHILQHG ,Q OLJKW RI WKLV FHUWDLQ FRQFHSWV UHODWHG WR D FDWDORJXHnV V\VWHP QHHG IXUWKHU FODULILFDWLRQ (LFKKRUQ f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

PAGE 15

LW LV SRVVLEOH WR FRUUHFW WKH V\VWHPDWLF WUHQGV RI HDFK LQGHSHQGHQW FDWDORJXH LQ RUGHU WR EULQJ WKHP DOO RQWR D FRPPRQ V\VWHP 7KLV UHVHDUFK LQYHVWLJDWHV WKH WHFKQLTXHV XVHG WR PRGHO WKH V\VWHPDWLF GLIIHUHQFHV EHWZHHQ WKH V\VWHPV RI VWDU FDWDORJXHV DV ZHOO DV WKH SURFHGXUHV XVHG WR HVWLPDWH WKH SDUDPHWHUV RI WKHVH PRGHOV 7KH ,QWHUQDWLRQDO 5HIHUHQFH 6WDU 3URJUDP 7KH ,QWHUQDWLRQDO 5HIHUHQFH 6WDU SURJUDP ,56f LV D PXOWLQDWLRQDO HIIRUW ZKRVH H[HFXWLRQ KDV UHTXLUHG PRUH WKDQ D TXDUWHU RI D FHQWXU\ ,WV DLP LV WR SURYLGH PRUH WKDQ DFFXUDWH DQG SUHFLVH VWDU SRVLWLRQV DQG SURSHU PRWLRQV RYHU WKH HQWLUH VN\ 6FRWW 6FRWW DQG 6FKRPEHUW 6PLWK &RUELQ f 7UDQVLW FLUFOH FDWDORJXHV IURP DURXQG WKH JOREH DUH EHLQJ FRPSLOHG LQWR FRPSLODWLRQ FDWDORJXHV ZLWK D GHQVLW\ RI DERXW RQH VWDU SHU VTXDUH GHJUHH :LWK WKHVH FDWDORJXHV WKH IXQGDPHQWDO V\VWHP RI WKH )RXUWK )XQGDPHQWDO &DWDORJXH ).f )ULFNH DQG .RSII f FDQ EH H[WHQGHG WR IDLQWHU PDJQLWXGHV VXFK WKDW RYHU VWDU SRVLWLRQV RI DOO VWDUV WR WKH WK PDJQLWXGH FDQ EH WLJKWO\ UHODWHG WR WKH IXQGDPHQWDO V\VWHP 7KH QRUWKHUQ KDOI RI WKLV SURJUDP 1,56f FDQ EH WUDFHG EDFN WR WKH &DWDORJ RI 5HIHUHQFH 6WDUV IRU WKH 'UL WWHU .DWDORJ GHU $VWURQRPLVFKHQ *HVHO,VFKDIW $*.5f 2QH RI WKH DLPV RI WKH 1,56 ZDV WR SURYLGH SURSHU PRWLRQV IRU WKH $*.5

PAGE 16

VWDUV 8QDYRLGDEO\ DQG IRUWXQDWHO\f WKLV DOVR OHG WR LPSURYHG SRVLWLRQV 7KH 1,56 ZDV FRPSLOHG IURP REVHUYHG SRVLWLRQV LQ LQGHSHQGHQW PHULGLDQ FDWDORJXHV ZKRVH PHDQ HSRFKV GDWH EDFN DV IDU DV 7KH FDWDORJXH RI 1RUWKHUQ ,QWHUQDWLRQDO 5HIHUHQFH 6WDUV 1,56f &RUELQ f FRQWDLQV SRVLWLRQV DQG SURSHU PRWLRQV RI VWDUV LQ WKH GHFOLQDWLRQ ]RQH WR GHJUHHV RI DSSDUHQW YLVXDO PDJQLWXGH WR 1,56 ZDV FRPSLOHG IURP LQGHSHQGHQW FDWDORJXHV ,&Vf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

PAGE 17

VWDU SRVLWLRQV EHWZHHQ LQGHSHQGHQW FDWDORJXHV DOVR EH PLQLPL]HG ZHUH QRW XVHG ,Q OLJKW RI WKLV IDFW LW LV DSSDUHQW WKDW EHWWHU HVWLPDWHV RI WKH SDUDPHWHUV DUH DYDLODEOH ZLWK SURFHGXUHV ZKLFK XVH DOO DYDLODEOH FRQVWUDLQWV RQ DOO DYDLODEOH GDWD FI (LFKKRUQ DQG &ROH f

PAGE 18

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

PAGE 19

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f IRU WKH GHULYDWLRQ RI WKH V\VWHPDWLF FRUUHFWLRQV IRU WKDW ,& 6\VWHPDWLF FRUUHFWLRQV DUH WKHQ GHWHUPLQHG IURP WKHVH LQGLYLGXDO FRPSDULVRQV RQO\ 6LQFH WKH VWDU GHQVLW\ LQ D W\SLFDO ,& LV )RU WKH SXUSRVHV RI WKLV UHVHDUFK WKH WHUP V\VWHPDWLF HUURU ZLOO EH XVHG WR GHQRWH WKH V\VWHPDWLF GLIIHUHQFH EHWZHHQ DQ ,& DQG WKH ).

PAGE 20

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f GHILQH DV WKH PHDVXUH IRU WKH V\VWHPDWLF GLIIHUHQFHV WKH VXP RI RUWKRJRQDO IXQFWLRQV %URVFKH 6FKZDQ f DQG WKHQ XVH LQGLYLGXDO SRVLWLRQV LQ D OHDVW VTXDUHV DOJRULWKP WR GHWHUPLQH WKH SDUDPHWHUV RI WKHVH IXQFWLRQV

PAGE 21

2Q WKH RWKHU KDQG D VLPXOWDQHRXV UHGXFWLRQ VHWV XS DOO FRQGLWLRQ HTXDWLRQV LQ FORVHG IRUP DQG VROYHV IRU WDUJHW SDUDPHWHUV VWDU SRVLWLRQV DQG SURSHU PRWLRQVf DQG PRGHO SDUDPHWHUV V\VWHPDWLF HUURUVf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

PAGE 22

,Q WKH VLPSOHVW FDVH RI D WDEXODU PHWKRG ZLWKRXW VPRRWKLQJ WKH V\VWHPDWLF HUURU RI DQ ,& LV FRQVLGHUHG D IL[HG FRQVWDQW LQ HDFK VXEMHFWLYHO\ GHOLQHDWHG GRPDLQ 7KH PRGHO IRU WKH REVHUYHG HUURU RI WKH SRVLWLRQ RI VWDU \ LQ GRPDLQ Y D LV 09 $ S H \ OQ Y OP f \Y 0Y \Y Y ZKHUH S LV WKH IL[HG EXW XQNQRZQ V\VWHPDWLF HUURU LQ GRPDLQ Y QXPEHU Y DQG LV DQ LQGHSHQGHQW DQG QRUPDOO\ GLVWULEXWHG UDQGRP HUURU ZLWK PHDQ ]HUR DQG FRQVWDQW YDULDQFH DA IRU DOO \Y 8QGHU WKHVH DVVXPSWLRQV RQH LQYRNHV WKH SULQFLSOH RI OHDVW VTXDUHV DQG PLQLPL]HV WKH VXP RI DOO ,Q WKLV ZD\ RQH REWDLQV HVWLPDWHV S IRU S DV WKH PHDQ RI DOO $ 9 9 09 Q D Y $ $ S ( Y LQ Y ,9 f Q RI FRXUVH EHLQJ WKH QXPEHU RI GLIIHUHQFHV IRUPHG LQ WKH YWK GRPDLQ $Q XQELDVHG HVWLPDWH V IRU D LV Q Y -O$LYQY3Y f§7Y7 f 6R IDU WKLV LV VWDWLVWLFDOO\ VRXQG EHFDXVH WKH HVWLPDWHV RI WKH V\VWHPDWLF HUURUV DUH XQFRUUHODWHG XQGHU WKH JLYHQ DVVXPSWLRQV 7KH HVWLPDWH RI WKHLU GLDJRQDOf FRYDULDQFH PDWUL[ LV 6 GLDJ6AQ 6QB6Qf PP f

PAGE 23

ZKHUH P LV WKH QXPEHU RI GRPDLQV LQYROYHG LQ WKH SURFHVV 8QIRUWXQDWHO\ WKH PRGHO LQ f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n D f ZKHUH WKH SV DUH DJDLQ IL[HG FRQVWDQWV U LV DJDLQ DQ 89 LQGHSHQGHQW DQG QRUPDOO\ GLVWULEXWHG UDQGRP HUURU DQG WKH DBV DUH VXEMHFWLYHO\ FKRVHQ VPRRWKLQJ FRQVWDQWV ZLWK VPRRWKLQJ RFFXUULQJ RYHU GRPDLQV LQ WKH QHLJKERUKRRG RI Y $ 7KH PHWKRG RI OHDVW VTXDUHV ZRXOG \LHOG WKH HVWLPDWHV S E\ PLQLPL]LQJ WKH TXDQWLW\ P Q P Q P = = Hs = = $LL = D S f L O L L O L O s A N O f

PAGE 24

,Q SUDFWLFH WKLV LV KRZHYHU QRW GRQH UDWKHU WKH SY V DUH REWDLQHG IURP HTXDWLRQ f 7KH DVVXPSWLRQV RI WKH PRGHO IXQFWLRQ DQG WKRVH RI WKH SURFHGXUH IRU HVWLPDWLRQ RI WKH PRGHO SDUDPHWHUV WKXV FRQWUDGLFW HDFK RWKHU 7KH PRGHO IXQFWLRQ f LV SUHGLFDWHG RQ WKH DVVXPSWLRQ WKDW WKH S V DUH FRUUHODWHG WKXV JLYLQJ Y MXVWLILFDWLRQ IRU WKH VPRRWKLQJ SURFHVV ZKLOH WKH HVWLPDWLRQ RI WKH PRGHO SDUDPHWHUV IURP f LV EDVHG RQ WKH DVVXPSWLRQ WKDW WKH SBV DUH LQGHSHQGHQW $VVXPLQJ WKH PRGHO f WKH HVWLPDWHV RI WKH PRGHO SDUDPHWHUV IURP f DUH WKHUHIRUH ELDVHG 7KH ELDV RI DQ HVWLPDWH LV WKH H[SHFWHG YDOXH RI WKH HVWLPDWH PLQXV WKH WUXH YDOXH RI WKH SDUDPHWHU RU P = M O D S f ZKLFK LV LQ JHQHUDO QRW HTXDO WR ]HUR 2QH UHVXOW RI WKHVH HVWLPDWHV EHLQJ ELDVHG LV WKDW RQFH V\VWHPDWLF GLIIHUHQFHV DUH FDOFXODWHG VPRRWKHG DQG DSSOLHG DV V\VWHPDWLF FRUUHFWLRQV LI V\VWHPDWLF GLIIHUHQFHV ZHUH DJDLQ FDOFXODWHG DQG VPRRWKHG XVLQJ WKH VDPH FRHIILFLHQWV WKH UHVXOWLQJ FRUUHFWLRQV ZRXOG QRW EH ]HUR 7KDW LV DIWHU D FDWDORJXH LV FRUUHFWHG XVLQJ WKHVH ELDVHG HVWLPDWHV LI V\VWHPDWLF FRUUHFWLRQV ZHUH DJDLQ FDOFXODWHG LQ WKH VDPH PDQQHU WKH VHFRQG VHW RI FRUUHFWLRQV ZRXOG EH GLIIHUHQW IURP ]HUR

PAGE 25

$V D GHPRQVWUDWLRQ RI WKLV SKHQRPHQRQ WKH &DWDORJXH 0HULGLHQ GH ‹WRLOHV 5HSHUHV GH OD =RQH r D r %RUG f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

PAGE 26

7$%/( 6XFFHVLYH &RUUHFWLRQV &RPSXWHG ZLWK %LDVHG (VWLPDWHV &RUUHFWLRQV FRPSXWHG IRU WKH %RUG GHFOLQDWLRQV GHFUD f f ‘ f f f ‘ &RUUHFWLRQV FRPSXWHG I RU FRUUHFWHG %RUG GHFOLQDWLRQV

PAGE 27

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

PAGE 28

FRPSXWH WKHVH HVWLPDWHV ,Q WKH WDEXODU SURFHGXUH RQH HVWLPDWHV WKH V\VWHPDWLF FKDUDFWHULVWLFV RI D FDWDORJXH DQG DGMXVWV WKH FDWDORJXH LQ RUGHU WR FRUUHFW WKHVH V\VWHPDWLF WUHQGV 2QFH DOO WKH FDWDORJXHV DUH RQ WKH VDPH V\VWHP HVWLPDWHV IRU WKH LQGLYLGXDO SRVLWLRQV DQG SURSHU PRWLRQV DUH FDOFXODWHG ,Q D VLPXOWDQHRXV UHGXFWLRQ V\VWHPDWLF FRUUHFWLRQV PRGHO SDUDPHWHUVf DQG SRVLWLRQV DQG SURSHU PRWLRQV WDUJHW SDUDPHWHUVf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f DQG ODWHU GHVFULEHG E\ KLP LQ PRUH GHWDLO (LFKKRUQ f :LWKLQ WKH IUDPHZRUN RI WKLV UHVHDUFK KDYH HPSOR\HG WKLV SULQFLSOH WR HVWLPDWH VLPXOWDQHRXVO\ V\VWHPDWLF FRUUHFWLRQV IRU DOO ,&V XVHG WR FRQVWUXFW WKH 1,56 RQ WKH EDVLV RI H[DFWO\ WKH VDPH PRGHO DQG IURP H[DFWO\ WKH VDPH UDZ PDWHULDO DV WKRVH XVHG E\ &RUELQ &RUELQnV PRGHO FRPSXWHV GLIIHUHQFHV RQ D JULG DW HDFK KRXU RI ULJKW

PAGE 29

DVFHQVLRQ DQG HDFK ILYH GHJUHHV RI GHFOLQDWLRQ DQG WKHQ XVHV WZRZD\ OLQHDU LQWHUSRODWLRQ WR FRPSXWH FRUUHFWLRQV WR LQGLYLGXDO ,& SRVLWLRQV 7KH VPRRWKLQJ FRHIILFLHQWV DQG WKH ZHLJKWV RI WKH LQGLYLGXDO FDWDORJXHV ZHUH DOVR WKH VDPH DV LQ WKH PRGHO XVHG E\ &RUELQ 7KH RQO\ GLIIHUHQFH EHWZHHQ WKH WKH UHGXFWLRQV ZDV WKH PHWKRG RI FRPSXWLQJ V\VWHPDWLF GLIIHUHQFHV &RQVLGHU WKH OLQHDU PDWUL[ HTXDWLRQ < [H =3 H f ZKHUH < LV D YHFWRU RI REVHUYDWLRQV M DQG 3 DUH WKH WDUJHW DQG PRGHO SDUDPHWHUV UHVSHFWLYHO\ ; DQG = DUH WKHLU UHVSHFWLYH FRHIILFLHQW PDWULFLHV DQG e LV D YHFWRU RI HUURUV ZLWK FRYDULDQFH PDWUL[ = 7KLV HTXDWLRQ FRXOG EH DOWHUQDWHO\ DQG PRUH FRPSDFWO\ ZULWWHQ < >;=@>_@ H $e H f $ VLPXOWDQHRXV UHGXFWLRQ HVWLPDWLQJ ERWK PRGHO DQG WDUJHW SDUDPHWHUV ZRXOG \LHOG OHDVW VTXDUHV HVWLPDWHV >@ >$;nB=$@ $7=< 3 ,I PRGHO SDUDPHWHUV DUH HVWLPDWHG ILUVW DQG WDUJHW SDUDPHWHUV VHFRQG WKH OHDVW VTXDUHV HVWLPDWHV DUH 3 =7==fB=7=<;ff LR DQG ,'

PAGE 30

7 B 7 a ; ,;f ; ,<=3f ZKHUH Jn DUH SUHOLPLQDU\ HVWLPDWHV IRU J ,Q WU\LQJ WR SHUIRUP D VLPXOWDQHRXV UHGXFWLRQ RI WKH 1,56 XVLQJ WKH VDPH PRGHO DV &RUELQ KDG WR GHFLGH KRZ WR KDQGOH WZR SUREOHPV )LUVW WKHUH ZDV WKH FRPSXWDWLRQDO GLIILFXOW\ RI LQYHUWLQJ WKH $ e$ PDWUL[ LQ f 6LQFH KDYH DSSUR[LPDWHO\ VWDU SDUDPHWHUV DQG PRGHO SDUDPHWHUV WKLV PHDQV WKDW D E\ HOHPHQW PDWUL[ PXVW EH LQYHUWHG $OWKRXJK WKHUH H[LVW SURFHGXUHV FI /DZVRQ DQG +DQVRQ f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f EXW ZLWK OHVV FRPSXWDWLRQDO GLIILFXOW\ DQG DOVR DOORZV IRU WKH XVH RI WUDGLWLRQDO WDEXODU PHWKRG RI HVWLPDWLQJ PRGHO SDUDPHWHUV

PAGE 31

&+$37(5 ,,, 5('8&7,21 352&('85(6 ,Q WKH SUHYLRXV FKDSWHU KDYH FULWLFL]HG WKH WDEXODU SURFHGXUH RQ WKUHH JURXQGV f WKH SURFHVV LV VXEMHFWLYH LQ QDWXUH f QRW DOO DYDLODEOH PRGHO FRQVWUDLQWV DUH XVHG DQG f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

PAGE 32

V\VWHP RULHQWDWLRQ RI WKH ). 7KH FDWDORJXHV XVHG LQ WKH UHFRPSLODWLRQ RI WKH 1,56 DUH JLYHQ LQ WDEOH DW WKH HQG RI WKLV FKDSWHU 7KH SUHFHVVLRQ ZDV FDUULHG RXW XVLQJ 1HZFRPEV FRQVWDQWV RI SUHFHVVLRQ 7KUHH DQJOHV e ] DQG ZHUH FRPSXWHG IRU HDFK FDWDORJXH HSRFK WKHVH DUH FI (LFKKRUQ f e > A W"fWI W] F > WLfWW@ J4 f S > WfWe L L I WLOW WO ZKHUH W LV WKH LQLWLDO HSRFK RI RULHQWDWLRQ UHODWLYH WR L DQG WA LV WKH GLIIHUHQFH ILQDO PLQXV LQLWLDO HSRFK RI RULHQWDWLRQ %RWK W DQG W DUH UHFNRQHG LQ %HVVHO L I PLOOHQQLD 7KH FRQVWDQW WW LV QHFHVVDU\ WR FRQYHUW IURP DUFVHFRQGV WR UDGLDQV 1H[W WKH ,& SRVLWLRQV DUH SUHFHVVHG WR ZLWK WKH DERYH DQJOHV DQG WKH IROORZLQJ IRUPXODH ; FRV FRV D e Mf < FRV VLQD e ‘Mf FRV VLQ VLQ = FRV VLQD e f§f VLQ VLQ FRV D4 DUFWDQ <;f ] M f

PAGE 33

BT DUFWDQ ]A[A \Af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f / DA FRV A =R 9AWDUHI SD7DfD@ f D EU ZKHUH DD f LV WKH V\VWHPDWLF GLIIHUHQFH LV WKH HVWLPDWHG YDULDQFH RI WKH UHIHUHQFH VWDU SRVLWLRQ DW WKH HSRFK RI WKH ,& SRVLWLRQ D UHI UHI DQG DUH WKH UHIHUHQFH

PAGE 34

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nV YHUVLRQ RI WKH 1,56 ZHUH XVHG $IWHU PDWFKLQJ VWDUV EHWZHHQ WKH 3HUWK DQG WKH 1,56 WKH RQH VLJPD GLVSHUVLRQ RI 3HUWK SRVLWLRQV DQG WKH 1,56 SUHGLFWLRQV RI WKH 3HUWK ZHUH IRXQG WR EH DUFVHFRQGV LQ ULJKW DVFHQVLRQ DQG DUFVHFRQGV LQ GHFOLQDWLRQ 7KLV GLVSHUVLRQ LV GXH WR WKH SRVLWLRQ HUURUV ZLWKLQ WKH FDWDORJXHV DV ZHOO DV WKH HUURUV RI WKH V\VWHPV RI WKH FDWDORJXHV 6LQFH WKH PHDQ HUURU RI D

PAGE 35

SRVLWLRQ LV SXEOLVKHG LQ HDFK FDWDORJXH WKH HUURUV RI WKH WKH V\VWHPV RI WKH FDWDORJXHV FDQ EH HVWLPDWHG B e1,56 e3 e61,56 f e63 f 7KH VTXDUH RI WKH GLVSHUVLRQ LV WKH VXP RI WKH VTXDUHV RI WKH PHDQ HUURUV RI D FDWDORJXH SRVLWLRQ DQG Hn DQG H 1,56 3 SOXV WKH VTXDUHV RI WKH HVWLPDWHG HUURUV LQ WKH FDWDORJXH V\VWHPV H f DQG H 7KH UHVLGXDO YDULDQFH FRXOG EH 61,56 63 VSOLW HTXDOO\ EHWZHHQ WKH V\VWHPV RI WKH WZR FDWDORJXHV EXW FKRVH WR KDYH WKH UDWLR RI V\VWHP HUURUV HTXDO WKH UDWLR RI WKH PHDQ SRVLWLRQ HUURUV 7KH V\VWHP HUURU XVHG IRU DQ 1,56 SRVLWLRQ ZDV DUFVHFRQG LQ ULJKW DVFHQVLRQ DQG DUFVHFRQG LQ GHFOLQDWLRQ 2QFH WDEOHV RI GLIIHUHQFHV IRU HDFK ,& ZHUH FDOFXODWHG WKHVH GLIIHUHQFHV ZHUH VPRRWKHG ZLWK DGMDFHQW GLIIHUHQFHV DFFRUGLQJ WR WKH IROORZLQJ VFKHPH K Q $ n D D f = = $%$DD L Mf f K r L L f K r Q = = $% QD L Mf O M n -n L M ZKHUH $ DQG % DUH WKH VPRRWKLQJ FRHIILFLHQWV LQ WDEOH L DQG QD f LV WKH VXP RI WKH UHFLSURFDO YDULDQFHV IRU WKH DSSURSULDWH ,& KRXU DQG GHJUHH 7KH VPRRWKLQJ FRHIILFLHQWV XVHG UHJXODU RU OLJKWf IRU HDFK FDWDORJXH DUH OLVWHG LQ WDEOH $IWHU GLIIHUHQFHV KDYH EHHQ VXPPHG DQG VPRRWKHG WKH\ DUH WKHQ DYHUDJHG RYHU ]RQHV RI ILYH GHJUHHV

PAGE 36

R $ n n DD f \ $nDD Mf M ZKHUH LV WKH GHQRPLQDWRU LQ DVVRFLDWHG $nD D f HTXDWLRQ f f RI WKH 7$%/( 6PRRWKLQJ &RHIILFLHQWV L 5HJXODU $ O % L /LJKW $ O M %M 2K 2 R K r OK OK r K R K r r r r r r r r r 2QFH WDEOHV RI V\VWHPDWLF GLIIHUHQFHV DUH FRPSXWHG IRU HDFK FDWDORJXH WKH\ ZHUH DSSOLHG WR WKH ,& SRVLWLRQV DV V\VWHPDWLF FRUUHFWLRQV XVLQJ WZRZD\ OLQHDU LQWHUSRODWLRQ 5LJKW DVFHQVLRQV ZHUH ILUVW PXOWLSOLHG E\ WKH FRVLQH RI WKH GHFOLQDWLRQ FRUUHFWHG DQG WKHQ GLYLGHG E\ WKH FRVLQH RI WKH GHFOLQDWLRQ 6WDU 3DUDPHWHU (VWLPDWLRQ $IWHU FRUUHFWLQJ WKH V\VWHPDWLF HUURUV RI WKH ,&V WKH SRVLWLRQ DQG SURSHU PRWLRQ ZHUH FDOFXODWHG IRU HDFK VWDU

PAGE 37

XVLQJ D ZHLJKWHG OHDVW VTXDUHV DOJRULWKP &RUELQ f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f )RU D GLVFXVVLRQ RI VHOHFWLQJ ZHLJKWV XVHG LQ FDWDORJXH FRPSLODWLRQ VHH .KUXWVND\D

PAGE 38

ZKHUH 7? LV HSRFK DQG 3A LV WKH SRVLWLRQ RI WKH VWDU LQ FDWDORJXH L DQG LV SURGXFW RI WKH WKH ZHLJKW DVVRFLDWHG ZLWK FDWDORJXH L DQG WKH QXPEHU RI REVHUYDWLRQV IRU WKDW ,& SRVLWLRQ GLYLGHG E\ WKH PHDQ QXPEHU RI REVHUYDWLRQV SHU ,& SRVLWLRQ IRU WKDW ,& 1H[W WKH 7 ZHUH UHIHUHQFHG WR WKH FHQWUDO HSRFK LS LML B US L L f DQG WKH SURSHU PRWLRQ ZDV FDOFXODWHG = Z 7 n 3 L O O = Z 7 ‘ L O f )LQDOO\ HVWLPDWHV IRU WKH YDULDQFH RI WKH SRVLWLRQ DQG SURSHU PRWLRQ 9 DQG 9A ZHUH FDOFXODWHG O LOL ZL3 S \7 nf Y A O f = Z L O P 9X L O ZLSL f S a \7Lnf L ? f = Z7 L O L L f 6HTXHQFH RI ,WHUDWLRQV 1RZ WKDW WKH EDVLF PHFKDQLFV RI WKH UHGXFWLRQ KDYH EHHQ GHVFULEHG D GLVFXVVLRQ RI WKH LWHUDWLRQ VHTXHQFH LV LQ RUGHU :LWKLQ DQ LWHUDWLRQ WKH ILUVW VWHS ZDV WR HOLPLQDWH

PAGE 39

RXWOLHUV ,& SRVLWLRQV ZLWK ODUJH UHVLGXDOVf WKH VHFRQG ZDV WR GHWHUPLQH DQG DSSO\ V\VWHPDWLF FRUUHFWLRQV DQG WKH WKLUG ZDV WR FRPSLOH D QHZ YHUVLRQ RI WKH 1,56 &RUELQ XVHG VHYHUDO FULWHULD IRU VHOHFWLRQ RI $*.5 VWDUV WR XVH LQ WKH 1,56 $PRQJ WKHVH ZDV WKH UHTXLUHPHQW WKDW D VWDU ZLWK RQO\ WZR REVHUYDWLRQV PXVW KDYH WKRVH WZR REVHUYDWLRQV VHSDUDWHG E\ D PLQLPXP RI \HDUV %HFDXVH RI WKH FRQYROXWLRQ RI WKHVH FULWHULD ZLWK WKH VHOHFWLRQ RI RXWOLHUV FKRVH WKRVH VWDUV ZKLFK DSSHDUHG LQ &RUELQn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

PAGE 40

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

PAGE 41

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

PAGE 42

DEVROXWH YDOXHV H[FHHGHG KXQGUHGWKV RI DQ DUFVHFRQG ZHUH UHSODFHG E\ KXQGUHGWKV ZLWK WKH DSSURSULDWH VLJQ

PAGE 43

7$%/( ,QGHSHQGHQW &DWDORJXHV 8VHG LQ WKH &RPSLODWLRQ RI WKH 1,56 $f %f 7LWOH &f 'f (f )f *f $*.5 &DWDORJ RI 5HIHUHQFH VWDUV IRU WKH 'ULWWHU .DWDORJ GHU $VWURQRPLVFKHQ *HVHOOVFKDIW UHJXODU $*.$ .DWDORJ GHU $QKDOWVWHUQH IU GDV =RQHQXQWHUQHKPHQ GHU $VWURQRPLVFKHQ *HVHOOVFKDIW UHJXODU : &DWDORJXH RI 6WDQGDUG DQG ,QWHUPHGLDU\ 6WDUV UHJXODU $OEDQ\ $OEDQ\ &DWDORJ RI 6WDUV IRU WKH (SRFK UHJXODU %RQQ .DWDORJ YRQ 6WHUQHQ UHJXODU %RUG &DWDORJXH 0ULGLHQ GH (WRLOHV 5HSKUHV GH OD =RQH r D r UHJXODU 6FK .DWDORJ YRQ VFKZDFKHQ 6WHUQHQ UHJXODU %RQQ .DWDORJ GHU ,QWHUPHGLDUHQ 6WHUQH YRQ r'HFOLQDWLRQ ELV ]XP 1RUGSRO UHJXODU : &DWDORJ RI 6WDUV IRU UHJXODU : &DWDORJ RI 6WDUV IRU UHJXODU *&+ )LUVW *UHHQZLFK &DWDORJXH RI 6WDUV IRU OLJKW

PAGE 44

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f &DSH &DSH *HQHUDO &DWDORJXH RI 6WDUV IRU UHJXODU 1LFH &DWDORJXH 'HGXLW GHV 3RVLWLRQV 2EVHUYHV D nDLGH GX &HUFOH 0ULGLHQ GH n2EVHUYDWRLUH GH 1LFH GH D OLJKW 1LFH &DWDORJXH 'H ‹WRLOHV ,QWHUPHGLDLUHV OLJKW *&+ = *UHHQZLFK &DWDORJXH RI 6WDUV IRU OLJKW 3DULV &DWDORJXH GH 2EVHUYDWRLUH GH 3DULV 6HFRQGH 3DUWLH OLJKW 3DULV 3DULV &DWDORJXH GH ‹WRLOHV GH 5HSUH GH OD &DUWH GX &LHO UHJXODU *&+ 6HFRQG *UHHQZLFK &DWDORJXH RI 6WDUV IRU OLJKW %HUO %HUOLQ%DEHOVEHUJ .DWDORJ YRQ 6WHUQHQ ]ZLVFKHQ r XQG r 1RUGOLFKHU 'HNOLQDWLRQ OLJKW *&+ *UHHQZLFK 6HFRQG 1LQH\HDU FDWDORJXH RI 6WDUV IRU WKH (SRFK OLJKW 7RXO 7URLVPH &DWDORJXH GH 7RXORXVH OLJKW &2 &2

PAGE 45

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f &DSH 6HFRQG &DSH &DWDORJXH RI 6WDUV IRU WKH (TXLQR[ OLJKW &DSH 7KLUG &DSH &DWDORJXH RI 6WDUV IRU WKH (TXLQR[ UHJXODU : :DVKLQJWRQ 5HVXOWV RI 2EVHUYDWLRQV PDGH ZLWK WKH QLQHLQFK UHJXODU 7UDQVLW &LUFOH : :DVKLQJWRQ5HVXOWV RI 2EVHUYDWLRQV ZLWK WKH 1LQHLQFK 7UDQVLW &LUFOH UHJXODU : =2' :DVKLQJWRQ&DWDORJ RI ]RGLDFDO 6WDUV EDVHG RQ 2EVHUYDWLRQV ZLWK WKH 6L[LQFK 7UDQVLW &LUFOH UHJXODU &DSH )LUVW &DSH &DWDORJXH RI 6WDUV IRU WKH (TXLQR[ OLJKW %RUG 6HFRQG &DWDORJXH GH /n2EVHUYDWRLUH GH %RUGHDX[ UHJXODU $/% $OEDQ\ =RQH &DWDORJXHV IRU WKH (SRFK &DWDORJXH RI VWDUV EHWZHHQ r RI 6RXWK DQG r RI 1RUWK 'HFOLQDWLRQ UHJXODU 0XQ LE 0QFKHQ 6WHUQZDUWH .DWDORJ OLJKW YRQ 6WHUQHQ r WR "f

PAGE 46

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f 0XQ 22LO 0QFKHQ 6WHUQZDUWH .DWDORJ YRQ 6WHUQHQ r WR rf UHJXODU .RQ & .RQLJVEHUJ 5HNWDV]HQVLRQV %HREDFKWXQJHQ YRQ 6WHUQHQ UHJXODU 3XON 3XONRYR $ &DWDORJXH RI UHJXODU 6WDUV EHWZHHQ r 6RXWK DQG r 1RUWK 'HFOLQDWLRQ 0DGQ 0DGLVRQ &DWDORJXH RI 6WDUV IRU WKH (SRFK OLJKW %HUJ (UVWHV %HUJHGRUIHU 6WHUQYHU]HLFKQLV UHJXODU $%% $EEDGLD &DWDORJXH GH (WRLOHV OLJKW %XFK %XFKDUHVW .6= &DWDORJXH RI )DLQW 6WDUV IRU OLJKW %RQQ %RQQ .DWDORJ YRQ 6WHUQHQ IU UHJXODU $%% $EEDGLD &DWDORJXH GH (WRLOHV OLJKW $%% $EEDGLD &DWDORJXH GH ‹WRLOHV OLJKW /XQG 0HULGLDQ 2EVHUYDWLRQV RI )DLQW $* 6WDUV OLJKW RR FQ

PAGE 47

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f 6WUDV 6WUDVERXUJ &DWDORJXH GH (WRLOHV )DLEOHV OLJKW &LQ &LQFLQQDWL &DWDORJ RI 6WDUV IRU WKH (SRFK UHJXODU 3).6= 3UHOLPLQDU\ *HQHUDO &DWDORJXH RI )XQGDPHQWDO )DLQW 6WDUV UHJXODU /XQG 0HULGLDQ 2EVHUYDWLRQV RI 0LVFHOODQHRXV 6WDUV UHJXODU &LQ &LQFLQQDWL &DWDORJ RI 6WDUV IRU WKH (TXLQR[ UHJXODU 0RVFRZ &DWDORJ RI )DLQW 6WDUV UHJXODU 7UL &DWDORJR GL 6WHOOH 2VVHUYDWH DO &HUFKLR 0HULGLDQR OLJKW %UXVV %UXVVHOV &DWDORJXH GH ‹WRLOHV )RQGDPHQWDOHV UHJXODU D /HLG /HLGHQ $ &DWDORJXH RI WKH 3RVLWLRQV DQG 3URSHU 0RWLRQV RI 5HG 6WDUV OLJKW /HLG /HLGHQ *HQHUDO &DWDORJXH RI 3RVLWLRQV DQG 3URSHU 0RWLRQV UHJXODU RI 6WDQGDUG 6WDUV

PAGE 48

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f /XQG .DWDORJ YRQ 6WHUQHQ GHU =RQH r ELV r $* /XQG OLJKW /HLG $ &DWDORJ RI 6WDUV LQ WKH =RQH RI 1RUWK 'HFOLQDWLRQ r WR r UHJXODU %HUO = .DWDORJ YRQ 6WHUQHQ ]ZLVFKHQ r XQG r UHJXODU .RQO .RQLJVEHUJ.DWDORJ YRQ 6WHUQHQ OLJKW 7RXO $SSHQGLFH ,, GX 7URLVLPH &DWDORJXH GH 7RXORXVH UHJXODU 3XON .DWDORJ YRQ 6WHUQHQ ]ZLVFKHQ r XQG r QUGOLFKHU 'HNOLQDWLRQ OLJKW /LFN 3XEOLFDWLRQV RI WKH /LFN 2EVHUYDWRU\ 9RO ;9 UHJXODU /LFN 0HULGLDQ FLUFOH 2EVHUYDWLRQV RI 6WDUV EHWZHHQ r DQG r 1RUWK 'HFOLQDWLRQ UHJXODU 7XULQ F &DWDORJR Gn$VFHQVLRQL 5HWWH GL 6WHOOH ILVVH UHJXODU %RUG 1RXYHOOHV 2EVHUYDWLRQV 'HV ‹WRLOHV FRQWHQXHV GDQV OH 6HFRQG &DWDORJXH OLJKW GH n2EVHUYDWRLUH GH %RUGHDX[

PAGE 49

7$%/( &217,18(' $f %f 7LWOH &f 'f (f )f *f WWZ 5HVXOWV RI 2EVHUYDWLRQV WKH 5HYHUVLEOH 0HULGLDQ &DWDORJXH RI PDGH ZLWK &LUFOH 6WDUV UHJXODU 2WWZ 5HVXOWV RI 2EVHUYDWLRQV WKH 5HYHUVLEOH 0HULGLDQ &DWDORJXH RI PDGH ZLWK &LUFOH 6WDUV UHJXODU .RQO .DWDORJ YRQ 6WHUQHQ OLJKW $f &DWDORJXH UHIHUHQFH QXPEHU DV SURYLGHG E\ &RUELQ %f &DWDORJXH DEEUHYLDWLRQ DV JLYHQ E\ &RUELQ &f 5LJKW DVFHQVLRQ ZHLJKW 'f 'HFOLQDWLRQ ZHLJKW (f 5LJKW DVFHQVLRQ UHVLGXDO OLPLW LQ DUFVHFRQGV )f 'HFOLQDWLRQ UHVLGXDO OLPLW LQ DUFVHFRQGV *f 6PRRWKLQJ FRHIILFLHQWV XVHG D 5HIHUHQFH QXPEHUV DQG KDYH QR FDWDORJXH DVVRFLDWHG ZLWK WKHP E 7KH 0XQ ZDV REVHUYHG LQ WZR VHSHUDWH ]RQHV DQG LV WUHDWHG DV WZR VHSHUDWH FDWDORJXHV F 7KH .RQ DQG WKH 7XULQ DUH WUDQVLW LQVWUXPHQW REVHUYDWLRQV RI ULJKW DVFHQVLRQV RQO\ WR RR

PAGE 50

7$%/( &RUUHFWLRQV $SSOLHG WR WKH $*.5 5LJKW $VFHQVLRQ GHF?UD &-

PAGE 51

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ ‘ S! R

PAGE 52

7$%/( &RUUHFWLRQV $SSOLHG WR WKH $*.$ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘ f ‘ ‘ ‘ BB f f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘

PAGE 53

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ f ‘ ‘ ‘ f ‘ ‘ f f f ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ UR

PAGE 54

7$%/( &RUUHFWLRQV $SSOLHG WR WKH : 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ f ‘ ‘ B ‘ ‘ ‘ ‘ S} &2

PAGE 55

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘

PAGE 56

7$%/( &RUUHFWLRQV $SSOLHG WR WKH $OEDQ\ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ BQ

PAGE 57

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ ‘ f B ‘ ‘ f ‘ f ‘ ‘ ‘ ‘ f 3r FU!

PAGE 58

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RQQ 5LJKW $VFHQVLRQ GHF?UD f f f f

PAGE 59

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ S RR

PAGE 60

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RUG 5LJKW $VFHQVLRQ GHF?UD f ‘ f f f ‘ f ‘ f 'HFOLQDWLRQ GHF?UD ‘ ‘ f ‘ ‘ ‘ ‘ f f f f f f ‘ ‘ ‘ ‘ f ‘ ‘ f 3r WR

PAGE 61

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 6FK 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘

PAGE 62

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ f ‘ f ‘ f ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘

PAGE 63

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RQQ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ f f ‘ ‘ f ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ f f ‘ ‘ ‘ f f ‘ ‘ ‘ f ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f 'HFOLQDWLRQ GHF?UD f ‘ &UR

PAGE 64

7$%/( &RUUHFWLRQV $SSOLHG WR WKH : 5LJKW $VFHQVLRQ GHF?UD

PAGE 65

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD f ‘ ‘ f f f ‘ ‘ f 62n 62 BB ‘ ‘ FQ 3A

PAGE 66

7$%/( &RUUHFWLRQV $SSOLHG WR WKH : 5LJKW $VFHQVLRQ GHF?UD ‘ f ‘ f f ‘ ‘ f ‘ ‘ f f f f f ‘ ‘ f ‘ ‘ ‘ f ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ f ‘ ‘ ‘ ‘ f ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ FQ FQ

PAGE 67

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD f f f O2 f OO ‘ f f ‘ ‘ ‘ ‘ f ‘ f FQ FU!

PAGE 68

7$%/( &RUUHFWLRQV $SSOLHG WR WKH *&+ 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 69

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &DSH 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ FQ

PAGE 70

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 1LFH 5LJKW $VFHQVLRQ GHF?UD ‘ 'HFOLQDWLRQ GHF?UD f RQ

PAGE 71

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 1LFH 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH *&+ = 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FU! R

PAGE 72

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 3DULV 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD f ‘ ‘ ‘ f ‘ f

PAGE 73

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 3DULV 5LJKW $VFHQVLRQ GHF?UD 'HF LQDWLRQ GHF?UD FU! UR

PAGE 74

7$%/( &RUUHFWLRQV $SSOLHG WR WKH *&+ 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FQ 2-

PAGE 75

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %HUO 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH *&+ 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FQ 3!

PAGE 76

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 7RXO 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FQ BQ

PAGE 77

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &DSH 5LJKW $VFHQVLRQ GHF?UD f ‘ f ‘ f ‘ ‘ ‘ ‘ f ‘ ‘ ‘ f ‘ f ‘ ‘ f ‘ f ‘ 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ f ‘ f f f ‘ ‘ ‘ ‘ f FQ FU!

PAGE 78

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &DSH 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD &7O A

PAGE 79

7$%/( &RUUHFWLRQV $SSOL 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD ‘ f ‘ ‘ f WR WKH : HG n 2n}

PAGE 80

7$%/( &RUUHFWLRQV $SSOLHG WR WKH : 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FU! LG

PAGE 81

7$%/( &RUUHFWLRQV $SSOLHG WR WKH : =2' 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ R

PAGE 82

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &DSH 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 83

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RUG 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH $/% 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD A UY!

PAGE 84

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 0XQ 22LL 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD ‘ ‘ A &2

PAGE 85

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 0XQ 22LL 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH .RQ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ A A

PAGE 86

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 3XON 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD FQ

PAGE 87

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 0DGQ 5LJKW $VFHQVLRQ GHF?UD 'HF OLQDWLRQ GHF?UD &7!

PAGE 88

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %HUJ 5LJKW $VFHQVLRQ GHF?UD

PAGE 89

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ ‘ Ar

PAGE 90

7$%/( &RUUHFWLRQV $SSOLHG WR WKH $%% 5LJKW L $VFHQVLRQ GHF?UD f 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH %XFK 5LJKW $VFHQVLRQ GHF?UD OL ‘ ‘ f n f f ‘ n 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ ‘n ‘ ‘ f n ‘ ‘ fn ‘ f ‘ ‘ ‘ ‘ ‘ /'

PAGE 91

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RQQ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ f ‘ ‘ ‘ f ‘ f ‘ 'HFOL PDWLRQ GHF?UD f 7$%/( &RUUHFWLRQV $SSOLHG WR WKH $%% 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 92

7$%/( &RUUHFWLRQV $SSOLHG WR WKH $%%2 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 93

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /XQG 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD RR UR

PAGE 94

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 6WUDV 5LJKW $VFHQVLRQ GHF?UD f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘

PAGE 95

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD RR

PAGE 96

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &LQ 5LJKW $VFHQVLRQ GHF?UD FQ

PAGE 97

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD

PAGE 98

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 3).6= 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f LL ‘ ‘ VV ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ f ‘ ‘ RR

PAGE 99

7$%/( &217,18(' LHF?UD ‘ ‘ f ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ f n ‘ f ‘ f ‘ ‘ f ‘ n n ‘ ‘ n f &;,

PAGE 100

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /XQG 5LJKW $VFHQV GHF?UD LRQ ‘ ‘ f ‘ R JR f f ‘ ‘ ‘ f ‘ ‘ n n n n f f ‘ f ‘ ‘

PAGE 101

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD f ‘ ‘

PAGE 102

7$%/( &RUUHFWLRQV $SSOLHG WR WKH &LQ 5LJKW $VFHQVLRQ GHF?UD ‘ f ‘ ‘

PAGE 103

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD

PAGE 104

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 0RVFRZ 5LJKW $VFHQVLRQ GHF?UD

PAGE 105

7$%/( 'HFOLQDWLRQ GHF?UD &217,18(' n [!

PAGE 106

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 7UL 5LJKW $VFHQVLRQ GHF?UD ‘ f ‘ 'HFOLQDWLRQ GHF?UD ‘ f ‘ ‘ ‘ WR FQ

PAGE 107

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %UXVV 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f f f W' &7!

PAGE 108

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD WR

PAGE 109

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /HLG 5LJKW $VFHQVLRQ GHF?UD ‘ f ‘ f ‘ f ‘ f f ‘ 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘ ‘ f ‘ ‘ e! RR

PAGE 110

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /HLG 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f f ‘ ‘ ‘ f ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ f ‘ ‘ f ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ f f ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ f ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ f ‘ ‘ f ‘ ‘ ‘ ‘ 'HFOLQDWLRQ GHF?UD e!

PAGE 111

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /XQG 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH /HLG 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 112

7$%/( &RUUHFWLRQV $SSOLHG WR WKH %HUO = 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD n ‘ f f fn n n ‘ f f ‘ ‘ 7$%/( &RUUHFWLRQV $SSOLHG WF L WKH .RQO 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ f f ‘ f ‘ ‘ ‘ ‘ ‘ f ‘ f f f ‘n ‘ fn f ‘ ‘ ‘ f f f ‘ ‘ fn f ‘ f ‘ f ‘ 'HFOLQDWLRQ GHF?UD ‘ ‘ ‘

PAGE 113

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 7RXO 5LJKW $VFHQVLRQ GHF?UD f ‘ f f f f ‘ 'HFOLQDWLRQ GHF?UD f 7$%/( &RUUHFWLRQV $SSOLHG WR WKH 3XON 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD =2 /

PAGE 114

7$%/( &RUUHFWLRQV $SSOLHG WR WKH /LFN 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH /LFN 5LJKW $VFHQVLRQ GHF?UD ‘ f f 'HFOLQDWLRQ GHF?UD f

PAGE 115

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 7XULQ 5LJKW $VFHQVLRQ GHF?UD 7$%/( &RUUHFWLRQV $SSOLHG WR WKH %RUG 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 116

7$%/( &RUUHFWLRQV $SSOLHG WR WKH 2WWZ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘

PAGE 117

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD

PAGE 118

7$%/( &RUUHFWLRQV $SSOLHG WR WKH WWZ 5LJKW $VFHQVLRQ GHF?UD ‘ ‘ ‘ ‘ ‘

PAGE 119

7$%/( &217,18(' 'HFOLQDWLRQ GHF?UD ‘ f ‘

PAGE 120

7$%/( &RUUHFWLRQV $SSOLHG WR WKH .RQO 5LJKW $VFHQVLRQ GHF?UD 'HFOLQDWLRQ GHF?UD

PAGE 121

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

PAGE 122

1R RI 6WDUV 1R RI 6WDUV )LJXUH 'LVWULEXWLRQ RI 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH LQ DUFVHFRQGV )LJXUH 'LVWULEXWLRQ RI 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH LQ DUFVHFRQGV

PAGE 123

1R RI 6WDUV 1R RI 6WDUV )LJXUH 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH LQ DUFVHFRQGV SHU FHQWXU\ )LJXUH 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH LQ DUFVHFRQGV SHU FHQWXU\

PAGE 124

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

PAGE 125

7$%/( 0HDQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH XQLWV GHFUD RI ‘

PAGE 126

7$%/( 0HDQ 'HFOLQDWLRQ 5HVLGXDOV XQLWV RI GHFUD ‘ &RUELQ PLQXV &ROH

PAGE 127

7$%/( 0HDQ 3URSHU 0RWLRQ LQ 5LJKW $VFHQVLRQ 5HVLGXDOV &RUELQ PLQXV &ROH XQLWV RI FHQWXU\ GHFUD &7L

PAGE 128

7$%/( 0HDQ 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 5HVLGXDOV &RUELQ PLQXV &ROH XQLWV RI &HQWXU\ GHFUD

PAGE 129

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f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

PAGE 130

DQG DQG DUFVHFRQGV SHU FHQWXU\ IRU SURSHU PRWLRQ LQ ULJKW DVFHQVLRQ DQG GHFOLQDWLRQ UHVSHFWLYHO\ 7KH UHGXFWLRQ RI PHDQ UPV HUURUV LV VKRZQ WR EH EHWZHHQ DQG SHUFHQW 7$%/( 0HDQ 506 HUURUV 5LJKW $VFHQVLRQ I 'HFOLQDWLRQ I" 5$ 3URSHU 0RWLRQ FHQWXU\ 'HF 3URSHU 0RWLRQ FHQWXU\ &RUELQ 1,56 &ROH 1,56 7KH GLVWULEXWLRQV RI WKHVH UPV HUURUV DUH JLYHQ IRU ERWK YHUVLRQV RI WKH 1,56 LQ ILJXUHV WKURXJK ,W LV ZHOO NQRZQ FI )LUQHLV DQG )LUQHLV f WKDW WKH IRUPDO LQWHUQDO HUURUV RI D SURFHVV RI GDWD UHGXFWLRQ DUH YHU\ GHSHQGHQW RQ WKH PRGHO WKH DVVXPSWLRQV RI WKDW PRGHO DQG WKH PHWKRG RI VROXWLRQ XVHG 7KXV RQH W\SLFDOO\ HQFRXQWHUV GLVFUHSDQFLHV EHWZHHQ WKH LQWHUQDO DQG H[WHUQDO HUURUV RI YDULRXV GHULYHG VHWV RI VWDWLVWLFDO SDUDPHWHUV &RQVLGHU IRU H[DPSOH WKH GHFDGHVORQJ FRQWURYHUV\ RYHU WKH YDOXH RI WKH +XEEOH FRQVWDQW 7ZR VHWV RI LQYHVWLJDWRUV XVLQJ GLIIHUHQW PHWKRGV KDYH DUULYHG DW WZR HVWLPDWHV IRU

PAGE 131

1R RI 6WDUV 1R RI 6WDUV )LJXUH 'LVWULEXWLRQ RI 5LJKW $VFHQVLRQ 506 (UURUV LQ DUFVHFRQGV )LJXUH 'LVWULEXWLRQ RI 'HFOLQDWLRQ 506 (UURUV LQ DUFVHFRQGV

PAGE 132

1R RI 6WDUV 1R RI 6WDUV $VFHQVLRQ 506 (UURUV LQ DUFVHFRQGV SHU FHQWXU\ )LJXUH 'LVWULEXWLRQ RI 3URSHU 0RWLRQ LQ 'HFOLQDWLRQ 506 (UURUV LQ DUFVHFRQGV SHU FHQWXU\ W

PAGE 133

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f +J DQG YRQ GHU +HLGH f LV D FDWDORJXH ZLWK D PHDQ HSRFK RI \HDUV ODWHU WKDQ WKH PHDQ HSRFK RI WKH 1,56 ZDV DEOH WR PDWFK VWDUV RI WKH 3HUWK ZLWK WKH 1,56 WKHQ SUHGLFWHG WKH 3HUWK SRVLWLRQV DQG FRPSXWHG UHVLGXDOV ZLWK WKH WZR YHUVLRQ RI WKH 1,56 ,W VKRXOG EH QRWHG WKDW WKH SRUWLRQ RI WKH 3HUWK ZKLFK ZDV DEOH WR PDWFK KDV D GHQVLW\ RI DERXW RQH VWDU SHU VTXDUH GHJUHH IURP GHJUHHV WR GHJUHHV EXW RQO\ DERXW RQH VWDU SHU ILIWHHQ VTXDUHV GHJUHHV QRUWK RI GHJUHHV 7DEOH JLYHV WKH RQH VLJPD GLVSHUVLRQ RI WKH SRVLWLRQ UHVLGXDOV EHWZHHQ WKH 3HUWK DQG WKH WZR YHUVLRQV RI WKH 1,56

PAGE 134

7$%/( 3RVLWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 0HDQ UHVLGXDOV 'LVSHUVLRQ 5$ '(& 5$ '(& &RUELQ 1,56 &ROH 1,56 6LJQLILFDQFH OHYHO RI GLIIHUHQFH b b b b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

PAGE 135

RI VWDUV ZDV FRPSDUHG WR WKH 3HUWK DQG LW LV VHHQ WKDW P\ PHDQ GHFOLQDWLRQ UHVLGXDOV DUH FORVHU WKDQ &RUELQn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

PAGE 136

1R RI 6WDUV 1R RI 6WDUV 3HUWK PLQXV 1O56 LQ DUFVHFRQGV )LJXUH 'LVWULEXWLRQ RI 'HFOLQDWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 LQ DUFVHFRQGV

PAGE 137

ZLGH 7KH ILQDO QXPEHU RQ WKH ERWWRP RI WKH ULJKW KDQG FROXPQ RI HDFK WDEOH JLYHV WKH RYHUDOO PHDQ RI WKH UHVLGXDOV :KHQ H[DPLQLQJ WKHVH WDEOHV LW PXVW EH UHPHPEHUHG WKDW WKH EORFNV QRUWK RI GHJUHHV KDYH DW PRVW WZR RU WKUHH VWDUV DQG RIWHQ QRQH 7KHUHIRUH WKHVH PHDQV QRUWK RI GHJUHHV DUH RIWHQ EDVHG RQ RQH RU WZR SRVLWLRQV

PAGE 138

7$%/( 0HDQ 5LJKW $VFHQVLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 3HUWK PLQXV &RUELQ XQLWV RI f ,W GHFUD ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ f ‘ 3HUWK PLQXV &ROH XQLWV RI GHFUD ‘ ‘ f ‘ f ‘ ‘ f ‘ ‘ f

PAGE 139

7$%/( 0HDQ 'HFOLQDWLRQ 5HVLGXDOV 3HUWK PLQXV 1,56 3HUWK PLQXV &RUELQ XQLWV RI GHFUD ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘ ‘ ‘ ‘ ‘ ‘ ‘ f 3HUWK PLQXV &ROH L XQLWV RI GHFUD f ‘ LOn ‘ ‘ OV ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ f ‘

PAGE 140

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

PAGE 141

FOHDUFXW SURFHGXUH DQG VHHQ LW WKURXJK ZLWKRXW DQ\ PLGn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

PAGE 142

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
PAGE 143

)DGGHHYD 9 1 &RPSXWDWLRQDO 0HWKRGV RI /LQHDU $OJHEUD WUDQVODWHG E\ & %HQVWHU 'RYHU 3XEOLFDWLRQV 1HZ
PAGE 144

%,2*5$3+,&$/ 6.(7&+ ZDV ERUQ LQ &ROXPEXV 2KLR RQ 6HSWHPEHU WK WR /\PDQ DQG 6WHOOD &ROH ZDV WKHLU IRXUWK DQG ODVW FKLOG KDYLQJ WKUHH ROGHU VLVWHUV :KHQ ZDV WKUHH P\ IDPLO\ PRYHG WR UXUDO 3HQV\OYDQLD DQG ZKHQ ZDV ILYH ZH PRYHG WR 5RFNIRUG ,OOLQRLV DWWHQGHG 6W 3HWHUnV 5RPDQ &DWKROLF JUDGH VFKRRO DQG JUDGXDWHG IURP 5RFNIRUG :HVW KLJK VFKRRO LQ EHJDQ P\ FROOHJH HGXFDWLRQ DW WKH 8QLYHUVLW\ RI ,OOLQRLV ZKHUH ZDV HQUROOHG LQ D SURIHVVLRQDO SLORWDLUFUDIW PDLQWHQDQFH FXUULFXOXP WUDQVIHUHG WR WKH &ROOHJH RI (QJLQHHULQJ DQG HDUQHG D %DFKHORU RI 6FLHQFH GHJUHH LQ DHURQDXWLFDO DQG DVWURQDXWLFDO HQJLQHHULQJ LQ QH[W PRYHG WR :HVW 3DOP %HDFK )ORULGD ZHUH ZDV HPSOR\HG DV D WHVW HQJLQHHU IRU 3UDWW t :KLWQH\ $LUFUDIW :KLOH ZRUNLQJ IRU 3UDWW t :KLWQH\ ZDV UHVSRQVLEOH IRU IXOO VFDOH HQJLQH WHVWV RI WKH 7) WKH HQJLQH XVHG LQ ) DQG )OOO DLUFUDIW HQWHUHG JUDGXDWH VFKRRO DW WKH 8QLYHUVLW\ RI )ORULGD LQ DQG HDUQHG D 0DVWHU RI 6FLHQFH GHJUHH LQ KDG YDULRXV RXWVLGH DFWLYLWLHV EHIRUH EHFRPLQJ D JUDGXDWH VWXGHQW DQG PD\ UHVXPH P\ LQWHUHVW LQ VFXED GLYLQJ PRWRUF\FOH UDFLQJ RU VN\GLYLQJ DIWHU JUDGXDWH

PAGE 145

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ +HLQULFK (LFKKRUQ &KDLUPDQ 3URIHVVRU RI $VWURQRP\ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ Vn /O/ +RZDUG / &RKHQ $VVRFLDWH 3URIHVVRU RI $VWURQRP\ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ ,PO,O KLWVnr )UDQN 0DUWLQ 3URIHVVRU RI 6WDWLVWLFV FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI --RSWRU RI 3KLORVRSK\ ? R b ? Y n\WY9n9 ? -RKQ 3 2OLYHU $VVRFLDWH 3URIHVVRU RI $VWURQRP\

PAGE 146

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

PAGE 147

81,9(56,7< QR 2, QU[ 2 $ 2FR $Dn ,r