• TABLE OF CONTENTS
HIDE
 Front Matter
 Half Title
 Frontispiece
 Title Page
 Preface
 Table of Contents
 Mechanics
 Astronomy
 Hydrostatics
 Pneumatics
 Optics
 Magnetism
 Electricity
 Galvanism
 Index and glossary






Title: Scientific dialogues
CITATION THUMBNAILS PAGE TURNER PAGE IMAGE ZOOMABLE
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Permanent Link: http://ufdc.ufl.edu/UF00061434/00001
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Title: Scientific dialogues
Series Title: Scientific dialogues
Physical Description: Book
Creator: Joyce, Jeremiah,
Publisher: Printed and published by W. Milner
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Table of Contents
    Front Matter
        Front Matter
    Half Title
        Half Title
    Frontispiece
        Frontispiece
    Title Page
        Page 1
        Page 2
        Page 3
        Page 4
    Preface
        Page 5
        Page 6
    Table of Contents
        Page 7
        Page 8
        Page 9
        Page 10
    Mechanics
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
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    Astronomy
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    Hydrostatics
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    Pneumatics
        Page 273
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    Optics
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    Magnetism
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    Electricity
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    Galvanism
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    Index and glossary
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Full Text











SCIENTIFIC DIALOGUES.











BVyJJ. OrYo.


1 &I if








SCIENTIFIC DIALOGUES:
IRTMWuND oB Tn
INSTRUCTION AND ENTERTAINOENT


YOUNG PEOPLE.


T2= MagT M PRI
or
NATURAL A XPBRIBNTAL PHILOSOPHY
ABRE ULLT IXPLIIEI.
BY THE REV. J. JOYCE.

IwT TDITWN. OOMuPrBT tn OI VOLUMX,
WITH TWO HUNDMUD WOOD OUTT




HALIAXi
RUTTD A rUXJUI D BT WILLIAM UMEa,I

MDCCCL. v









PREPAUL.



ThI Author s bhunmelf tremely happy Ia b. oppf w
tunlty which this publicalton atords him of acknowle*diag
the bbllgatlo he is under to the sathors of *'Presal
Edultiou,' for the pleasure sad Intruction which he has
derived from that valuable work. To this b h I oedy ia-
debted for the Idea of writing on the object of Natural
Philoophy for the ue of children. How far bi pla eor-
respondi with that gue bted by Mr. Bdgworth, In his
bapter Om Meehaal, must be left with a m ild public to

The Author eonelves, at leat, he shall e Justfied la
aserlng, that no introduction to natural ad aperimental
philoophy b been attempted tn a method s fmillar and
my u that which be now of~rto the pubUe:--ame wMah
appears to him so property adaptd to the cspeltlee of
yourn peop of ten or elv year of ge, a period of
life which, from the Author' own experienw he i ca- e
dent i by no meau too ery to ltdue ia eblidre hablt
o lf eatlM reonta.l In this opinion he la smoetlld by
the Sathrty of Mr. dgeworth. "Parents," es he,
".ae anuiou that hildrn should be coavernt with ome
eaWbe., ad with what are Wled tbh meehalahl posn.
Cetelnly no spedl of kIowledge I better eitd to the
tet snd empdty ot youth, nd yet It eldom torm a prt
at ely imrction. Eiy body talks of the ler, the
wedge, and the pulley, ut mot people prdve that th
nooam whih they hbve of their re pectiU u ue is u *.
fasery nd AUdain t, and many ndeavour, at sa period
of lUe, to asuire a leni and uaet hkowledg of th
*ects that a prodded by Implemenmt whoh Ma in






1 PABPACL
eery body% hbads, or that are absolutely newery l the
daily oouations of mankind."
The Author tru tht the whole work will be fund
complete oompandlum of natural and eperimental philo-
sophy, not c(ly adapted to the undermtandnp of yong
people, but well calculated also to connvy that kId of tfal
Ilr Imumcia which I* absolutely aeuer before peso
as aettd public leture i thee branches of mne with
ad~utage. ',If," my Mr. Edgwort, spMkIng on thi
m)dJe, the loeture doe not communleate much of that
uowmedc which he eandr aours to explat, It is not to be
tributed either to his want of skill, or to the Insumeleqy
of bUi apparatus, but to the novelty of t te erms which e
is obliged to u. Ignorane of the language n whbih ay
aslmce i taught, Iban Insuperable bar to its baI suddamly
acquired; beldes a precise knowledge of the meanJtg of
teer, we mut have an instantaneous ide excited in er
malds hmeuver Uthy e repeated; and, as thib es be a
quined erly by pactice. it is Impossible that philosophleal
lause beoe muk miriem to thee who are aot hl-
~Ir a qualted wit the tochnb al eug e l walh tmey
as devrerd **
I i prermmed that an atetirv ponsel of theme Dales ,
to which the prtinlpal and meot oommon terms of sceae
me ue ally explained and Illuttd, bya variety of h&l.
ua temples, will be the msor o obviatian thil objdoeao
wh raspet to pernau who may be desirous of ailadhag
ths plia c phUsophlal lectures, to which the imabaltant
e ne mtrUoposl have lmeet coaai mSO m.
*Mr. tieeweuth-ed r M c Mdeslr a.lh i- s Mresaet ai
huIMam eof the o. but the amtke so wlle l us enr t.
w oa ook. the Wh.e ot M.ebet th d e
Im s S eiu. e tseer yet almi. (L l l -48










CONTENTS.
1


MECHANICS&

II. Of Mate. Ofthe D Thlbtlty o Mtt.......... 14
11 Of the Attraction of Cohesion .................. 1
IV. Of te Attraction of Coheson ..................
V. Of tUr Attmation of Graviuatio ................. a
VI. Of e Attation of Gravitation ................
VII. Of tim Atraction of Omravitaton ................ 81
VIII. Of the Attrctio f O vitation ................ U
I Of the CLetra of Orlty.......................... a
X. Oft L bare of Or"t : .............. 43
XL Of te La of Motoon ........................
XI. Of bo Laws of log on ........................ at
XI. Of the Laws of Mot ...................... a
XIV. Of MMed. aal Pows:: ....................
XV. Of UeLeW ................................... a
XVI Of h L rw.................................. a
VIL Of rte Wh~ l a Axi ...................... .
xV1. oJ OfPas U .............................. i
XX. Of thelBia pl m ........................ n
XX.Of Wd .......W......................... a
XXL Ofl*ABwe ............................... ..
XXIL Of eth Ptdlum ............................ f
ASTRONOMY.
iL Of tt Rg d U .............................. M
O. lbo f lamd eta".
IlL Of IM eadd Stear td e l .................. 8
IT. Of t O rt ....... ...................... I*$
v. Of t o systje ............................'. 'a
V. Of tl Miu of Ut Rua ...................... IU
VIL O tlhrdinal Motoa the F arEuth ............ IU
VILL Of ay and MIght .............................
IX. Of U Amn al Motion of &W Eurth ............ 1
x. Of* fuamo ................................ u
XL Of tMleB S ................................ 35
XIL Ofh 6lEqUtB o( TlM ...................... IM






vi1i CONTENTS.


IV; Ot~Fb.e ".......... .... 144K:..
xv. Ofr clp ................................... 14
XVL Ofihe Tde ............................... 153
XVII. Of the MIarseMoon ........................ 146
XIX. Of V.nu 164
XX. Of Mr .................................... 167
XXI. Of Jupt .................................. 170
XXIL Of Saturn .................................. 17
XXIIL Of the Herschel Planet ..................... 174
XXIV. Of Co t ...................................... 17
XXV. Of the 8an ................................. 179
XXVI. Of th fxed Star ......................... 180

HYDROSTATICS
I. latodatio .................................... 184
IL Of the Weigt and Preure of Fluids .......... 189
III. Of th W t ad Pressure of Fluids .......... 194
IV. Of the L al Pre urof Flul .id.............. 198
V. Of Ut Hydretttal Paradox .................. 90
VL Of th Hydrostatm Belows.....................
VII. Of th PreesureofFluldsaag st the ides o Vems 10
VIIL Of the Motio of Plldu ...................... 1S
IX. Of the Motio of Fluids ....................... III
X. Of the Spelf Gravity of Bodks ................ 4
XI. Ofr te Spde vity of Bodies................ 7
XI. Of t Mtebods of finding the SpeM o Gravity of
Bodies ................................. W
XII. Of the Mehodi of ending the Bpef Gravity of
Bodies .......... .....................
XIV. Of t Mebthods of hiding the Speclie Oravity of
Bodte .....................ooo ...oo ..o...o
XV. Of the Methods of fdung th Speci Gravity of
Bod ..... ........................... 9.
XVL Of the Hydrometer........................... 47
XVIL Of the Hydrometer and Swimming............ Sdl
XVIII. Of the Syphon and Tantalus's Cup .......... 964
XIX. Ofthe Diver's Bll........................... 95
XX. Of t Diver's Bel ................. .......... 3S
XXI. Of Pump ............................... a
XXIL Of the Poarig-pump-Rope-u. pump-Chata-
pump--ad Water-preu ............ ... on







CONTENTS. ix
PNEUMATICS.
i. Of th Natm of r ............................ 7
II. Of th Air-pump ................... .......... ..
II. Of the Torl ed ipperim nt ....... .........
IV. Of the Preern of the Air ...................... M
V. Of te Prmur of the Ar ..................... M
VI. Ofthm Weight of Air ......... ............ .. 1
VII. Of the lstlty of Air ....................... go
VIII. Of the Comprlo of Air ...................... 00
IX. M-sdluaous Brzprlmeotson the Air-pump ...... 304
X. Of the Air-gu and Sound ...................... 307
XI. Of Sound .................................... 311
XIL Of the Speding Trumpet ...................... 317
XIII Of Uthe cho................................. 313
XIV. Of the Echo................................ 384
XV. Of th Winds.................................. 38
XVI. Of thi Te 8 m-egine ......................... 354
XVII. Of the Steam-ongne ....................... 33
XVIIL Of th Steam-enine and Papln' Digester.... 841
XIX. Of the Baromet .......................... 34
XX. Of the Barometer and it Application to the
Meuring of Alttud ........................
XXL Ofth Thermomet............................. 5
XXII. Of the Thermomter ....................... 3M
XXIIL Of the Pjrometer and Hygrometr .......... 361
XXIV. Of the Rain-pou, and Rulm for Judging th
Weatr ............................ ..... s7
OPTICS.
L Lihbt: the mallnes and velocity of It ar e .. 371
IL Rays of Light :-Re ftlon and Refracton ........ 376
III. Refract of Li4ght .............................. 380
IV. Reflection and Refratlo of Light ............ 364
V. Di nt Kinds of L '........................ 388
VL Parallel diverging nd oonverng Rays .......... 303
VII. Images o Obfl l.--ldoptro Ball .............. 37
VIII. Nature and Advantages of Light .............. 401
IX. OolounM........................................ 404
XL SeetWd Light and Plain Mirror ................ 407
XI. Conmav Mirrors................................ 410
XILO Coea s Mlrrors.-Epertlmente. ............. 414
XIII. Comeve and Convex Mirror.................. 417
XIV. Optin Decptions, Anamorphoses, &c......... 490
XV. D rt Part of the ye ....................... 44
XVI. Mane of Viton ............................ 4*7






SCoTCOTENTS.

XII. pectade, and their .................... 4
XVIII. abow ................................ 4W
XIX. Raftiu Tlamopm .....***................ 4a
XX. .lt.d"SlnTdolemp *......................... 444
XXL Microcope ................................. T
XXUI. Casms Obcula. Maio Lthorn, ad NldU-
plyag Gl .........******.................. 44
MAGNETI1M.
L The OM- ............. ................. 4s
IL Mnt Att on and Repulon ............. 1
nI. Method ofmakin a Mgnet .................... 44
IV. Marines Comn m ............................. t4
ELECTRICITY.
L BEarly HiLtor of Electricit ...................... 47
II. BLtrgLel Attraction nd Repulsion .............. 47
II. electrical Mahlne............................. 47
IV. seJriasl Machine ............................. 4
V. lectrial Attraction and Rpulsion .............. 41
VI. ElUmialcs Attraction uad Repulon .............. 48
VII. Te Leydem Phial............................. 497
VIIL La ms Mb trometa, d the BRletrie Barl y
IX. Baperimat with EZltral BtIry ............ Ms
X. t-lluIamu Blierit.......... ............. s
XL ElmophMM Izk omnwrT-T der-Hou...... alt

XI-. At tw ........................ a
Xu. Of Atmosphr MO .IVCt -ot FaLbq Sl.-

XIJ. edet ** *************............. ...
XV. An Zeetric theO Teepd-of the Gym-
not3 tahee5 B ilarm letlimn.... asm
KTL A Gefmal Demmiar O Euthldul, wt w pot-
nam. I ......... ..... .....*................ .a
GALVANISM.
L Of Galdttaba; IU Org per; Rpwl mat.d th De.

IIL. Galwraleonduntos-Cals--TablU-lxspilmt SI
IV. misasteu r.1 sperimmta .................. a
Glomry ad *lde ............................ .I









MECHANICS.


CONVERSATION I.
INTRODUCTION.
1ATIn--CHALUE-m LA.
CHALS. Father, you toldsister Emmaandme that,
afterwehad nishedreadingthe Eavnigs t Hom,'
you would explain to us some of the principle of
natural philosophy : will you begin this morning
Father. Yes, I am quite at leisure: and I shall
indeed at ll time take delight in communicating to
you the elemets ofueful knowledge ; and the more
so in proportion to the desire which you have of ool-
letingand storing those facts that may enableyou to
understand the operations of nature, as well a the
works of ingiou artists. Thee,I trust, willlend
youinsenbly to dmirthe wisdom and goodunemb
means of which the whole system of the universe s
eostrted and ported.
Emma. But an philoph be eomprehendedby
children so young as we are I thought that it had
been the busine of men, and of old men too.
F. Philosophy is a word which in itsorigins seaw
fimee only a loe or deire of widom ; and you
wi not allow that you and your brother are too
yang to wish for knowledge.
L So fr from it, that the more knowledge Iget
th better I seem to likeit ; and the number of new
idM which, with a little of your distance, I hve
o ibtaIle fh the Erwa elie BHo,' and tlheg
pl1m w0 ih0 I have received from the pean- of






12 MECHANCSa.
that work, will, I am sure, excite me to read it again
and in.
F. Yon will find very little, in the introductory
parts of natural and experimental philosophy, that
will require more of your attention than many part
of that work with which you were so delighted.
C. Butin some books of natural philoophy, which
I have occasionally looked into, anumberofnew and
uncommon words have perplexed me; I have also
seen references to figures, by means of large letters
and small, the use of which I did not comprehend.
F. It ia frequently a dangerous practice for young
minds to dip into subjects before they are prepaed,
by some previous knowledge, to enter upon thm ;
one it may create distaste for the moet mtereting
topics. Thus,thosebooks which younowreadwlthso
much pleasure would not have afforded you thesmal-
est entertainment a few years ago, when you mnt
have spelt out almost every word in each page. T
same sort of disgust will naturally be felt by par-e
who should attempt to read works of science bebe
the leading terms are explained and underatod.
The word angle is continually recurr inn bjsecd
of this sort ; do you know what an angle is I
E. I do not think I do ; will you explain whWit
means
F. An eagle is made by the opening of two stbll
line. Inthe figuretherearetwo straights e .
lines ab and e meetingat the point b, and
the opening made by them s called an p
angle. '**0.
C. Whether that opening be small or greak I
still called an angle I
F. it is; your drawing compasses may faalMi
8dt lUm, In wor o of sl ea, arse usu V dl
atd rtiet Hl.






INTRODUCTION. 13
to your mind the idea of an angle ; the lines in this
Agure will aptly represent the legs of the compasses,
and the point the joint upon which they more or
tun N ow you may open the legs to any distance
youplease, even so farathey shall form onestraigt
line; in that position only they do not form an angle.
In eery other situation an angle is made by the
opening of these legs, and the angle is said to be
greater or less, a that opening is greater or less.
An angle is another word for a corner.
E. Are not some angles called right angles I
F. Angles are either right, acute, or obtul. When
the line ab meets another line cd in such
a manner as to make the angles abd and
abe equal to one another, then those an- --'
glesare calledright angles. And theline Fi. .
ebissaidtobeperpendiculartood.Hence e .
to be perpendicular to, or to make right angles with,
a line, means one and the same thing.
. C. Does it signify how you call the letters of an
P. It is usual to call every angle by three letters,
and that at the angular point mustbe always |
the middle letter of the three. There are
cases, however, where an angle may be de-
nomated by a single letter; thus the angle
de may be called simply the angle b, for
there is no danger ofmistake, because there Fi. .
is but a single angle at the point b. g. .
C. I understand this; forif, inthe second figure
I were to deserbe the angle by the letter 6 onl,
ye would not know whether I meant the angl
That is the preciare why it is necessary
l meet deseriptions to make use of three lettrs.
hAa mo angle (Fig. I.) oe& is less than a right






14 MECHANICS.
angle; and an obtus angle (Fig. 8.) e is greater
than a right angle.
E. You ee the rea now, Charles, why letters
reld against or by the figure, which pushed
you Mbeore.
C. I do; they're intended to distinguish the
parate parts of each in order torender the descrip-
tion of them easier both to the author and the reader.
E. What is the difference, papa, between an
angle and a triangle I
F. An angle being made by the opening of two
lines, and a you know that two straight lines cannot
enclose a space, so atrigle a6 is a space
bounded by three straight lines. Ittakesaza
its name from the property of containing 4.
three angles. There are various sorts of 'g.
triangles, but it is not necessary to enter upon theae
particulars, s I do not wish to burden your memories
with mwe technical terms than we have ooeaio for.
C. n then, i a space or fgure contaning
three a l, and bounded by as many straight li.
F. Ye, that description will aMwr o present

CONVERSATION n.
OF NATTU.-OF TRH DIVISIBILITY OF MATTER.
F. Do you understand what philosopher mean
when they make use of the word matter I
E. Are not all things which wesM ad fed oom-
posed of matter t
SF. Every thing which isthe object ofer se-sis
eompoed of matter differetly modifid sarmngd.
But in a philosophical sene matter is deaed t be
an e~sud, solid, innoete, and m i embhelam
C. If by extension Is meat length, breadth
thelknae, matter, u abtredly, is an esamJ .






DIVISIBILITY OF MATTIBL 16
stnee. Its solidity is manifest by the rnrtance it
makes to the touch.
E. And the other properties nobody will d(ny tor
lmterial objeteareofthemselveswithoutmotion;
and yet it my be readily conceived,that, by applied
tion of a op force, there no body whieh eanot
bemoved But I remember p that you told as
something stage bout the disTibility of matter
which you aid might be continued without end.
F. I did, ome time back, mention this curious
and intereting subject, and this is a very fit time
for me to explain it.
C. Can matter indeed be infinitely divided; for
I suppose that this is what is meant by a division
without and I
F. DiMiult as this may at t appear, yet I
think it very capable of proof. Can you conceive
of a particle of matter so small as not to have an
upper and under surface I
C. Certainly every portion of matter, however mi-
nute, must have two surfaes at least, sad then I seo
that it follow of ourse that it is divitibe; that is,
the upper and lower surfaes may be separated.
F. Yor conclusion is just; ad, though thefe
may be paricle of matter too mall for us actually
to divid, yet this aries from the imperfetion of
our intrumets; they must nevrtbes, in their
nature, be diviible.
E. But you wee to give us so remarkable in.
stances of the minute division of matter.
F. A few year agoa lady pun single poudof
wool nto a thread 168,000 yards long. And Mr.
Beyle actions that two grains and ahalfof milk was
u nato thread 00 yards in length. Ifapound
f Silver, whi. yeo know, contains 5,760 Mins,
and a sile of old be malted together, the






10 MECHANICS.
gold will be equally diffused through the whole sil-
ver, insomuch, that if one grain of the mass be dis-
solvedin a liquid called aquaforti, the gold will fall
to the bottom. By this experiment, it is evident
that a grain maybe dividedinto 5,761 visible parts,
for only the 5,761 t partof the gold is contained in
a single grain of the mass.
The goldbeaters, whom you have seen at work in
the shops in Long-acre, can spread a grain of gold
into a leaf containing 50 square inches, and thisleaf
may be readily divided into 500,000 parts, each of
which is visible to the naked eye: and by the help of
a microscope, which magnifies the area orsurface of
body 100 times, the 100th part of each of these be-
comes visible; that is, the 50 millionth part of a
grain of gold will be visible, or a single grain of that
metal may be dividedinto 50 millions of visible parts.
But the gold which covers the silver wire used in
making what is called gold lace, is spread over a
much larger surface, yet it preserves, even if exa-
mined byamicroscope, anuniformappearance. It
has been calculated that one grain of gold, under
these circumstances, would cover a surface of nearly
thirty square yards.
The alura divisions of matter are still more sur-
prising. In odoriferous bodies, such as camphor,
musk, and ssafoetida, a wonderful subtilty of part
is perceived; for, though they are perpetual filling
a considerable space with odoriferous particles, yet
these bodies lose but a very small part of their
weight in a great length of time.
Again, it s aid by those who have examined the
subjectwith the bstglasses, and whose accuracymay
be relied on, that there are more animals in the milt
of a single cod-fish, than there are men on the whole
earth, and that a single grainof sand is larger than






DIVIrlBILITY OF MATTER. 17
bur millions of these animals. Now if it be admitted
hat these little animals are possessed of organized
rts, such as a heart, stomach, muscles, vein, arte-
res, &c. and that they re possessed of a complete
stem of circulating luids, similar to what is found
Slar e animals, we seem to approach to an ideaof
he infinite divisibility of matter. It has indeed been
slated, that a particle of the blood of one of these
culse isasmuch smallerthan globe one-tenth
San inch in diameter, as that globe is smaller than
whole earth. Nevertheless, if these particles be
mpared with the particles of light, it is probable
they would be found to exceed them in bulk as
uch as mountains do single grains of sand.
I might enumerate many other instances of the
kind, but these, I doubt not, will be sufficient
oyovince you into what very minute parts matter
scpable of being divided.
Captain Seoraby, in his Account of the Greenland
,states, that, in July 1818, his vesel sailed for
erallesgues in water of a very uncommon appear-
e. The fae was variegated by la patches
a yellowsh-green color. It was ondtobe pro-
ed by animnlcule and microsopes were ap
their examination. In a single drop of the watr,
ad by a power of 28,224 (magni edsuper
es), there were 50 in number, on an average, i
square of the micrometer glass of 1-840th of an
ch in diameter; and, as the drop occupied a circle
a plate of glass containing 529 of these squares,
ere must have been in this single drop of water,
en at random out of the sea, andinaplace not the
lot discoloured, about 26,450 animalcule. How
coucelvably minute must the vessels, orans, and
ds, of these animals be I A whale requires a sea
sport in : a hundred and ffty million of thse
10 a






18 MECHANICS.
eould kaw ample sope for tlAir evolatiUo in a
tum 6er of 0atr I
CONVERSATION III.
OF THE ATTRACTION OP COHESION.
F. Well, my dear children, have you reflected
upon what we last conversed about 1 Do you com-
prehend the several instances which I enumerated
s examples of the minute division of matter I
E. Indeed, the examples which you gave us, very
much excited my wonder and admiration, and yet,
from the thinness of some leaf gold which I once
had, I can readily credit all you have said on that
part of the subject. But I know not how to conceived
of such small animals as you described ; and I am
still more at a loss how to imagine that animals M
minute, should possess all the properties of the
larger ones, such as a heart, blood, veins, &c.
F. I can, the next bright morning, by the help of
my solar microscope, show you very distinctly, the
circulation of the blood in a flea, which you may get
from your little dog; and with better glasses thai
those of which I am poesesed, the same appearance
might be seen in animals still smaller than the flea
perahap even in those which are themselves invisible
to the naked eye. But we shall converse more at
lare on this matter, when we come to consider the
subeat of optics, and the construction and uses of
tho olarw mcroecope. At present we will turn our
thoughts to that principle in nature, which philoso-
phers have agreed to call gravity, or attraction.
C. If there be no more difficulties in philosophy
than we met with in our last lecture, I do not fear
but that we shall, in general, be able to understand
it. Are there not several kinds of attraction.
F. Yes, there are; two of which it will be sam-






ATTRACTION OF COUSION. 19
dent for ourpre t prpoae to describe ; the one
i the atstratio o/f odioS; the other, that of gre-
kittion. The aUranNoo of oedrai is that power
which keep the parts of bodies together when the
touch, and prevents them from separting,or whioh
inclines the part of bodies to umte, when they are
placed efficiently near to each other.
C. Is it then by the attraction of cohesion tha
the parts of this table, or of the penknife are kept
together I
F. The instances which you have selected are
accurate, but you might have sid the same of every
other solid substance in the room ; and itis in pro-
portion to the different degrees of attraction with
which different sumbtances are affected, that some
bodies are hard, others soft, tough, &e. A philo.o-
pher in Holland, almost a century ago, took great
pin in pertaining the different degrees of cohe-
ion which belonged to various kinds of wood, me
ta, and many other nbetances. A short account
the experiment made by M. Musehenbroek,
on will hereaft nd in your ow language, in
. Eneld's Intitutes of Natural Philosophy.
C. You once showed me that two leaden bullet
having a little scraped from the surfaces, would
itk together with great free ; you called that, I
biee, the attraction of cohesion
F. I did: some philosopher, who have made this
Experiment with great attention and accuracy, a-
% that if the flat nrfaces, which are presented
one another, be but a quarter of an inch in dia-
rsaped very smooth, and forcibly presed
their with twist, a weight of hundred pounds
gently required to separate them.
As it is by this kind of attraction that the partsof
ldbodiesare kept together, o, when anysubetanee






30 MECHANICS.
is separate or broken, it is only the attraction of
cohesion that is overcome in that particular part.
E. Then whenI had the misfortunethis morning
at breakfast to let my saucer slip from my hands, by
which it was broken into several pieces, was it only
the attraction of cohesion that was overcome by the
parts of the saucer being separated by its fall on the
ground I
F. Just so ; for whether you unluckily break the
china, or cut a stick with your knife, or melt lead
over the fire, as your brother sometimes does, in
order to make plummets ; these, and a thousand
other instances which are continually occurring,
are but examples in which the cohesion is over-
come by the fall, the knife, or the fire.
E. The broken saucer being highly valued by
mamma, she has taken the pains to join it again with
white lead ; was this performed by means of the
attraction of cohesion I
F. It was, my dear ; and hence you will easily
learn that many operations in cookery are in fact
nothing more than different methods of causing this
attraction to take place. Thus, flour, by itself has
little or nothing of this principle, but when mied
with milk, or other liquids, to a proper consistency,
the parts cohere stronly, and this cohesion in many
instances becomes still stronger by means of the
heat applied to it in boiling or baking.
C. You put me in mind of the fable of the man
blowing hot and cold ; for in the instance of the
lead, fire overcomes the attraction of cohesion; and
the same power, beat, when applied to puddings,
bread, &c. causes their parts to cohere more pow-
erfully. How are we to understand this
F. I will endeavour to remove your difficulty.
Heat expands all bodies without exception, as you






ATTRACTION OF COBMION. 21
shall see before we have finished our lectures. Now
the fire applied to metals in order to melt them,
cause such an expansion, that the particle are
thrown out of the sphere, or reach, of each other's
attraction ; whereas the heat communicated in the
operation of cookery, is sufficient to expand the
particles of flour, but is not enough to overcome the
attraction of cohesion. Besides, your mamma will
tell you, that the heat of boiling would frequently
disunite the parts of which her puddings are com-
posed, if she did not take the precaution of enclosing
them in a cloth, leaving them just room enough to
expand without the liberty of breaking to pieces;
and the moment they are taken from the water, they
lose their superabundant heat, and become solid.
E. When Ann the cook makes broth for little
brother, it is the heat then which overcomes the
attraction which the particles of meat have for each
other, for I have seen her pour off the broth, and
the meat is all in rage. But will not the heat over.
come the attraction which the parts of the bones
have for each other I
F. The heat of boiling water willnever effect this,
but a machine was invented several years ago, b
Mr. Papin, for that purpose. It is called Papin's
Digester, and is used in taverns, and in many large
families, for the purpose of dissolving bones as com-
pletely as a lesser degree of heat will liquefy jelly.
On some future day I will shew-you an engraving
of this machine, and explain it different parts,
which are extremely simple.
CONVERSATION IV.
or THR ATTRACTION OF COBlION.
F. I will now mention some other instances of this
ee Pneumatics, Conversation XVIII.






22 MECHANICS.
great law of nature. If two polished platesofmarbl%
or brass, be put together, with little oil between
them to fill up the pores in their surfaces, they wil
cohereso powerfully asto required very considerale
force to separate them.-Two globules of quicksilver
placed very near to each other, will rn together and
form one large drop.-Drope of water will do the
same.-Two circular pieces of cork placed upon
water at about an inch distant will run together.-
Balance a piece of smooth board on the endofa scale
beam; then let it lie flat on water, and five or six
times its own weight will be required to separate it
from the water. If a small globule of quicksilver be
laid on clean paper, and a piece of glass be brought
into contact with it, the mercury will adhere to it, and
be drawn away from the paper. But bring a larger
globule into contact with the smaller one, and itwill
Jorsaketheglass,and unite with the other quicksilver.
C. Is it not by means of the attraction of cohe-
sion, that the little tea which is generally left at the
bottom of the cupinstantly ascends in the sugar when
thrown into it I
F. The ascent of water or other liquids in sugar,
sponge, and all porous bodies, is a species of this at-
traction,andis called opillary* attraction: itisthus
denominated from the property which tubesofa very
mall bore, scarcely larger than to admit hair, have
of causing water to stand above its level.
C. Is this property visible in no other tubes than
those the bores of which are so exceedingly fine I
F. Yes, it is very apparent in tubes whose diame-
ters are one-tenth of an inch or more in length, but
the smallerthe bore, the higher the fluid rises; for it
ascends, in all instances, tillthe weight of the column
of water in the tube balances, or is equal to, the at-
From epitllu, the Latin word for hair.






ATTrACTION OF OOIISIO1. 23
tractionofthetube. Bylimensingtnbesofdlteremt
bores n a vesel of coloured water, ou will ee th
the water rise as much higher in the mller tabe,
thanin the larger, asits bore islethan that ofthe
larger. The water will rise a quarter of an inch,
and there remain suspended in a tube, whoe bore
is about one-eighth of an inch in diameter.
This kind of attraction is wellillutrated, by taking
two pieces ofglass, joinedtogether at
the side be, and kept a little open at
the opposite side ad, bya small piece
of cork e. In this position immerse
them in a dish of coloured water fg,
and you will observe that the at-
traction of the glass at and near b0, Fig. 5.
will cause the fluid to ascend to b, where about the
parts d, it scarcely rises above the level of the water
I the vessel.
C. I see that a curve is formed by the water.
F. There is, and to this curve there are many ca-
rious properties belonging, as you will hereafter be
able to investigate for yourself
E. Is it not upon the principle of the attraction of
chesion, that earpentrs glue their work together I
F. It is upon ti principl that carpenter and
abinet-makers make e ofglue; that brazier, tin-
men, plumbers, e. solder their metals; and that
smiths unitedifferent bar of iron by mea of heat.
These, and a thousand other operations of which we
are continually the witnesses, depend on the same
principle as that which induced your mamma to use
the white lead in mendinher saucer. And y onuht
to be told, that though white lead is frequently uasd
a cement for broken china, glass, and erthenware,
yet,ifthevesselsare tobe broughtagain into ue, tis
not a propercement, being an active poison; besides,






Z4 MECHANICS.
one much stronger has beendiscovered, I believe, by
a very able andingenious philosopher, the late Dr.
ugenhouz ; at least I had it from him several years
ago; it consists simply of a mixture of quicklime
and Glocester cheese, rendered soft by warm water,
and worked up to a proper consistency.
E. What I do such great philosophers, as I have
heard you say Dr. Ingenhouz was, attend to such
trifling things as these I
F. He was a man deeply skilled in many branches
of science; and I hope that you and your brotherwill
one day make yourselves acquainted with many of
his important discoveries. But no real philosopher
will consider it beneath his attention to add to the
conveniences of life.
C. This attraction of cohesion seems to pervade
the whole of nature.
F. It does, butyou will not forget thatitactsonly at
very small distances. Some bodies indeed appear to
possessa power the reverse of the attraction of co.
hesion.
E. What is that, papa t
F. It is called repulsion. Thus water repels most
bodies till they are wet. A small needle carefully
placed on water will swim: flies walk upon it without
wetting their feet: the drops of dew which appear
in a morning on plants, particularly on eabbage
plants, assume a globular form, from the mutual at-
traction between the particles of water; and upon ex-
amination it will be found that the dropedonottouch
the leaves, for they will roll off in compact bodies,
which could not be the case, if there subsisted any
degree of attraction between the water and the leaf.
If a small thin piece of iron be laid upon quick-
silver, the repulsion between the different metals
will cause the surface of the quicksilver near the
ir'ui to be deiprroesd.






ATTRACTION F0 GRAVITATION. 3.
The repelling force of the particle of a fluid is
bat small ; therefore, if a fluid be divided, it easily
unites again. But if a glass or any hard saubtanee
be broken, the parts cannot be made to cohere
without being first moistened, because the repulsion
is too great to admit of re- union.
The repelling force between water and oil is like-
wisesogreat, thatitisalmostimposibletomixthem
in such a manner that they shall not separate again.
If a ball of light wood be dipped in oil, and then
put into water, the water will recede so as to form
a small channel around the ball.
C. Why do cane, steel, and many other things,
bear to be bent without breaking, and, when set at
liberty again, recover their original form I
F. That a piece of thin steel, or cane, recovers its
usual form after being bent, is owing to a certain
power, called elasticity, which may, perhaps, arise
frm the particles of those bodies, though disturbed,
not being drawn out ofeach other's attraction; there-
fore, a soon as the force upon them ceases to act,
they restore themselves to their former position.-
But our half hour is expired ; I must leave you.
CONVERSATION V.
OF THU ATTRACTION 01 OBAVITATION.
F. We will now proceed to discuss another very
important general principle in nature ; the attrae-
tie of gravitation, or, as it i frequently termed,
preity, which is that power by which distant bodies
tend towards each other. Of this we have perpetual
instances in the falling of bodies to the earth.
C. Am I, then, to understand that whether this
marble falls from my hand, or a loose brick from
the top of the house, or an apple from the tree in
the orchard, that all these happen by the attraction
of gravity 1






26 MCCHANIU.
F. Itisby the power which is commonly expressed
under the term greity, that all bodies whatever
have a tendency to the earth ; and, unless supported,
will fall in lines nearly perpendicular to its surface.
E. But are not smoke, steam, and other light
bodies, which we see ascend, exceptions to the
general rule t
F. It appears so at first sight, andit wasformerly
received as general opinion, that smoke, steam, tc.
possessed no weight: the discovery of the air-pump
has shewn the fallacy of this notion, for in an ex-
hausted receiver, that is, in a glass jar from which
the air is taken away by means of the air-pump,
smoke and steam descend by theirown weights com-
pletely as a piece of lead. When we come to con-
verse on the subjects of pneumatics and hydrostatics,
you ill understand that the reason why smoke and
other bodies ascend is simply because they are lighter
than the atmosphere which surround them, and the
moment they reach that part of it which has thesame
gravity with themselves they cease to rise.
C. Is it, then, by this power that all terrestrial
bodies remain firm on the earth I
F. By gravity, bodies on all parts of the earth
(which you know is of a globular form) are kept on
its surface, because they all, wherever situated,
tend to the centre; and, sinee all have a tendency
to the centre, the inhabitants of New Zealand, al-
though nearly opposite to our feet, stand frm as
we do in Great Britain.
C. This is difiult to comprehend; nevertheless,
if bodies on all parts of the surface of the earth have
a tendency to the centre, there seems no reason
why bodies should not stand as firm on one part as
weU as another. Does this power of gravity act
alike on all bodies I






ATTRACTION O GRAVITATION. 27
F. It does, without any regard to their igure or
sise; for attraction or gravity acts upon bodies in
proportion to the quantity of matter which they
contain, that is four times a greater force of gravity
is exerted apon a weight of four pounds than upon
one of a single pound. The onseence of this
principle is, that all bodies at equal distaes from
the earth fall with equal velocity.
E. What do you mean papa, by edloeiy t
F. I will explain it by an example or two: if you
and Charles set out together, and you walk a mile in
half an hour, but he walk and run two miles in the
same time, how much swifter will he go than you I
E. Twice as swift.
F. He does, because is the same time, he passes
over twice as much space; therefore, we say his
velocity is twice as great as your's. Suppose a
ball, fired from a cannon, pass through 800 feet in a
second of time, and in the same time your brothers
arrow pass through 100 feet only, how much swifter
does the cannon-ball fly than the arrow I
E. Eight times swifter.
F. Then it has eight times the velocity of the arz
row ; and hence you understand that swiftness and
velocity are synonymous terms; and thatthe velocity
of a body is measured by the space it passes over
in a given time, as a second, a minute, an hour, &e.
E. If I let a piece of metal, as a penny-piece,
and a feather, fall from my hand at the same time,
the penny will reach the ground much sooner than
the feather. Now how do you account for this, if
all bodies are equally affected by gravitation, and
descend with equal velocities, when at the same
distance from the earth I
F. Though the penny and feather will not, in the
open air, fal with equal velocity, yet, if the air be





28 MECHANICS.
taken away, which is easily done, by a little appera-
tus connected with the air-pump, they will descending
the same time. Therefore the true reason why light
and heavy bodies do not fall with equal velocities, is
that theformer, in proportion to itsweight, meets with
a much greaterresistance from the air than the latter.
C. It is then, I imagine, from the same cause that
if I drop the penny and a piece of light wood into
a vessel of water, the penny shall reach the bottom,
but the wood, after descending a small way, rises
to the surface.
F. In this case the resisting-medium is waterin-
stead of air, and the copper, being about nine times
heavier than its bulk of water, falls to the bottom
without apparent resistance. But the wood, being
much lighterthan water,cannot sinkinit; therefore,
though by its mojsentum it sinksa small distance, yet,
as soon as that is overcome by the resisting medium,
it rises to the surface, being the lighter substance.
CONVERSATION VI.
OF THa ATTRACTION 0O ORAVITATION.
E. The term momentum, which you made use of
yesterday is another word which I do not understand.
F. If you have understood what I have said re-
specting the velocityof movingbodies, you willeasily
comprehend what is meant by the word momentum.
The momentum, or moving force, of a body, isits
weight multiplied into its velocity. You may, for
instance, place this pound weight upon a china-plate
without any danger of breaking, but, if you let it fall
from the height of only a few inches, it will dash the
china to pieces. In the first case, the plate has only
the pound weight to sustain ; in the other, the weight
must be multiplied into the velocity, or, to speak n a
popular manner, into the distance of the height from
which it fell.






ATTrACTION OF ORAITATION. 19
If a bell a len against the obeta- .
de 6, it will not be able tooverturnl -- .
it, but if it be taken up to and suf-
fered to roll dowi the inclined plane Fig. 6.
do against b, it will certainly overthrow it; in the
former case, 6 would only have to resist the weight of
the ball a, in the latter it has to resist the weight
multiplied into its motion or velocity.
C. Then the momentum of a small body, whose
velocity is very great, may be equal to that of a very
large body with a slow velocity.
F. It my, and hence you see the reason why
immense battering-rams, used by the ancients in
the art of war, have given place to cannon balls of
but a few pounds weight.
C. I do, for what is wanting in weight, is made
up in velocity.
F. Can you tell me what velocity a cannon ball of
28 pounds mut have, to effect the same purposes, a
wouldbe produced by a battering-ram of 1,0001be.
weight, and which, by manual strength, could be
moved t the rate of only two feet ina second of time
C. I think I can :-the momealsm of the bettering-
ram must be estimated by its weight, multiplied into
the pace passed over in a second, which is 15,000
multiplied by two feet, equal to 30,000 ; now if this
momentum, which must also be that of the cannon
ball, be divided by the weight of the bell, it will give
the veloityrequired ; and 80,000 divided by 28, will
give for the quotient 1072 nearly, which is the num-
berof feet which the canon ball must pas over in a
econd, in order that the moment of the battering-
ram and the ball may be equal, or, in other words,
that they may hav e same effect in beating down
an many's wall.
& I now fully comprehend what the momentum






0S MECHANICs.
of a body is, for if I let a common trap-ball accident.
ally fall from my hand upon my foot, it occasions
more pain than themere pressure of a weight several
times heavier than the ball.
F. If you let a pound, or hundred pounds, fall on
the floor, only from the height ofan inch and a quar-
ter, it will strike the floor with a momentum equalto
double its weight: and if you let it fall from four
times that height, or five inches, it will have double
that effect;- and if it fall nine times that height, or
eleven inches and a quarter, it will have treble the
effect;-and by falling sixteen times the height, or
twenty inches, it will have four times the effect, and
soon. Hence itis plain, that if you let the ball dop
from your hand at the height of twenty inches only,
it will have eight times more effect in causing pain
than the mere pressure of the ball itself.
C. If the attraction of gravitation be a power by
which bodies in general tend towards each other,
why do all bodies tend to the earth a a centre
F. I have already told you that by the great law of
gravitation,theattraction ofallbodiesisin proportion
to the quantity of matter which they contain. Now
the earth, being so immensely large n comparison of
all other substances in its vicinity, destroys the effect
of this attraction between mailer bodies, by bring-
ing them all to itself.-If two balls are let fall from a
high tower at a small distance apart, though they
have an attraction for o e another, yet it wil be as
nothing when compared with the attraction by which
they are both impelled to the earth, and consequently
the tendency which they muatally have of apprach-
ing one another will not be perceived in the fa. If,
however, any twobodies werpiaeedinfreespese,and
ontofthe sphereofthe earth's attraction, theywould
in that ease asuredly fall toward each ether, and






ATrrACTION oF GRAVITATION 31
that with increased velocity as they came nearer. If
the bodies were equal, they would meet in the middle
point between the two; but if they were unequal,
they would then meet as much nearer the larger
ue, as that contained a greater quantity of matter
than the other.
C. According to thi, the earth ought to move to-
ward falling bodies, as well as they move to it.
F. It ought, and, in just theory, it des; but when
you calculate how many million of times larger the
earth is than any thing belonging to it; and if you
reckon the smalldistances from which bodiescan fal,
nyu will then know that the point where the falling
bodie and earth willmeet, is removed only to an in-
deinitely mall distance from its surface; distance
much too small to be conceived by the human imagi-
nation.
We will resume the subject of gravity to-morrow.
CONVERSATION VII.
OF THe ATTRACTION OF GRAVITATION.
E. Has the attraction of gravitation, papa, the
sme effect on all bodies, whatever be their distance
from the earth I
F. No; this, like every power which proceeds
rom a centre, decreases a the squares of the dis-
tanes from that centre increase.
I. I fear that I shall not understand this unless
you illustrate it by examples.
F. Suppoee you e reading at the distance of me
foot fro a candle, and that you receive a certain
uantity of lighton your book; now if you remove to
the disence of two feet from the candle, you will, by
ths law, enjoy four times lees light than you had be-
fore; here then though you haveincreaed your dis-
tame but two-fold, yet the light i diminished four






33 MECHANICS
fold, because four is the square of two, or two multi-
plied by itself. If, instedofremovingtwo feetfrom
the candle, you take your station at 4, 5, or 6 feet
distance, you will then receive, at the different dis-
tances, 9, 16, 25, 86 times less light than when you
were within a single foot from the candle, for these, a
you know, are the squares of the numbers, 8,4, 5 and
6. The same is applicable to the heat imparted by a
fire; at the distance of one yard from which, a per-
son will enjoy four times as much heat, as he who
sits or stands two yards from it; and nine times as
much as one that shall be removed to the distance
of three yards.
C. Is then the attraction of gravity four times
less at a yard distance from the earth, than it is at
the surface
F. No; whatever be the cause of attraction, which
to this day remains undiscovered, it acts from the
entreofthe earth,and notfrom its surface, andhence
the difference of the power of gravity cannot be dis-
eerned at the small distances to which we cae have
access; for amileor two, which is much higher than,
in general, we have opportunities of making experi-
ments, is nothing in comparison of 4000 miles, the
distance of the centre from the surface of the earth.
But could weascend 4000 milesabove the earth, and
of course be double the distance that we now are from
the centre, we should then find that the attractive
force would be but one-fourth of what it is here; or
in other words that body, which at the surface of the
earth weighs one pound, and, by the fore of gravity,
falls through sixteen feet in a second of time, would
at 4000 mies above the earth weigh but a quarter of
a pound, and fall through only four feet in a second."
SR. Bapposs It we required to And the weight of a
lesdM ba aU theg top of a mountsal three muse hlfh, wrhac






ATTRACTION OF ORAVITATION. 83
B. Howis that known, papa, for nobody ever was
there
F. Youareright,mydear,forGarnerin,who sme
years ago astonished all the people of the metropelie
and its neighbourhood, by his light in a bhJoom,
ascended but a little way m comparison of the dis-
tance that we are peaking of. However, I will try
to explain in what manner philosophers have come
by their knowledge on thi subject.
The moon is heavy y by connected with the earth
by this bond of attraction; and by themost accurate
observations it is known to be obedient to the same
laws as other heavy bodies are ; its distance is also
clearly ascertained, being about 240,000 miles, or
equal to about sixty semi-diameters of the earth, and
of course the earth's attraction upon the moon ought
to diminish in the proportion of the square of this
distance ; that is, it ought to be 60 times 60, or
8600 times lees at the moon than it is at the surface
of the earth. This is found tobe the case, by the
measure of the deviation of its orbitfrom right line.
Again, the earth is not a perfect sphere, but a
spheroid, that s, of the shape of an orange, rather fat
at the twoendscalled the poles, and the distance from
the centre to the poles is about seventeen or eighteen
miles less than its distance from its entire to the
equator; consequently, bodiesoghtto be somenthng
heavier at, and near the poles, than they are at the
equator, which is lso foundto bethe ease. Hence
it is inferred that the attraction of gravitation varies
onthm ser of the erth weighs SMb. Ifthe semil-ditme
of thr wth be tsa at 4000, tb add to thist hrhtof
the Uutal, a y,d my t square of 4008 is to tMhe squm
of 40UO, so s 90M. to a fourth proportional: or as 100o400:
1000000::Dl:tI osmrething mon than ISib, ios.,
which I the weight o the eodes ball at the top of th
mountain
90 a






4 MECHANICS.
at all distances from the centre of the earth, in pro
portion as the square of those distances increase.
C. Itseemsverysurprising that philosophers, who
have discovered so many things, have not been able
to find out the cause of gravity. Had Sir Iaae
Newton been asked why a marble, dropped from
the hand, falls to the ground, could he not have as-
signed the reason I
F. That great man, probably the greatest man
that ever adorned the world, was as modest as he
was great, and he would have told you he knew not
the cause.
The late learned Dr. Price, in a work which he
published forty-five yearsago, asks, "who does not
remember a tume when he would have wondered at
the question, wky does water run dows kill ? What
ignorant man is there who is not persuaded that he
understands this perfectly I But every improved
man knows it to be a question he cannot answer."
For the descent of.water, like that of other heavy
bodies depends upon the attraction of gravitation,
the case of which is still involved in darkness.
E. You just now said that heavy bodies by the
force of gravity fall sixteen feet in a second of time;
is that always the case I
F. Yes, a bodies near the surface of the earth fall
at that rate in the first second of time, but as the at-
traction of gravitation is continually acting, so the
velocity of aling bodies is an increasing, or, as it is
usually called, an aceelerating velocity. It is found
by very accurate experiments, that a body, descend-
ingfrom a considerable height by the force ofravity,
tils 16 feet in the first second of time; 8 times 1
feet in the next ; 5 times 16 feet in the third ; 7
times 16 feet in the fourth second of time; and so
SSee Conver. VI. on Astronomy.






ATTRACTION OF OGAVITATION. U
on, continually inreasing according to the odd
numbers, 1, ,, 5, 9, 11, &o. In our latitude the
true distance fallen is 16 feet one-twelfth ; but, by
reason of the centrifugal force, this distance varied
a little in different latitudes. But this shall be
explained to you hereafter.
CONVERSATION VIII.
OF THI ATTRACTION 0 O ORVITATION.
E. Would a bell of twenty pounds' weight here,
weigh half an ounce lees on the top of a mountain
three miles high I
F. Certainly ; but you would not be able to as-
certain it by means of a pir of scale and another
weight because both weights being in similar situ-
ations would lose equal portions of their gravity.
E. How, then, would you make the experiment I
F. By means of one of those steel spral-spring
instruments which you have seen occasionally used,
the feet might be ascertained;
C. I think, from what you told usyesterday, that
with the assistance of your stop-watch, I could tell
the height of any place, by observing the number of
seconds that a marble or any other heavy body would
take in falling from that height.
F. How would you perform the calculation I
C. I should go through the multiplieatione as
cording to the number of seconds, and then add
them together.
F. Explain yourself more prtioularly:-sup-
posing you were to let a marble or a penny-plee
fal down that deep well which we saw lat summer
in the brick field near Ranmgate, and that it was
exactly five seconds in the descent, what would be
the depth of the well t
C. In the first second it would fall 16 feet; in the






86 MECHANICS,
neit 8 time 16 or 48 feet; in the third a times 16
or 80 feet ; in the fourth 7 times 16 or 112 feet;
and in the fifth second 9 times 16 or 144 feet; now
if I add 16, 48, 80, 112, and 144 together, the sum
will be 400 feet, which according to your rule is the
depth of the well. But was the well so deep I
F. I do not think it was, but we did not make
the experiment; should we ever go to that place
again you may satisfy your curiosity. You recol-
lect that at Dover Castle we were told of a well
there 860 feet deep.
Though your calculation was accurate, yet it was
not done as nature effects her operations ; it was
not performed in the shortest way.
C. I should be pleased to know an easier method;
this however is very simple, it required nothing but
multiplication and addition.
F. True, but suppose I had given you an exam-
pie in which the number of seconds had been fifty
instead of five, the work would have taken you an
hour or more to have performed; whereas, by the
rule which I am going to give, it might have been
done in half a minute.
C. Pray let me have it; I hope it will be easily
remembered.
F. It will; I think it cannot be forgotten after it
is one. understood. The rule is this, "tie paces
dawribd by a body falling frely from a tate of rea
increase as tA* SQUARs oftLAe times inereas ." Con-
sequently you have only to square the number of
seconds, that is, you know, to multiply the number
into itself, and then multiply that again by sixteen
feet, the space which it describes in the first second,
and you have the required answer. Now try the
example of the well.
C. The square of 5, for the time, is 25, which mul-






ATTRACTION Of OzATITATION. 57
tiplied b 16 give400, ijstsI broughtitoutbefre.
Now if the seconds had been 60, the answer would
be 50 times 50, which is 2500, and this multiplied
by 16, gives 40,000 for the space required.
F. I willnow ask yoursistera question, totryhow
she has understood this subject. Suppose you ob-
serve by this watch that the time of the flight ot
your brother's arrow is exactly six seconds, to what
height does it rise t
E. This is a different question, because here the
ascest as well as the fall of the arrow is to be con-
sidered.
F. But you will remember that the time of the
ascent is always equal to that of the descent; for
as the velocity of the descent is generated by the
force of gravity, so is the velocity of the ascent de-
stroyed by the same force.
E. Then the arrow was three seconds only in fall-
ing ; now the square of 8 is 9, which multiplied by
16, for thenumberoffeet described in thefrst second,
is equal to 144 feet, the height to which it rose.
F. Now, Charles, if I get you a bow which will
carry an arrow so high as to be fourteen seconds
in its flight, can you tell me the height to which it
ascends t
C. I can now answer you without hesitation ;-it
will be 7 seconds in falling, the square of which is 49,
and this again multiplied by 16 will give 784 feet,
or rather more than 261 yards, for the answer.
F. If you will now consider the example which you
did the long way, you will see that the rule which I
have given you answers very completely. In the first
second the body fell 16 feet, andin the next 48, these
added together make 64, which is the square of the 2
secondsmultipliedby 16. The sameholdstrueofthe
3 first seconds, for in the third second it fell 80 feet,






88 MECHANICS.
which added to the 64, give 144, equal to the square
of 8 multipliedby 16. Ain, in the fourth second it
fell 112 feet, which added to 44, give 26, equal to
the square of 4 multiplied by 16 ; and in the fifth
second it fell 144 feet, which added to 286, gve 400,
equal to the square of 5 multiplied by 16. Thus you
will find the rule holds in all cases, that the space
described by bodies fallingfreell from a state of res
norease as the SQUARas of the times increase.
C. I think I shall not forget the rule. I will also
shew my cousin Henry how e may know the height
to which Iis bow will carry.
F. Thesurest way of keeping what knowledge we
have obtained, is by communicating it to our friends.
C. It isa very pleaantcircumstanceindeed, that
the giving away is the best method of keeping, for
I am sure the being able to oblige one's friends is a
most delightful thing.
F. Your sentiments are highly gratifying to me;
fain would I confirm them by adding to your stock of
knowledge. And, in reference to this subject, it may
benecessry toguard you against the notion, that be-
carse the spaces described by falling bodies are as the
squaresofthe times,the elooitia eincreseinthesame
ratio. Thi is not the case. The velocity acquired
by a body falling freely, at the end of the first second
of its motion, s such as, if it continued uniform,
would carry it over 32 feet in the next second,
And in all succeeding intervals the velocities are as
thetime: that is, at the end of 2, 3,4 and seconds,
the velocities acquired will be respectively, twice,
thrice, four times, and five times 32 feet; or, 64,
96, 128, and 160 feet.
E. Before we quit this part of the subject, papa,
let me try if I thoroughly comprehend you. A fall-
ing body having been in motion 4 seconds, will have






CETRS OF oRAVITY. 89
descended 256 feet, and will then have a velocity of
128 feet; but themotion l tll accelerates and auss
the body to pas over nine times 16, or 144 feet, in
the Sth second, making in all 400 feet: it will then
have acquired a velocity ofb times 82, or 160 feetin
a second, which if it continued uniform for another
5 seconds, would carry the body over 800 feet, or
just twice the space described by the body in the
first 5 seconds, during which its motion was equa-
bly accelerated by gravity.
F. You have most accurately caught the distinc-
tion I wished you to understand.
With this we conclude our present conversation.
CONVERSATION IX.
ON THU CENTRE orP OIG ITY.
F. We are now going to treat upon the Centre of
Gravity, which is that point of a body in which its
whole weight is as it were concentrated, and upon
which, if the body be freely suspended, it will rest;
and in all other positions it will endeavour to des-
cend to the lowest place to which it can get.
C. All bodies then, of whatever shape have a
centre of gravity I
F. They have and if you conceive aline drawn
from the centre o gravity of a body towards the can-
tre of the earth, that line is called the liU of di-
rectio, along which every body not supported, en-
deavours to fall. If the lie of directio fall within
the base of any body, it will stand; but it it does
not fall within the base, the body will fall. b
If I place the piece of wood a on the edge
of a table, and from a pin e at its centre of
gravity be hung a little weight d, the line
of direction ed falls within the base, and
therefore, though the wood leans, yet it Fi 7
stands secure. But if upon a anotherpiece g..






40 MECHANICS.
of wood 6 be placed, it is evident that the centre of
gravityof the whole will benow raised to e, at which
point f a weight be hung, it will be found that the
line of direction falls out of the base, and therefore
the body must fall.
E. I think I now see the reason of the advice
which you gave me, when we were going across the
Thames in a boat.
F. I told you thatif ever you were overtaken by a
storm, or by a squall of wind, while you were on the
water, never to let your fears so get the better of you
as to make you rise from your seat, because, by so
doing, you would elevate the centre of gravity, and
thereby,asis evident by the lastexperiment,increase
the danger; whereas, if all the persons in the vessel
were, at the moment of danger, instantly to slip from
their places on to the bottom, the risk would beex-
ceedingly diminished, by bringing the centre of gr-
vity mu lower within the vessel. The same princi-
pie is applicable to those who may be in danger of
being overturned in any carriage whatever.
E. Surely then, papa, those stages which load
their tope with a dozen or more people, cannot be
safe for the passengers.
F. Theyare very unsafe; but they would be more
so were not the roads about the metropolis remark-
ably even and good; and, in general, it is only with-
in twenty or thirty miles of London, or other great
towns, that the tops of carriages are loaded to excess.
C. I understand, then, that the nearer the centre
of ravit is to the base of the body the firmer it
will stand.
F. Certainly; andhenceyou learn the reason why
conical bodies stand so sure on their bases, for, the
tops being small in comparison of the lower parts, the
centre of gravity is thrown very low; and, if the cone






CENTBZ OP GRAVITY. 41
be upright, or perpendicular, theline of direction falls
in the middleof thebase, which isanotherfundamen.
tal propertyofsteadiness in bodies. For the broader
the base, and the nearer the line of direction is to the
middle of it, the more firmly does a body stand ; but
if the line of direction fall near the edge the body is
easily overthrown.
C. Is that the reason why a ballis so easily rolled
along a horizontal plane I
F. It is; for in all spherical bodies the base is but
a point, consequently almost the smallest force is suf-
ficient to remove the line of direction out of it. Hence
it is evident that heavy bodies situ- /f,
ated onan inclined plane will, while "?
the line of direction falls within tile
base, slide down upon the plane ;
but theywill roll when thatline falls
without the base. The body a will Fig. 8.
slide down the plane de, but the bo-
dies b and c will roll down it.
E. I have seen buildings lean very much out of a
straight line; why do they not fall I
F. It doesnotfollow, because building leans,that
the centre of gravity does not fall within the base.
There is a high Tower at Pisa, a town in Italy, which
leans fifteen eet outof the perpendicular; strangers
tremble to pass by it; stillit is found by experiment
that the line of direction falls within the base, and
therefore it will stand while its materials hold toge-
ther. A wall at Bridgenorth, in Shropshire, which
I have seen, stands in a similar situation, for so long
as a line let fall from the centre of gravity of the
building, passes within the base, it will remain
firm, unless the materials with which it is built go
to decay.
C. It must be of great use, in many cases, to know






49 NECHANlS.
the method offending the centre of gravity in different
kinds of bodies.
F. There are many easy rules for this with respect
to all manageable bodies: I will mention one, which
depends on the property which the centre of gravity
ha, ofalways endeavouring to descend to the lowest
point. a d
If a body a be freely suspended on
Spin b, and a plumb line be be hung by j 'T
the same pin, it will pass through the f
centre of gravity, for that centre is not F. 10.
in the lowest point, till it fall in the sme ig.
line as the plumb line. Marktheline ke; then hang
the body up by any other point, as d, with the plumb
line d, which will also pas through the centre of
gravity, for the same reason before; and therefore,
as the centre of gravity is somewhere in be, and also
in some point of d, it must be in the point d where
those lines cross.
CONVERSATION X.
OP TBR CENTRa OF GRAvITT.
C. How do those people who have to load carts
and waggons with light goods, as ha, wood, &c.
know where to fnd the centre of gravity I
F. Perhaps the generality of them never heard
of such a principle ; and it seems surprising that
the should nevertheless make up their loads with
u accuracy as to keep the line of direction in or
near the middle of the base.
E. I have sometimes trembled to pas by the hop
waggons which we have met on the Kent Road.
F. And without any impeachment ofyour courage,
for they are loaded to such an enormous height, that
they totter every inch of the road. It would indeed
be unposible for one of these to pas with tolerable






CENTRE OP GRAVITY. 43
security along a road much inclined ; the centre of
gravity being removed so high above thebody of the
carriage, a small delination on one side or the other
would throw the line of direction out of the base.
E. When brother James falls about, is it because
he cannotkeepthe centreofgravity between hisfeett
F. That is the precise reason why any person,
whether old or young, falls. And hence you learn
that a man stands much firmer with his feet a little
apart, than if they were quite close, for by separating
them he increasesthebase. Hencealso the difficulty
of sustaining a tall body, as a walking cane, upon a
narrow foundation.
E. How do rope and wire dancers, whom I have
seen at the Circus, manage to balance themselves 1
F. They generally hold along pole, with weights
at each end, across the rope on which they dance,
keeping their eyes fixed on someobject parallel to the
rope, by which means they know when their centre
ofgravity declinesto one sideoftherope orthe other,
and thus, by the help of thepole, they are enabled to
keep the centre ofgravity over the base, narrows it
is. It is not, however, rope-dancers only who pay
attention to this principle, but the most common
actions of the people in general are regulated by it.
C. In what respects I
F. We bend forward when we go up stairs, or rise
from our chair, for.when we are sitting our centre of
gravity is on the seat, and the line of direction falls
behindour base; we therefore lean forward to bring
the line of direction towards our feet. For the same
reason a man carrying aburthen on his back leans
forward; and backward if hecarries iton his breast.
If the load be placed on one shoulder, he leans to
the other. If we slip or stumble with one foot, we
naturally extend the opposite arm, making the same
use of it as the rope-dancer does of his pole.






44 MvcHANICs.
This property of the centre of gravity always
endeavouring to descend, will account for appear-
ances, which are sometimes exhibited to excite the
surprise of spectators.
E. What are those, papas
F. One is, that ofa double cone, appearing to roll
up two inclined planes, forming an angle with each
other, for as it rolls it sinks between them, and by that
means the centre of gravity is actually descending.
Let a body ef, consisting of dL-e
two equal cones united at their br"
bases, be placed upon the edges ---
of two straight smooth rulers
ab and ed, which at one end
meet in an angle at a, and rest Fig. 11.
on a horizontal plane, and at
the other are raised a little above the plane; the
body will roll towards the elevated end of the rulers,
and appear to ascend; the parts of the cone that
rest on the rulers growing smaller as they go over
a larger opening, and thus letting it down, the cen-
tre of gravity descends. But you must remember
that the height of the planes must be less than the
radius of the base of the cone.
C. Is it upon this principle that a cylinders made
to roll up hill.
F. Yes it is, but this can be effected only to a
small distance. If a cylinder of pesteboard, or very
light wood, ab, having its centre of
gravity at o, be placed on the in- d 0
lined plane de, it will roll down
the inclined plane, because a line of
direction from that centre lies out B
of the base. If I now fill the little 1.
hole o with a plug of lead, it will roll ig. 1
up the inclined plane, till the lead gets near the base,






LAWS OF MOTION. 45
whereit will liestill: becausethecentre of gravity,
by meanof the lead, is removed from a towards the
plug, and therefore is descending, though the cylin-
der is ascending.
Before putan endtothissubject, I will hew you
another experiment, which without understanding
the principle of the centre of gravity cannot be ex-
plained. pon this stick o, which,
ofitselfwouldfall,becauseitscentre
of gravity hangs over the table b, I
suspend a bucket e, fixing another
stick d, one end in a notch between a
and e, and the other against the in- Fi. 13
side of the pail at the bottom. Now g. 13
you will see that the bucket will, in this position, be
supported, though filled with water. For the bucket
being pushed a little out of the perpendicular, by the
stick d, the centre of gravity of the whole is brought
under the table, and consequently supported by it.
The knowledge of the principle of the centre of
gravity in bodies, will enable you to explain the
structure of a variety of toys which are put into the
hands of children, such as the little sawyer, rope-
damer, tumbler, 4o.
CONVERSATION XI.
ON TBn LAWS OF MOTION.
C. Are you now-going, papa, to describe those
machines, which you mcll meaon l powers ?
F. We must, I believe, defer that a day or two
longer, as I have a few more general principles with
which I wish you previously to be acquainted.
E. What are these, papa I
F. In the first place, you must well understand
whatare denominatedthe threegeneral laws of mo-
tion: thefirst of which is, "that evry body will ooN






40 MECHANICS.
tiee n its stats of red, or of saiform motion, satiis
iseompflledbysomneforsetokchae its state." This
constituteswhatidenominated theirIaorinacti.
ity of matter. And it may be obsered that, in all
case, the quantity of motion gained by one body is
always equal to that lost by some other body.
C. There is no difficulty ofoonceiving that a body,
as this ink-stand, in a state of rest must always re-
main so, if no external force be impressed upon it
to give it motion. But I know of no example which
will lead me to suppose, that a body once put into
motion would of itself continue so.
F. You will, I think, presently admit the latter
part of the assertion as well as the former, although
it cannot be established by experiment.
E. I shall be glad to hear how this is.
F. You will not deny that the ball which you
strike from the trap has no more power either to
destroy its motion, or case any change in its ve-
locity, than it has to change its shape.
C. Certainly; nevertheless, in a few seconds
after I have struck the ball with all my force, it
falls to the ground, and then stops.
F. Do you find no difference m the time that is
taken up before it comes to rest, even supposing
your blow the same I
C. Yes, if I am playingon the grass, it rolls to a
lessdistance than when I play on the smooth graveL
F. You find a like difference when you are play.
ing at marbles, if you play in the gravel court, or
on the even pavement in the arcade.
C. The marbles run so easily on the smooth stones
in the arcade, that we can scarcely shoot with a force
small enough.
E. And Iremember Charles and my ousin were
last winter trying how far they cold shoot their






LAWS OF MOTION. 47
marbles along the ice in the eanal; and they went
a prodigious distance, in comparison of that which
they would have gone on the gravel, or even on the
pavement in the arcade.
F. Now these instances properly applied will con-
vince you, that a body once put into motion would
go on for ever, if it were not compelled by some ex-
ternal force to change its state.
C. I perceive what you are going to say:-itis the
rubbing or friction of the marbles against the ground
which does the business. For on the pavement there
are fewer obstacles than on the gravel, and fewer on
the ice than on the pavement; and hence you would
lead us to conclude, thatifall obstacles were removed,
they might proceed on for ever. But what are we
to say of the ball; what stops that I
F. Besides friction, there is another and still
more important circumstance to be taken into con-
ideration, which affects the ball, marbles, and every
other body in motion.
C. I nderstandyou,thatistheaction ofgravitation.
F. It is; for from what we said when we con-
versed on that subject, it appeared that gravity hab
Tendency to bring every bod in motion to the earth;
consequently, in a few second, your ball must come
to the around by that cause alone; but besides the
attraction ofgravitation, theisthe reistanee whieh
the air, through which the ball moves, makes to ito

That cannot be much, I think.
F. Perhamp, with regard to the ball struck from
yourbrother' trap, it isof no great consideration, be-
aeme the velocity is but mall ; but in all great velo-
eities as that of bll from a musket or cannon, there
will be a material difference between the theory and
practice, ifitbeneglectedinthe calculation. Move






48 MECHANICS.
your mamma's riding-whip through the air slowly,
and you observe nothing to remind you that there
is this resisting medium ; but if you swing it with
considerable swiftnes, the noise which it occasions
will inform you of the resistance it meets with from
something, which is the atmosphere.
C. If I now understand you, the force which com-
pels a body in motionto stop, is of three kinds; I. the
attraction ofgravitation ;-2.the resistance ofthe air;
-and 3. the resistance it meets with from friction.
F. You are quite right.
C. I have now no difficulty of conceiving, that a
body in motion will not come to a state of rest, till
it is brought to it by an external force, acting upon
it in some way or other. I have seen a gentleman,
when skating on very slippery ice, go a great way
without an exertion to himself, but where the ice
was rough he could not go half the distance without
making fresh efforts.
F. will mention another instance or two of this
law of motion. Put basin of water into your little
sister's waggon, and when the water is perfectly still
move the wagon, and the water, resisting the motion
of the veel, will at firt rise up in the direction
contrary to that in which the vessel moves. If,
when the motion of the vessel is communicated-to
the water, you suddenly stop the waggon, the water,
in endeavouring to continue the state of the motion,
rises up on the opposite side.
In like manner, if, while you are sitting quietly
on 7our horse, the animal starts forward, you will
be m danger of falling off backward ; but if, while
you are galloping along, the animal stops on a sud-
den, you ill be liable to be thrown forward.
C. This I know by experience, but I was not
aware of the reason of it till to-day.






LAWS OF MOTtO!. 49
F. One of the firet, and not leat important, me
of the principle of atual hilaobphy i*, that tey
may be applied to, and will explain, many of the
common conemrs of life.
We now come to the second law of motion ; which
is, thatt the clhng of motion i proportional to the
force impresed, and in the direction of that fore."
C. There is no difficulty in this ; for if, while my
cricket-ball is rolling along, after Henry has struck
it, I strike it again, it goes on with increased velo-
city, and that in proportion to the strength which I
exert on the oeeasion; whereas, if, while it is roll.
ing, I strike it back again, or give it a side blow, I
change the direction of its course.
F. In the same way, gravity, and the resistance
of the atmosphere, change the direction of a cannon-
ball from its course in a straight line, and bring it
to the ground; and the ball goes to a farther or les
distance in proportion to the quantity of powder used.
The third law of motion is, tht, to eery action
of one body upon another, there is an equal and on-
trary reaesion." If I strike thi table, I eommuni-
eats to it (which you perceive by the shaking of the
glasses) the motion of my hand : and the table r-
acts against my hand, just as muh as my hand aets
against the table.
Ifyou press with your fngerone sealofabalones,
to keep it in equilibrio with a poud weight in the
otherseale, you will perceive that the sale presed
by the finger acts against it with a force equal to a
pound, with which the other seale endeavours to
descend. In all eases, the quantity of motion gained
hy one body is always equal to that lost by the other
in the same diretion. Thus, if a ball in motion
strike another at rest, the motion communicated to
the latterwill be taken from the former, and the velo-
10 D






50 MECsANICs.
city of the former will be proportionally diminished.
A horse drawing a heavy load, is as much drawn
back by the load as he draws it forward.
E. I do not comprehend how the cart draws the
horse.
F. But the progress ofthehorse is impeded bythe
lead, which is the same thing; for the force which
the hore exerts would carry hun togreater distance
in the same time, were he freed from the incumbrance
of the load, and, therefore, as much as his progress
falls short of that distance, so much is he, in effect,
drawn back by the re-action of the loaded cart.
Again, if you and your brother were in a boat, and
if, by means of a rope, you were to attempt to draw
another to you, the boat in which you were would
be as much pulled towards the empty boat as that
would be moved to you ; and, if the weights of the
two boats were equal, they would meet m a point
half way between the two.
If you strike a glass bottle with an iron hammer,
the blow will be received by the hammer and the
glass; and it is immaterial whether the hammer be
moved against the bottle at rest, or the bottle be
moved against the hammer at rest, yet the bottle
will be broken, though the hammer be not injured,
because the same blow which is sufficient to break
glssisnotsuficient tobreak orinjure lump ofiron.
From this law of motion you may learn in what
manner a bird, by the stroke of its wings, is able to
support the weight of its body.
Pray explain this, papa.
F. If the force with which it strikes the air below
it is equal to the weight of its body, then the re-action
oftheair upwardsislikewise equalto it; andthebird,
being acted upon by two su e forest in contrary di-
rections, wll restbetwes tm. Iftheforce of te






LAWS OF MOTION. 81
stroke is grater than its weight, the bird will rise
with the difijrece of these two force ; and, if the
stroke be lem than its weight, then it will sink with
the difereroe.
CONVERSATION XII.
ON THe LAWS OF MOTION.
C. Are those laws of motion which you explained
yesterday of great importance in natural philosophy?
F. Yes, they are, andshould be arell comit-
ted tomemory. They were assumed by Sir I. New-
ton as the fundamental principles of mechanics, and
you will find them at the had of most books writ-
ten on these subjects. From these also we are
naturally led to some other branches of science,
which, though we can but slightly mention, should
not be wholly neglected. They are, in fact, but
corollaries to the laws of motion.
E. What is a corollary, papa I
F. It is nothing more than some truth clearly de-
ducible from some other truth before demonstrated
oradmitted. Thus by therrt law of motion eery
body must endewaor to continue in the state into
tkih is is put, sAer it U of res, or sl(form me-
tion in a straight liM: from which it follows, as a
corollary, that when we see a body move in a carve
line, it must be acted upon by at least two forces.
C. When I whirl a stone round in a sling, what
are the two forces which act upon the stone t
F. There is the force by which, if you let go the
string, the stone will fly off in a right line ; and
there is the free of the hand, which keeps it in a
circular motion.
E. Are there any of these circular motions in
nature 1
F. The moon and all the planets move by this






52 unctAxNici.
law :-to take the moon s an instance. It has a
oostant tendency to the earth, by the attraction of
ravitation, and it has also a tendency to proceed in
aright line, by that projectile force impressed upon
it by the Creator, in the mine manner as the stone
flies from your hand; now, by the joint action of
these two forces it deeeribes a circular motion.
E. And what would be the consequence suppo-
ing the projectile force to cease I
F. The moon must fall to the earth ; and if the
force of gravity were to cease acting upon the moon,
it would fly off into infinite space. Now the pro-
jectile force, when applied to the planets, is called
the centrifugal force, as having a tendency to recede
or fly from the centre; and the other force is termed
the ceatripetal force, from its tendency to some
point as a centre.
C. And all this isin consequence of the inactivity
of matter, by which bodies have a tendency to con-
tinue inthe same state they are in, whether of rest
or motion I
F. You are right, and this principle, which Sir
Isaac Newton assumed to be in all bodies, he called
their eis iuerti, which has been referred to before.
C. A few mornings ago you showed us that the
attrition of the earth uMo the moon' is 3600 times
less, than it is upon heavodis near the earth'ssur-
face. Now as this attracLo*ismeasured by the space
fallen through ii a given teI have endeavored to
calculate the space which moon wouldfall through
in a minute, were the projectile force to eease.
F. Well, and how have you brought it out t
C. A body falls here 16 feet in the first second,
consequently in a minute, or 60 seconds, it would
fall 60 times 60 feet, multiplied by 16, that is 3600
Se CvmCo sa IV.






LAWS OFr m0IOn. sb
feet, which is to be multiplied by 16; and a the
moon would fall through 8600 times less smee in
give time than a body here, it would fall only 16
feet in the first minam.
F. Your calculation isaeeurate. I will recallto
your mind the second law, by which it paper t
every motion, or ai ofmotion, prodod i a body,
msst in proportion to, and in te direction of, 9&
fornimpresud. Therefore,ifamovingbodyreceives
an impulse in the direction of its motion, its velocity
will be increased ;-if in the contrary direction, its
velocity will be diminished ;-but if the force be im-
presed in a direction oblique to that in which it
moves, then its direction will be between that of its
former motion, and that of the new foree impressed.
C. This I know from the observations I have
made with my cricket-ball.
F. By this second law of motion, you will easily
andertand, that if a body at rest receive two im-
pulses at the smne time, from force whose direc-
tions do not coincide, it will, by their joint action,
be made to move in a line that lies between the
direction of the forces impressed.
B. Have you any machle to prove this mstibao-
torly to the senses I
F. Thearaemany smuh Invented by different pr-
ons, deseriptionsof which you will hereafter fnd in
various books on these subjects. But it is easily an-
dertood by algare. If n the ball a
force be impressed sufie t to make it t
move with an uniform velocity to the "
point b, i a second of time; and If an-
otherforce be also impressed on the ball, 1
whih alone would make it move to the E* .
point e, in the same time; the ball, by means of th
two forces, will deribe the Ue ad, whieh is a diago.
al of the figure, whose sides are o and a6.






84 incANICS.
C. How then is motion produced in the direction
of the fore 1 According to the second law, it ought
to be m one cae in the direction ac and in the other
in that of ab, whereas it is in that of ad.
F. Examine theflgurea little attentively, carrying
this in your mind, that for a body to move in the
same direction, itis not necessary that itshould move
in the same straight line; but that it is suffcient to
move either in that line, or in any one parallel to it.
C. I perceive then that the ball when arrived at d,
has moved in the direction ac, became bd is parallel
to ae ; and also in the direction ab, because od is
parallel to it.
F. And in no other possible situation but at the
point d could this experiment be conformable to the
second law of motion. When bodies move in a
curve, it must be kept in mind that there must be a
continued action to external force; otherwise, if
that action were to cease at any point, the body
would continue its motion in a straight line.
CONVERSATION XIII.
OP THr LAWS OF MOTION.
F. Ifyou reflect a little upon what we said yester-
dayon the second law of motion,you will readily de-
duce the following corollaries. (Fig. 14.)
1. That if the forest be equal,nd act at right
angles to one another, the line described by the ball
will be the diagonal of a suare. But in all other
cases, it will be the diagonal of a parallelogram of
some kind.
2. By varying the angle, and the forces, you vary
the form of your parallelogram.
C. Yes, papa, and I see another consequenee, vis.
thatthe motionsoftwoforceesatingconjointlyin this
way, are not so great as when they act separately.






LAWS OF NOTION. 50
F. That is true, and you are led to the conclusion,
I uppose,from thereollection,tht in every triangle
any two sides taken together are greater than the re-
amining side; and therefore you infer, andjustly too,
that the motions which the ball amusthavereceived,
had the forces been applied separately, would have
been equal to ac and ab, or, which is the same thing,
to ae and ed, the two sides of the triangle ado, but
by their joint action, the motion is only equal to ad,
the remaining side of the triangle.
Hence then you will remember, thatin the eompo-
sition, or adding together of forces (as this is called),
motion is always hlat: and in the resolution of any
one force, as ad, into two others, ae and ab, motion
is gained.
C. Well, papa, but how is it that the heavenly
bodies, the moon for instance, which is impelled by
two forces, performs her motion in a circular curve
round the earth, and not in a diagonal between the
direction of the projectile force, and that of the
attraction of gravity to the earth I
P. Because, in the a just mentioned, there
was but the action of a single impulae in each diree-
tion, whereas the action of gravity on the moon is
continual, and causes an accelerated motion, ad
hence the line is a curve.
C. Suppoing then, that represent the moon, and
ae the ixteenfeet through which it would fall in a
minute by the attraction of gravity towardatheerth,
and ab represent the projectile forceting upon ittor
these metime. Ifabandaoactedas ing eimpsee,
the moon would in that eae describe the diagonal
ad; but since these forces are constantly eating,
and that of gravity is an accelerating force also,
therefore instead of the straight line ad, the moon
will be drawn into the curve line aid. Do I under-
stand the matter right I






Ji MECANIS.
F. You do; and hence you easily comprehend
how, byoodinstrument and calculation, the ttrae-
tion of the earth upon the moon was discovered.
The third law of motion, viz. that action and re-
astio ae equal and in contrary direXteons, may be
illustrated by the motion communicated by the per-
cussion of plastic and non-elauic bodies.
E. What are these, papa
F. Elastic bodies are thoee which have a certain
spring, by which their parts upon being pressed in-
wards, by percussion, return to their former state;
this property is evident in a ball of wool or cotton,
or in sponge compressed. Non.elastio bodies are
those which, when one strikes another, do not re
bound, but move together after the stroke.
Let two equal ivory balls a nd 6 be sus-
pended by trends ; if a be drawn a little
outoftheperpendicur, andletfallupon 6,
it will loseite motion by communicating it
to b, which will be driven to a distance e,
equal to that through which a fell; and
hence it appear that the re-action of bwa Fig.S.
equal to the action of a upn it.
BE But do the parts of the ivory balls yield by
te stroke, or, as you call it, by the pereusion I
F. They do; forif I lay a little painton a, and let
it 8s"o b, it will make buta very mall peck upon it;
but If it fal upon 6, the speek will be much larger;
which proves that the balls are elastic, and that a
little hollow, or dint, was made in each by culli-
sion. If now two equal soft balls of clay, or glazier's
putty, which are non-elastic, meet each other with
equal velocities, they would stop and stick togetherat
the place of their meeting, as their mutual actions
destroy each other.
C. I have sometime sl*.t my white alley against






LAWS OF NOTION. 57
another marble so plumply, thatthe marble has gone
off as swiftly as the alley approached it, and that re-
mained in the place of the marble. Are marbles,
therefore, as well as ivory, elastic I
F. They are.-If three elastic balls a,
b, be hung from adjoiningcentre, and
a be drawn a little out of theperpendieu-
lar, and let fall upon b, then will a and
6 become stationary, and will be driven Jb
to d, the distance through which a fell
upon 6. Fig. 16
If you hang any number of balls, a F.
six, eight, &c. so as to touch each other, and if you
draw the outside one away to a little distance, and
then let it fall upon the others, the ball upon the op-
posite side will be driven off, while the rest remain
stationary, so equally is the action and re-action of
the stationary balls divided among them. In the
mine manner, if two are driven aside and suffered
to fall on the rest, the opposite two will fly off, and
the others remain stationary.
There is one other eircunmtanee depending upon
the action and re-etion of bodies, and also upoe
the fi inertli of matter, worth noticing : by some
authors you will find It laely treated upon.
If I strike a blakmaaitha anvil with a hammer,
action and re-action being equal, the anvil strikes the
hammer as forcibly as the hammer strikes the anvil.
If the anvil be large enough, I might lay it on my
breast, and suffer you to strike it with a sledg
hammer with all your strength without pain or risk,
for the vie isertio of the anvil resists the fore
theblow. Butiftheanvil werebuta poedortwo
in weight, your blow would probably kill me.






8 UlMCHANIC5.

CONVERSATION XIV.
ON THE MECHANICAL POWERS.
C. Will you now, papa, explain the mechanical
powers t
F. I will, and I hope you have not forgotten
what the momentum of a body is.
C. No, it is the force of a moving body, which
force is to be estimated by the weight, multiplied
into its velocity.
F. Then a small body may have an equal momen-
tum with one much larger I
C. Yes, provided the smaller body moves as much
swifter than the larger one, as the weight of the
latter is greater than that of the former.
F. What do you mean when you say that one
body moves swifter, or has a greater velocity, than
another I
C. That it passes over a greater space in the same
time. Your watch will explain my meaning : the
minute-hand travels round the dial-plate in an hour,
but the hour-hand takes twelve hours to perform its
course in, cosequetly, the velocity of the minute-
hand is twelve time greater than that of the hor-
hand ; because, in the same time, vis. twelve hours,
it travels twelve times thespace that is gone through
by the hour-hand.
F. But this can be only true on the supposition
that the two circles are equal. In my watch, the
minute-hand is longer than the other, and conse-
quently, the circle described by it is larger than that
described by the hour-hand.
C. I ee at once that my reasoning holds good
onl in the cae where the hands are equal.
I. There is however, a particular point of the
longer hand, of which it may be said, with the strict-






ICIHANICAL POWEiR. 9
est truth, that it has exactly twelve time the velo-
city of the extremity of the shorter.
C. That is the point at which, if the remainder
were cut off, the two hands would be equal. And,
in fact every different point of the hand describes
different spacee in the same time.
F. The little pivot on which the two hands seem
to move, (for they are really moved by different
pivots, one within another) may be called the centre
of motion, which i a fixed point; and the longer
the hand is, the greater is the space described.
C. The extremities of the vanes of a wind-mill,
when they are going very fast, are scarcely distin-
guishable, though the separate parts, nearer the
mill, are easily dicered ; this is owing to the velo-
city of the extremities being so much greater than
that of the other parts.
E. Did notthe swiftness of the round-abouts, whiel
we saw at the fair, depend on the ameprinciple, via.
the length of the poles upon which the sets were
fixed I
F. Yes; the greater the distance, at which these
eats were placed, from the centre of motion, the
greater the space which the little boys and girls
travelled for their halfpenny.
E. Then those inthe secondrowhad aaborterride
for their money than those at the end of the poles I
F. Yes, shorter as to space, but the same as to
time. In the same way, when you and Charles go
round the gravel-walk for half an hour's exercise,
if he run while you walk, he will, perhaps have gone
six or eight times round, in the same time that you
have been but three or four times ; now, as to time,
your exercise has been equal, but he may have
pawsed over double the space in the same time.
C. How does this apply to the explanation of the
mechanical powers I






oU MECUAMNIO.
F. You will find the application very asy :-
without clear ideas of what is meant by lim and
pe, it were in vain to expect you to comprehend
Spriniples of mechanics.
There e six mechanical power. The lever;
the wheel and xle ; the pulley ; the inclined pleae;
the wedge ; and the screw.
F. Why ae they called mechanical powers I
F. Because, by their means, we are enabled me-
dssicalUy, to raise weights, move heavy bodies,
and overcome resistances, which, without their
asistance, could not be done.
C. But is there no limit to the assistance gained
by theme powers for I remember reading of Ar-
ehimedes, who said, that with a place for hiserlrum
he would move the earth itself.
F. Human power, with all the asistanee which
art can give, is very soon limited,and upon this prin-
ciple, thawaei at wein ipowerm low satis. Ihat
is, i by yourown aasisted strength,you re able to
raie fifty pound to certain distance m one minute,
adif by e help of machinery wishte raise five
bndred pounds to the same hg yo will require
tealtesto perfmitia; thusyeeuinreseyo
power ten-fold, but it is at the expense of time. Or
n other words, you are enabled to do that with one
eobrt in ten minutes, which you could have done in
ten eprate efforts in the name time.
E. the importance of meehanis, then, is not so
very considerable as one, at frt eight, weuld ima-
gine; since there is no real gala of force acquired
by the mechanical powers.
F. Though there be not any etual increase of
fore gained by thee powers, yet the advantages
which men derive from them are inestimable. If
there are several mail weights, manageable by






MBOENcamU PWr s. 91
human stronth, to be saisd to a ortain height,
it my be fall as m*vent to elovto them oa by
one, a to take the dvtage of tohe mehbtal
powers, in raising them ll at once. Became a
we have shewn, same time will be neeeuar la
both ass. But suppose you have a airge bok
of stone of a ton weight to carry away, or a weight
still greater, what is to be done I
E. I did not think of that.
F. Bodies of this kind cannot be separated into
parts proportionable to the human strength without
immense labour, nor, perhaps, without rendering
them unfit for those purpose for which they are
to be applied. Hence then you perceive the great
importance of the mechanical powers, by the se of
which, a man is able with ease to manage a weight
many times greater than himself.
C. I have, indeed, seen a few men, by means o
pullies, and seemingly with no very great exertion
raise an enormoMu oak into a timber-earrage, is
order to convey it to the dock.yard.
F. A very excellent instance; for if e tre hbad
been cut into seh plees as could have been ma.-
aged by the natul strength of the men, it would
not have been worth carrying to Deptford or Chat-
ham for the purpose of ship-building.
E. I acknowledge my error; what is a fulcrum,
!F. It is a fed point, or prop, rond which the
other prt of a muahine move.
C.The pivot, upon which the hands of your
watch move, is a fulcrum then I
F. It is, and you remember we called it asi the
centre of motion ; the rivet of these csiaars is also
a fulcrum, and also the centre of motion.
E. Is that a fixed point, or prop t






62 MKCHANICI.
F. Certainly it is a fixed point, as it regards the
two parts of the scissar ; for that always remains
in the sme position, while the other pats move
about it. Take the poker and stir the fire; now
that part of the bar on which the poker rests is a
fulcrum, for the poker moves upon it as a centre.
CONVERSATION XV.
OF THI LEVEB.
F. We will now consider the Lever, which is
generally called the first mechanical power.
'The lewvr is any inflexible bar of wood, iron, &c.
which serves to raise weights, while it is supported at
a point by a prop or fulcrum, on which, as the ceu-
treof motion all the other parts turn.
ab willrepresentalever,andthe point
a the fulcrum or centre of motion.
Now itis evident if the lever turn on
its centre of motion e, so that b comes
into the position d; a at the same Fig. 17.
time must come into the position e. If both the
arms of the lever be equal, that is, if as is equal to
be, there is no advantage gained by it, for they pass
over equal spaes in the same time; and, according
to the fundamental principle already laid down,
"as advantages or power is pined, time must be
lost:" therefore, no time being lost by a lever of
this kind, there can be no power gained.
C. Why then is it called a mechanical power I
F. Strictly speaking, perhaps, it ought not to be
aumberedasone. But it is usually reckonedamong
them, having the fulcrum between the weight and the
power which is the distinguishing property of levers
of the first kind. And whenthefulcrum is exactly
the middle point between the weight and power it
is the common balance: to which, if scales be sus.






TB< LVTEL. 9
ended at a and 6, it is fitted for weighing all
sorts of commodities.
E. You say it is a lever of the finr kind; ae
there several sorts of levers I
F. There are three sorts ; some persons reckon
four; the fourth, however, is but a bended one of
the first kind. A lever of the first kind has the
fulcrum between the weight and power.
b


Fig. 18. Fig. 19.
The second kind of lever has the fulcrum at one
end, the power at the other, and the weight between
them.



Fig. 0. Fig. 21.
In the third kind, the power is between the fl-
crmn and the weight.
Let us take thelever of the first kind, (Fig. 18.)
which if it be moved into the position ed, by turning
on its fuerum e, it is evident that while a has ta-
veiled over the short space ao, 6 has travelled over
the greater spee bd, which paces are to one another
exactly in proportion to the length of the armu sand
Us. If, now, you apply your hand first to the point
a, and afterwrds to 6, i order to move the lever
into the position ed, using the same velocity in both
eases, you will find, that the time spent in moving
the lever when the hand is at b, will be a much
greater, as that spent when the hand is at a, as the






04 WmCUANICS.
arm ib is longer than the arm a ; but then the
exertion required will, in the same proportion, be
lee at b than at a.
C. The arm be appears to be four times the
legth of a<.
F. Then it is a lever which gains power in the
proportion of four to one. That is, a single pound
weight applied to the end of the arm be, as at p,
will balance four pounds suspended at a, as w.
C. I have seen workmen move large pieces of
timber to very small distances, by means of a long
bar of wood or iron ; is that a lever 1
F. It is; they force one end of the bar under the
timber, and then place a block of wood, stone, &c.
beneath, and as near the same end of the lever as
possible, for a fulcrum, applying their own strength
to the other ; and power is gained in proportion as
the distance from the fulcrum tothepart where the
men apply their strength, is greater than the dis
tance from the fulcrum to that end under the tim-
ber. Handspikes are levers of this kind, and by
these the heaviest cannon are moved, as well as other
heavy bodies.
C. It must be very considerable,for I haveseen
two or three men move a tree in this way, of sev-
eral tons' weight I should think.
P. That is not difficult; for supposing a leverto
gain the advantage of twenty to one, and a man by
his natural strength is able to move but a haudred
weight, he will flndthatbyalever ofthissortheem
move twenty hundred weight, or a ton; but for
single exertions, a strong man can put forth a much
greater power than that which is sufficient to re-
move a hundred weight; and levers are also fre-
quently used, the advantage gained by which is siill
more considerable than twenty to one.






THE LEVER. 65
C. I think you said, the other day, that the com-
mon steelyard made use of by the butcher is a lever I
F. I did ; the short arm as (Fig. 19.) is, by an
increase in size, made to balance the longer one be
and from e, the centre of motion, the divisions must
commence. Now if be be divided intoasmany parts
as it will contain, each equal to ae, a single weight,
as a pound, p will serve for weighing any thing as
heavy as itself, or as many times heavier as there are
divisions in the arm c. If the weight be placed at
the division I in the arm be, it will balance one
pound in the scale at a ; if it be removed to 3, 5, or
, it will balance 3, 5, or 7 pounds in the scale ; for
these divisions being respectively 3, 5, or7 times the
distance from the centre of motion v, that a is, it
becomes a lever, which gains advantage, in those
points, in the proportion of 3, 5, and 7. If, now
the intervals between the divisions on the longer
arm be subdivided into halves, quarters, &e. any
weight may be accurately ascertained, to halves,
quarters of pounds, &c.
CONVERSATION XVI.
OF THE LTVEL.
E. What advantage has the steelyard, which you
described in our last conversation, over a pair of
scales I
F. It may be much more readily removed from
place to place; it requires no apparatus, and only
a single weight for all the purposes to which it can
be appied.-Sometimes the arms are not of equal
weight. In that case the weight p must be moved
along the arm be, till it exactly balance the other
arm without weight, and in that point a notch must
be made, marking overit a cypher 0, from whence
the divisions must commence.
90 a






66 MrCHANICS.
C. Is there not required great accuracy in the
manufacture of instruments of this kind I
F. Yes; of such importance is it to the public
that there should be no error or fraud by means
of false weights, or false balances, that it is the
business of certain public officers to examine at
stated seasons the weights, measures, &c. of every
shopkeeper in the land. Yet it is to be feared that,
after all precautions, much fraud is practised upon
the unsuspecting.
E. I one day last summer,bought, asI supposed,
a pound of cherries at the door; but Charles think-
ing there was not a pound, we tried them in your
scales, and found but twelve ounces, or three quar-
ters, instead ofu pound, and yet the scale went down
as if the man had given me full weight. How was
that managed I
F. It might be done many ways : by short
weights ; or by the scale in which the fruit was put
being heavier than the other ;-but fraud may be
practised with good weights and even scales, by
making the arm of the balance on which the weights
hang shorter than the other, for then a pound weight
will be balanced by as much lew fruit than a pound
as that arm is shorter than the other; thiswaspro-
bably the method by which you where cheated.
E. By what method could I have discovered this
cheat I
F. The scales when empty are exactly balanced,
but when loaded,though still in equilibrio,the weights
are unequal, and the deceit is instantly disovereby
changing the weights to the contrary scales. I will
give you a rule to find the true weight of any body
by such a false balance; the reason of the rule yon
will understand hereafter: "fird the weiglt of the
body by bo"t scale, mutiply ther together, and them






Tru LETVE. 67
fiad the square root of the product, stliec is ti trms
Oretqht."
Let me see if I understand the rule : suppose
a body we;gh 16 ounces in one seale, and in the
other 12 ounces and a quarter, I multiply 16 by
12 sad a quarter, and I get the product 196, the
square root of which is 14 ; for 14 multiplied into
itself gives 19G ; therefore the true weight of the
body s 14 ounces.
F. That is just what I meant.-To the leverof the
first kindmay be referred manycommoninstruments,
such as scissors, pincers, snuffers, &c., which are
made of two levers, acting contrary to one another.
E. The rivet is the fulcrum, or centre of motion,
the haud tile power used, and whatever is to be
cut is the resistance to be overcome.
C. A poker stirring the fire is also a lever, forth
bar is the fu!crum, the hand the power, and the coals
the resistance to be overcome.
F. We now proceed to levers of the second kind,
iii which the fulcrum a (Fig. 20.) is atone end, the
powtrp applied at the other 6. and the weight to be
raised at w, somewhere between the fulcrum and
the power.
C. And how is the advantage gained.to be esti-
mated by this lever I
F. By looking at the figure, you will find that
power or advantage is gained in proportion a the
distance of the power p greater than the distance
of the weight from the fulcrum.
C. Then if the weight hang at one inch from the
fulcrum, and the power act at five inches from it,
the power gained is five to one, or one pound at p
will balance five at w e
F. Itwill; for youperceivethat the power phase
over five times aq great a space as the weight, or






68 MECRAIICB.
while the pint e in tie lever moves over one inch,
the point 6 will move over five inches.
E. What things in common use are to be referred
to the lever of the second kind I
F. The most common and useful of all things;
every door, for instance, which turns on hinges is a
lever of this srt. The hinges may be considered as
the fulcrum, or centre of motion, the whole door is
the weight to be moved, and the pon er is applied
to that side on which the lock is usually fixed.
E. Now I see the reason why thereis considerable
difficulty in pushing open a heavy door, if the hand is
applied to the part next the hinges, although it may
be opened with the greatest ease n the usual method.
C. This sofa, with sister upon it, represents a
lever of the second kind.
F. Certainly; if whileshe issitting uponit, in the
middle, you raise one end, while the other remains
fixed as a prop or fulcrum. To this kind of lever
maybe also reduced nut-crackers; oars ; ruddersof
ships; those cutting kniveswhich haveoneendfixed
in a block, such as are used for cutting chaff, drugs,
wood for pattens, &c.
E. I do not see how oars and rudders are levers
of this sort.
F. The boat is the weight to be moved, the water
is the fulcrum, and the waterman at the handle the
power. The masts of ships are also levers of the
second kind, for the bottom of the vessel is the ful-
crum, the ship the weight, and the wind acting
against the sail is the moving power.
The knowledge of this principle maybe useful in
many situations and circumstances of life :-if two
men unequal in strength have a heavy burden to
carry on a pole between them, the ability of eaeh
may be consulted, by placing the burden as much






TaE LEVER. 69
nearerto the stronger man, as his strengths greater
than that of his partner.
E. Which would you call the prop in this case
F. The stronger man, for the weight is nearest to
him ; and then the weaker mst be considered as the
power. Again, two horses may be so yoked to a
carriage that each hliall draw a part proportionalto
his strength, by dividirgthe beam in such manner
that the point of reaction, or drawing, may be as
much nearer to the stronger horse than to the weaker,
as the strength of the former exceeds that of the
latter.
We will now describe the third kind of lever. In
this the prop or fulcrum e (Fig. 21.) is at one end,
the weight r at the other, and the power p is applied
at b, somewhere between the prop and weight.
C. In this case, the weight being farther from
the centre of motion than the power, must pass
through more space than it.
F. And "hat is the consequence of that.
C. Thatthe powermust be greater than the weight,
and as much greater as the distance of the weight
from the prop exceeds the distance of the powerfrom
it, that is, to balance a weight of three pounds at a,
there will require the exertion of a power p, acting
at b, equal to five pounds.
F. Since, then, a lever of this kind is a disadvan-
tage to the moving power, it is but seldom used, and
only in cases of necessity; such as in that of a lad-
der, which being fixed at one end against a wall, or
other obstacle, is by the strength of a mar's arm
raised into aperpendiculr situation. But the most
important application of this third kind of lever, is
manifestin thestructureof thelimbsof animals, par-
ticularly in those of man ; to take the arm as an in-
stance: when we lift a weight by the hand, it is






70 MECHANICS.
effected by means of muscles cuLling from the
shoulder-blade, and terminating about one-tenth as
far below the elbow as the hand is: now the elbow
being the centre of motion round which the lower
part of the arm turns, according to the principle just
laid down, the muscles must exert a force ten times
as great s the weight that is raised. Atfirst view
this may appear a disadvantage, but what is lost in
power is gained in velocity, and thus the human
figure is better adapted to tle various functions it
has to perform.
CONVERSATION XVII.
OF THE WIIELL AND AXIS.
F. Well, Emma, do you understand the prin-
ciple of the lever, which we discussed so much at
large yesterday t
E. The lever gains advantage in proportion to the
space eedthrough by the acting o er; that's, if
the weight to be raised be at the distance of one inch
from the fulcrum, and the power is applied nine
inches distant from it, then it is a lever which gains
advantage as nine to one, because the space passed
throg by the power is nine times greater than that
passedthrough by the weight; and, therefore, what
is lost in time, by passing through a greater space,
is gained in power.
F. You recollect also what the different kinds
of levers are, I hope t'
E. I shall never see the fire stirred without think-
ing of a simple lever of the first kind; my scissars
will frequently remind me of a conibination of two
levers uf the same sort. The opening and shutting
of the dcor will prevent me from forgetting the na-
ture of the lever of the second kind ; and 1 am sure
that 1 slall never see a workman raee a ladder






THEI WHEEL AND AXIS. 71
against a house without recollecting the third sort
of lever. Besides, I believe a pair of tongs is a
lever of this kind I
F. You are right; for the fulcrum is at the joint,
and the power is applied between that and the parts
used in taking up coals, &c.- Can you, Charles,
tell us how the principle of momensts applies to
the lever 1
C. The momentum of a body is estimated by its
weight multiplied into its velocity ; and the velocity
must be calculated by the space passed through in a
given time. Now, if I examine the lever (Fig. 1U.
20.) and consider it as an inflexible bar turning on a
centre of motion, it is evident that the same time is
used for the motion both of the weight and the power,
but the spaces passed over are very different; that
which the power passes through being as much
greater than that passed by the weight, as the length
of the distance of the power from the prop is greater
than the distance of the weight from the prop ; and
the velocity being as the spaces passed in the same
time, must be greater in the same proportion. Con-
sequently, the velocity ofp, the power, multiplied
into its weight, will be equal to the smaller velocity
of 0, multiplied into its weight, and thus their mo-
menta being equal, they will balance one another;
F. This applies to the first and second kind of
lever; what do you say to the third I
C. In the third, the velocity of the power p, (Fig.
21.) being less that that of the weight I, it is evi-
dent, in order that their moment may be equal,
that the weight acting atp must be as much greater
than that of w as as is less than be, and then they
will be in equilibrio.
F. The second mechanical power is the Wkeet
asd Aris, which gains power m proportion as the






72 MBCIANIum .
elreamference of the wheel is greater than that of
thaxis; this machine may be
referred to the principle of the
lever. 46 is the wheel, a its
xis ; and if the circum'ereuce
of the wheel be eight times as
great as that of the axis, then
Single pound, p, will balance Fig. 22.
a weight, 0, of eighty pounds.
C. Is it by an instrument of this kind that water
is drawn from those deep wells so common in many
parts of the country I
F. It is; but as in most cases of this kind only
a single bucket is raised at once, there requires but
little power in the operation, and therefore, instead
of a large wheel, as ab, an iron handle fixed at a is
made use of, which, you know, by its circular mo-
tion, answers the purpose of a wheel.
C. I once raised some water by a machine of this
kind, and I found that as the bucketascended nearer
the top the diffBlulty increased.
F. That must always be the case, where the wells
are so deep as to cause, in the ascent, the rope to
coil more than once the length of the axis, because
the advantage gained is in proportion as the cir-
eamference of the wheel is greater than that of the
axis; so that if the circumference of the wheel be
12 time greater than that of the axis, one pound
applied at the former will balance twelve hanging
at the latter; but by the coiling of the rope round
the axis, the diferenoe between the circumference
of the wheel and that of the axis continually dimin-
ishes; consequently the advantage gained is less
every time a new coil of rope is wound on the whole
length of the axis: this explains why the difficulty
of drawing the water, or any other weight, increases
as it ascends nearer the top.






TUI WiHEL AXD AXIS. 73
C. Then by diminishing the axis, or by iunress-
ing the length of the handle, advantage is gained I
F. Yes, b either of tthse method you may gain
power; but it is very evident that the axis cannot
be diminished beyond a certain limit, without ren-
dering it too weak to sustain the weight; nor can
the handle be managed, if it be constructed on a
scale much larger than what is commonly used.
C. We must, then, have recourse to the wheel
with spikes standing out of it, at certain distances
from each other, to serve as levers.
F. You may by this means increase your power
according to your w.sh, but it must be at the expense
of time, for you know that a simple handle may be
turned several times while you are pulling the wheel
round once.-To the principle of the whee an ad ais
may be referred the cailtan, windlass, and all those
numerous kinds of cra les, which are to be seen at
the different wharfs on the banks of the Thames.
C. I have seen a crane, which consists of a wheel
large enough for a man to walk in.
F. In this the weight of the man, or men (for
there are sometimes two or three), is the moving
power; for, as the man steps forward, the part upon
which he treads becomes the heaviest, and conse-
quently descends till it be the lowest. On the same
principle,you may see at the door of many bird-age
makers, a bird, by its weight, give a wicker cage a
circular motion ; now, if there were a small weight
suspended to the axis of the cage, the bird by its
motion would draw it up, for, as it hope from the
bottom bar to the next, its momte tum causes that
to descend; and thus the operation is performed,
both with regard to the cage, and to those large
cranes which you have seen.
E. Is there no danger if the man happens to slip I





74 MECHANICS.
F. If the weight be very great, a slip with the foot
maybe attended with very dangerous consequence.
To prevent which, there is generally fixed at one end
of the axis a little wheel, f, (Fig 22,) called a
racket-wheel, with a catch, e, to fall into its teeth ;
this will, at a:y time, support the weight in case of
an accident. Sjmetimcs, instead of mea walking
within the great wheel, cogs are sot round it on the
outside, and a small trundle-wheel made to work
in the cogs, and to be turned by a winch.
C. Are there not other sorts of cranes, in which
all danger is avoided I
F. The crane is a machine of such importance to
the commercial interests of this country, that new
inventions of it are continually offered to the pub-
lic ; I will, when we go to the library, shew you in
the 10th vol. of the 'Iransactions of the Society for
the Encouragementof Arts and Sciences,an engrav-
ing of a safe, and, I believe, truly excellent crane.
It was invented by a friend of mine, Mr. James
White, who possessed a most extraordinary genius
for mechanics.
C. You said that this mechanical power might
be considered as a lever of the first kind.
F. I did ; andif you conceive the wheel and axis
to be cut through the middle in the di-
rection ob, fgb will represent a section
of it. a6 is a lever, whose centre of a
motion is e; the weight w, sustained
by the rope aw, is applied at the dis-
tanoe ea, the radius of the axis; and
the power p, acting in the direction bp, 23
is applied at the distance c-, the radius Fig. 23.
of the wheel ; therefore, according to the principle
of the lever, the power will balance the weight when
it is as much less than the weight as the distalice
e6 is greater than the d:itance of the weight to.






THE PULLEY.


CONVERSATION XVIII.
or THE PULLEY.
F. The third mechanical power, the Palley,may
be likewise explained on the principle of the lever.
The line ab may be conceived to be a
lever, whose arms ae and be are equal,
and e the fulcrum, or centre of motion.
If now two equal weights, wr and p be acr
hung on the cord passing over the pul- ]
ley, they will balance one another, and .
the fulcrum will sustain bath.l
C. Does this pulley, then, like the Fig. 24.
common balance give no advantage 1
F. From the single field pulley no mechanical
advantage is derived: it is, nevertheless, of great
importance in changing thle direction of a power,
and is very much used in buildings for drawing up
small weights, it being much easier for a man to
raise such burthens by means of a single pulley,
than to carry them ap a long ladder.
E. Why is it called a mechanical power I
F. Though a single fixed pulley gives no advan-
tage, yet when it is not fixed, or when two or more
are combined into what is called a system of pul-
leys, they then possess all the properties of the
other mechanical powers. Thus in cdb e
is the fulcrum ; therefore a power p act-
ing at b, will sustain a double weight r,
acting at a, for be is double the distance Ia
of ae from the fulcrnm. b e
Again, it is evident, in the presentease,
that the whole weight is sustained by the pi
cord edp, and whatever sustains half the
co d, sustains also half the weight ; but Fig. 25.
one half is sustained by the fixed hook






76 NKCIANICS.
e, consequently the power at p has only the other
half to sustain, or, in other words, any given power
at p will keep in equilibrio a double weight at v.
C. Is the velocity ofp double that of w
F. Undoubtedly: ifyoucorimare the spacepassed
through by the hand atp with that passed by tw,you
will find that the former is just double that of the
latter, and therefore the moment of the power and
weight, as in the lever, are equal.
C. I think I see the reasoii of this; for if the
weight be raised an inch, or afoot, both sides of the
cord muEt also be raised an inch, or foot, but this
cannot happen without that part of the cord at p
passing through two inches or two feet of space.
F. Yon will now easily infer from what
has been already slhewn of the single more-
able pulley, that in a system of pulleys the a
power gained must be estimated by dou-
bling the number of pulleys in the lower
or moveable block. So that when thoe
fixed block a contains two pulleys which
only turn on their axes, and the lower
block b contains also two pulleys, which
not only turn on their axes, but also rise b
with the weight, the advantageisas four
that is a single pound at p will sustain
four at w P1
C. In the present instance, also, I per- F. 26
ceive, that by raising wan inch, there are Fg.
four ropes shortened each an inch, and therefore the
handmust have passed through four inches of space
in raising tleweight asingleinch; which establishes
the maxim that what is gained in power is lost in
space. But, papa, you have only talked of the
power balancing or sustaining the weight; somo-
thing more must, I suppose, be added to raise it.






THE PELLET. 77
F. Theremust; considerableallowanceniust like-
wise be made for the friction of the cords, and of the
pivots, or axes, on which the pulleys turn. In the
mechanical powers, in general, one-third of power
must be added for the loss sustained by friction, and
for the imperfect manner in which machines are com-
nonly constructed. Thus, if by theory you gain a
power of 600, in practiceyou must reckon only upon
400. In those pulleys which we have been describ-
ing, writers have taken notice of three things, which
take much from the general advantage and conve-
nience of pulleys as a mechanical power. The ret
is, that the diameters of the axes bear a great propor-
tion to their own diameters. The second is, that in
working they are apt to rub one against another, or
against the side of the block. And the third disad-
vantage is the stiffness of the rope that goes over
and under them.
The two first objections have been, in a
great degree, removed by the concentric
pulley, invented by Mr. James White:
Sis a solid block of brass, in which
grooves are cut, in the proportion of 1,
8, 5, 7, 9, &c. and a is another block of
the same kind, whose grooves are in the
proportion of 2, 4, 6, 8, 10, &c. and round
thee grooves a cord is passed, by which
means they answer the purpose of so
many distinct pulleys, every point of
which moving with the velocity of the
string in contact with it, the whole friction Fi. .
is removed to the two centres of motion Fg.2.
of the blocks a and b; besides, it is of no small
advantage, that, the pulleys being all of one piece,
there is no rubbing one against the other.
E. Do you calculate the power gained by this pl-
ley in the same method as with the common pulleyst






T8 MECHANICS.
F. Yes, for pulleys of every kind the rule is gene-
ral; the advantage gained is found by doubling the
number of the pulleys in the lower block: in that
before you there are six grooves, which answer to as
many distinct pulleys, and consequently the power
gained is twelve, or one pound at p will balance
twelve pounds at w.
CONVERSATION XIX.
OF THE INCLINED PLANE.
F. We may now describe the inclined plane,
which is the fourth mechanical power.
C. You will not be able, I think, to reduce this
a!so to the principle of the lever.
F. No, it is a distinct principle, and some writers
on these subjects reduce at once the six mechanical
powers to two, viz. the lever and the inclined plane.
E. How do you estimate the advantage gained
by this mechanical power I
F. The method is very easy, for just as much as
the length of the plane exceeds its perpendicular
height, so much is the advantage ,.
gained. Supposeabisaplane stand- L 0*>r
mg on the table, and ed another d-
plane inclined to it; if the length ;4
ed be three times greater than the a
perpendicular height, then the cy- Fi. 28
lender s will be supported upon the 2
plane ed by a weight equal to the third part of its
own weight.
E. Could I then drawup a weight on such a plane
with a third part of the strength that I must exert
in lifting it up at the end I
F. Certainly you might; allowance, however,
mustbe made for overcoming the friction ; but then
youperceive, asin theother mechanical powers, that






MTE INCLINED PLAN 79
you will have three times the space to pass over, or
that as you gain power you wi lose time.
C. Now I understand the reason why sometimes
there are two or three strong planks laid from the
street to the ground-floor warehouses,making there-
with an inclined plane, on which heavy packages
are raised or lowered.
F. The inclined plane is chiefly used for raising
heavy weights to small heights, for in warehouses
situated in the upper part of buildings, cranes, and
pulleys are better adapted for the purpose.
C. I have sometimes, papa, amused myself by ob-
serving the difference of time which one marble has
taken to roll down a smooth board, and another
which has fallen by its own gravity without any
support.
su And if it were a long plank, and you took
care to let both marbles drop from the hand at the
same instant, I dare say you found the difference
very evident.
C. I did, and now you have enabled me to account
for it very satisfactorily, by shewing me that as much
more time is spent in raising a body along an inclined
plane, than in lifting it up at the end, as that plane is
longer than its perpendicular height. For take it
for granted that the rule holds in the descent as well
as in the ascent.
F. If you have any doubt remaining, a few words
will make every thing clear. Suppose your marbles
placed on a plane, perfectly horizontal, as on this
table, they will remain at rest wherever they are
placed : now if you elevate the plane in such a
manner that its height should be equal to half the
length of the plane, it is evident from what has been
shewn before, that the marbles would require a forev
equal to half their weight to sustain them in any pml






0O MECII ANICS.
ticular position: suppose then the plane perpendieu-
lar to he table, the marbles will descend with their
whole weight, for now the plane contributes in no
respect to support them, consequently they would
require a power equal to their whole weight to keep
them from descending.
C. And the swiftness Aith which a body falls is to
be estimated by the force with which itis acted upon
F. Certainly; for you now are sufficiently ac-
quainted with philosophy to know that the effect must
be estimated from the cause. Suppose an inclined
plane is thirty-two feet long, and its perpendicular
height issixteen feet, what time will marble take in
falling down the plane, and also in descending from
the top to the earth by the force of gravity I
C. By the attraction of gravitation, a body falls
sixteen feetinasecond; therefore themarble will be
one second in falling perpendicularly to the ground;
and as the length of the plane is double its height,
the marble must take two seconds to roll down it.
F. I will try you with another example. If there
be a plane 64 feet perpendicular height, and 8 times
64, or 192 feet long, tell me what time a marble will
take in falling to the earth by the attraction ofgravitv,
and how long it will be in descending down the
plane.
C. By the attraction of gravity it will fall in two
seconds ; because, by multiplying the sixteen feet
which it falls in the first second, by the square of two
seconds (the time), or four, I get sixty-four, the
height of the plane. But the plane being three times
as long saitis perpendicularly high, it must be three
times s many seconds in rolling down the plane, as
it was in descending freely by the force of gravity,
that is, six seconds.
E. Pray, papa, what common instrument are to





THE WEDGE. *1
be referred to this mechanical power, in the ram
wva as scisears, pincers, e. arereferred to the levert
'. Chisels, hatchets, and whatever other sharp
instruments which are chamfered, or sloped down
to an edge on one side only, may be referred to the
principle of the inclined plane.

CONVERSATION XX.
OF THE WEDGE.
F. The nextmechanical power is the wedge, which
is made up of the two inclined planes a A
def and if joined together at their bases
hefg; do is the whole thickness of thed /
wedge at its back abod, where the power
is applied, and dfand of are the length N '
of its sides; now there will bean equili- Fi. 29.
brium between the power impelling the
wedge downward, and the resistance of the wood, or
other substance acting against its sides, when the
thickness de of the wedge is to the length of the two
sides, or, which is the same thing, when half the
thickness d of the wedge at its back is tothe length
of dfoneofitssides, a the power is to the reistanee.
C. This is the principle of the inclined plane.
F. Itis,andnotwithtandingall the disputes which
the methods of calculating the advantage gained by
the wedge have occasioned, I see no reon to depart
from the opinion of those who consider the wedge
as a double inclined plane.
E. I have een people cleaving wood with wedges,
but they seem to have no effect, unleo great frorc
wad great velocity are also used.
F. No, the power of the attraction of cohesion, by
which the parts of wood stick together, is so great as
torequireaconsiderablemmeas stoseparatetem.
90 P






OV MUCHANICs.
Didyou observe nothing else in the operation worthy
of your attention 1
C. Yes, I also took notice that the wood generally
split a little below the place to which the wedge
reached.
F. This happens in cleaving most kinds of wood,
and then the advantage gained by this mechanical
power, must be in proportion as the length of the
sides of the cleft in the wood is greater than the
length of the whole back of the wedge. There are
other varieties in the action of the wedge, but at
present it is not necessary to refer to them.
E. Since you said that allinstruments which sloped
off to an edge on one side only, were to be explained
by the principle of the inclined plane ; so, I suppose,
that those which decline to an edge on both sides,
must be referred to the principle of the wedge.
F. They must, which is the case with many
chisels, and almost all sorts of axes, &c.
C. Is the wedge much used as a mechanical power I
F. It is of great importance in a vast variety of
cases, in which the other mechanical powersare of
no avail ; and this arises from the momentum of the
blow, which is greater beyond comparison than the
applicationof any dead weight or pressure, such asis
employed in the other mechanical powers. Henceit
is used in splitting wood, rocks, &c. and even the
largestshipmaybe raised toasmall height by driving
a wedge below it. It is also used for raising up the
beam of a house when the floor gives way, by reason
of too great a burden being laid upon it. Itis usual
also in separating large mill-stones from the silicious
sand-rocks in some parts of Derbyshire, to bore hori-
zontal holesunderthem in circle, and fill these with
pegs or wedges made of dry wood, which gradually
swell by the moisture of the esrth, and in a day or
two lift up the mill-stone without breaking it.






Ton scaMw. 88

CONVERSATION XXL
Or THn sCnEW.
F. Let us now examine the properties of the
sixth aid last mehanical power, the Mre; which,
however, cannot be caled
animplemeehanicalpower,
since it is never uead with-
out the assistance of a lever
or winch ; by which it be-
comes a compound engine,
of great power in pressing
bodies together, or in rai-
ing great weights. ab is Fig. 3.
the rep mention of one, Fg. .
together with the lever h.
E. You aidjustnow, pap, thatallthemechanieal
powers were reducible either to the lever or inclined
plane ; how can the crew be referred to either I
F. The screw is composed of two parts, one of
which ab is called the screw, and consists of spiral
protuberance, called the thread, which may be sup-
posed tobewraptrounds linder; the otherpart,
called the se, is perfoated to the dimeneions of the
cylinder; and inthe internal cavity is alo a piral
groove adapted to receivethethread. Now if you ut
a slip of writing-paper in the form of an inclined
plane od, and then wrap it round a cylinder of wood,
you will find that it makes a spiral answering to the
spiral pert of the crew ; moreover, if you consider
the ascent of the screw, it will be evident that it is
precisely the aesent of an inclined plane.
C. By wht means do you calculate theadvantage
gained by the screw I
F. There are, atfrstight, evidently two thinguto
be taken into conideratio ; the irt is the distant






84 IMCHANICS.
between the threads of the screw ;-and the second
is the length of the lever.
C. Now I comprehend pretty clearly how it is an
ineined plane, and that its recent is more or less
easy as the threads of the spiral are nearer or far-
ther distant from each other.
F. Well, then, let me examine by a question
whetheryour conceptions be accurate; suppose two
screws, the circumference of whose cylinders are
equal toone another; butin one, the distance of the
threads to be an inch apart; and that of the threads
of the other only one-third of an inch ; what will be
the difference of the advantage gained by one of
the screws over the other I
C. The one whose threads are three times nearer
than those of the other, must, I should think, give
three times the most advantage.
F. Give me the reason for what you assert.
C. Because, from the principle of the inclined
plane, I learnt that if the hsigt of two planes were
the same, but the length of one twice, thrice, or four
times greater than that of the other, the mechanical
advantage gained by the longer plane would be two
thee, or four times mor than that gained by tih
sorter. Now in the present ease, theeight gained
in both serv is the ame, one inch, but the space
passed in that, three of whose threads go to an inch
must be three times as great as the space p ed
in the other; therefore, as space is pased, or time
let, just in proportion to the advantage gained, I
infer that three times more advantage is gained by
the screw, the threadsof which are one-third of an
inch apart, than by that whose threads are an inch
apart.
F. Your inference is just, and naturally follows
from an aeurate knowledge of the principle of tho






Tru scaIC 85
inclined plane. But we have said nothing about
the lever.
C. This seemed hardly necessary, it being so
obvious to any one, who will think a moment, that
power is gained by that as in levers of the first kind,
according to the length A from the nut.
F. Let us now calculate the advantage gained by
a screw, the threads of which are half an inch dis-
tance from one another, and the lever 7 feet long.
C. I think you once told me, thatif the radius of
a circle were given, in order to find the circumfer-
ence I must multiply that radius by 6.
F. I did ; for though that is not quite enough, yet
it will answer all common purposes, till you are a
little more expert in the use of decimals.
C. Well, then, the circumference of the circle
made by the revolution of the lever will be 7 feet,
multiplied by 6, which is 42 feet, or 504 inches;
but, during this revolution, the screw is raised only
half an inch, therefore the'pacepaesed by themoving
power will be 1008 times greater than that gone
through by the weight, consequentlythe advantage
gained is 1008, or one pound applied to the lever
will balance 1008 pound acting against the screw.
F. You perceive that it follows as a corollary
from what you have been saying, that there are two
methods by which you may increase the mechanical
advantage of the screw.
C. I do; it may be done either by taking longer
lever, or by diminishing the distance of the threads
of the screw.
F. Tell me the result then, supposing the threads
of thescrew so fine asto stand at the distance of but
one quarter of an inch asunder; and that the length
of the lever were 8 feet instead of 7.
C. The circumference of the circle made by the






5o MECHANICS.
lever will be 8 multiplied by 6, equal to 48 feet or
576 inches, or 2304 quarter inhes, and athe eleva-
tion of the screw is but one quarter of an inch, the
pace passed by the power will, therefore, be 2304
times greater than that passed by the weight, which
is the advantage gained in this instance.
F. A child then capable of moving the lever suf-
ficiently to overcome thefriction, with the addition of
a power equal to one pound, will be able to raise
2304 pounds or something more than 20 hundred
weight and half. The strength of a powerful man
would be able to do 20 or 30 times as much more.
C. But I have seen at Mr. Wilmot's paper-mills
to which I once went, six or eight men use all their
strength in turning a screw, in order to press out the
waterof the newly-made paper. Thepowerapplied
in that case must have been very great indeed.
F. It was; but I dare say that you e aware that
it cannot be estimated by multiplying the power of
one man by the number of men employed.
C. That s, becausethemen standing by the deof
one another, the lever is shorter to every man the
nearer he stands to thescrew, consequently though
he may exert the mme strength, yet it is not so effe-
tual in moving the machine, as the exertion of him
who stands nearer the extremity of the lever.
F. the true method therefore of calculating the
power of this machine, aided by the strength of these
men, would be to estimate accurately the power of
each man according to his position, and then to add
all these separate advantages together for the total
power gained.
E. A machine of this kind is, I believe, used by
bookbinders, to press the leaves of their books to-
gether before they are stitched I
F. Yes, it is found in every bookbinder's work-






tan PNDULUM. 87
Sand particularly useful where persons are
of having mall books reduced to a still
smaller size for the pocket. It is alsotheprincipal
machine used for ng money ; fortakingof cop
per-plate prints ; an forprintngin general. Mr.
oulton invented a magmncent apparatus for coin-
ing ; thewholemachinery is workedby an improved
steam engine which rolls the copper for half-pence ;
works the screw-preses for cutting out the circular
pieces of copper, and coins both the faces and edge
of the money at the same time : and since the cir-
culation of the new half-pence, we are all acquainted
with the superior excellence of the workmanship.
By this machinery four boys, of ten or twelve years
old, are capable of striking 30,000 guineas in an
hour, and the machine itself keeps an unerring ac-
count of the pieces struck.
E. And I have seen the cyder-press in Kent,
which consists of the same kind of machine.
F. It would, my deer, be an almost endless task,
were we to attempt to enumerate all the purposes
to which the screw is applied in the mechanical
arts of life; it will, be sufficient to tell
you, that wherever great pressure is required, there
the power of the screw is uniformly employed.
CONVERSATION XXII.
OF THE PENDULUM.
E. I have been so delighted with the Conversa-
tions you have permitted us to have with you, my
dear papa, that I can scarcely think of any thing
but what you have been explaining to us; and now
when I see a machine of any kind, I begin to ex-
amine the various combinations of levers, wheels,
and pulleys.
F. I am very glad to find that my explanations






88 MECHANICS.
of the mechanical powers have excited your curi-
osity so much ; and I shall always feel a pleasure
in communicating any thing I know.
E. I am very much obliged toyou, papa. When
Charles and I were down stairs, we were examining
the kitchen clock ; we saw wheels and axles, levers,
screws, pulleys, &c. but neither of us knew what to
call the pendulum. Is that a mechanical power I
F. It is not called a mechanical power, because
it does not convey any mechanical advantage, but
the theory of the pendulum depends on that of the
inclined plane.
E. What is meant by the term pendulum 1
F. The name is applied to any body so suspended,
that it may swing freely backwards and forwards,
of which the great law is, that its oscillations are
always performed in equal times; and it is this
remarkable property which makes it a time-keeper.
A common pendulum cousists of a ball, as a, sus-
pended by a rod from a fixed
point, at b, and made to swing
backwards and forwards un-
derthispoint. Theballbeing
raised to c, and then set at
liberty, falls back to a, with
an accelerating motion, like
a ball rolling down a slope
(or inclined plane) ; and Fig. 31.
when arrived there, it has
just acquired force enough to carry it to d, at an
equal elevation on the other side ; from this it falls
back again, again to rise, and would so continue on
for ever, if there was no impediment either from
the air or friction.
C. Are the laws which regulate these movements
so simple that we can understand them I






THE PENDULUM. i9
F. I think they we; the mot important of thm
are these:- If pendulum vibratesin very smll
circles, the times of vibration may be considered
equal, whatever be the proportion of the cirles.-
2. Pendulums which areof the same length vibrate
in the same manner, whatever be the proportion of
the weight of the bob.-3. The velocity of the bob
or ball, in the lowest point, will be as the length of
the chord of the arch which it describes inits descent.
-4. The times of vibration of different pendulums
in similar arches are proportional to the square roots
of their different lengths.-5. Hence the lengths of
pendulums are as the squares of the times of vibra-
tions.- 6. In the latitude of London, a simple pen-
dulum will depart once ina second in a small arch,
if its length be thirty-nine and one-fifth inches.
C. Does the length of a pendulum influence the
time of its vibrations t
F. Yes; longpendulumsdepart more slowlythan
short ones; because, in corresponding are, or paths,
the bob or ball of the large pendulum has a greater
journey to perform, without having a steeper line of
descent.
C. IfI understand you rightly, a pendulum which
describes seconds i thirty-nine and one-flfth inches
in length, and the lengths are as the square roots of
thetimes; therefore, the length ofa haf-seond pen-
dulum is nine and four-fifths inches, and the length
of a quarter-second pendulum sill be two and nine-
twentieth inches.
F. You are quite correct.
E. But, if you wished the pendulumtobeatlonger
than one second, how could that be done
F. As abodyfallsfour timesas fast in two seconds
as in one, a pendulum must be four times as long to
beat once in two seconds a to beat every second.







90 ATRONOIY.
E. Howisitmadetodenotethetimeon theelooks
F. A common lock is merely a pendulum with
wheel-work attached to it to record the number of
vibrations The wheels show how many swings of
the pendulum have taken place, because at every
beat a tooth of the last wheel is allowed to pau ;
now, if this wheel have 60 teeth, it will just turn
round once for 60 beats of the pendulum, or seconds,
and a hand fixed on the axis projecting through the
dial-plate will be the secondhand of the clock. The
other wheels are so arranged,and their teeth so pro-
portioned, that one turns 60 times slower than the
fist, to fit its axis to carry a minute-hand, and
another, by moving twelve times slower still, is
fitted to carry an hour-hand.

ASTRONOMY.

CONVERSATION I.
OF THE FIXED STARS.
TUTOR-CHABLEB-JAMES.
CHAu.rs. The delay ocasioned by our unusually
long walk has afforded us one of the most brilliant
views of the heavens that! ever Saw.
James. It is uncommonly clear, and the longer I
keep my eyes fxed upwards the more stars seem to
appear: howisitpoisbletonumberthesestarst and
yet I have heard that they are numbered, and even
and in catalogues according to their apparent
mgiude Pry, sr, explain tous how this busi-
ness was formed.
Tutor. This I will do, with great pleasure, some
time henee; but at present I must tell you, that in
viewing the bhavn withthenakedeye, we are very






or Ta n1n1D WARS. I1
much deceived as to the sppoed nmbr of starf
that are atny time ible. It igenerally admitted,
and on good authority too, that therearenever more
than one thousand stars visible to the sight, unamls-
ted by glase, at any one time, and in one place.
J. What I caI se no more than a thoasad
tars if I look all around the heavens I should sup-
pose there were millions.
T. This number is certainly the limitofwhatyou
can at present behold; and that which leads you,
and persons in general, to conjecture that the number
is so much larger, i owing to an optical deception.
J. Are we frequently lible to be deceived by our
senses t
T. We are, if we depend on them n .sy : but
where we havean opportunity of calling in the ssist-
ance of one sense to the aid of another, we are seldom
subject to this inconveenie.
C. Do you not know, that if you place a small
marble on the palm of the left hand, and then eras
the second finger of the right hand over the Arst, aad
in that position, with your eyes shut,move the marble
with thosepartof the two fngersat one which are
not seeutomed to come into contact with any object
at the same time, that the one marble will appear to
the touch as two I In this instance, without the -
sistanee of our eyes, we should be deceived by the
sense of feeling.
T. This it to the point, and shews that the judg-
mentformed by means of a single sewis notalways
to be depended upon.
J. I eol thexperiment very well; we had
it from papa, a great while But that has no-
thing to do with the false judgment which we re
said to form about the number of tar.
T. Youare right; itdoes nothmediateyeeern





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14 ASTeOWoUT.
small, C00, then the single candle would have given
yeu the idea of 60, or 600. What think you now
about the stars
J. Since I have seen that rejection and ref/raeaio
will each, singly, afford such optical deceptions, I
can no longer doubt but that, if both these cause
ar combined, a you say they are, with respect to
the rays of light coming fromthe fixed stars, a thou-
sand real luminaries may have the powerof exciting
in my mind the idea of millions.
T. I will mention another experiment, for which
you maybe prepared against the next clear starlight
night. Get along narrow tube, the longer and nar-
rower the better, provided its weight does not render
it unmanageable : examine through itany one of the
largest fixed stars, which are called stars of thejfst
magnitude, and you will find that, though the tube
takes in a much sky as would contain many such
star, yet that the single one at which you are look-
ing is scarely visible, by the few rays which come
dirmetl from it: this is another proof that the bril-
liaey of the heavens is much more owing to refee-
Ut and refraoed light, than to the direct rays fow-
tog from the tars.
CONVERSATION II.
OF TEH PIXID ITARS.
C. Another beautiful evening presents itself;
shall we take the advantage which it offers of going
on with our astronomical lecture
T. I have no objection, for we do not always
enjoy such opportunities as the brightness of the
present evemng affords.
J. I wish very much to know how to distinguish
th stars, and to be abl to call them by their proper
mal"mm






o0 TRI 11WXI STAB. lS
T. Thisyou may verysoenlea; afewesening
well improved, will enable you to ditingih ll
stars of the first magnitude which are viable, and al
the relative positions of the different eonstellatn.
J. What are constellations, sir
T. Theancients, that they might thebetterdista-
guiah and describe the tear,with regardto theirita-
ation in the heavens, divided them into constellations,
that is, systems of stare, each system consisting of
such stars as were near to each other, giving them
the names of such men or things as they fancied the
space wlichtheyoccupiedintheheavensrepreeented.
C. Is it then perfectly arbitrary, that one collec-
tion is called the great bear, another the dragon, a
third Hereules, and so on I
T. It is; and though there have been additions to
the number of starein each constellation, and various
new constellations invented by modern astronomers,
yettheoriginal divisionof thetars into these olleo-
tions was one of those few arbitraryinventions which
have descended withoutalteration, otherwise than by
addition, from the days of Ptolemy down to t e-
sent time.- Do you know how to find the four
cardinal points, as they are unally called, the
North, South, West, and East
J. 0 yes, I know that if I look at the sun at
twelve o'clock at noon, I am also looking to the
South, where he then is; my back is towards the
North; the West is on my right hand, and the East
on my left.
T. But youmust learn to find these points without
the assistance of the sun, if you wish to be a young
astronomer.
C. I have often heard of the orth pole ar; that
will perhaps answer the purpose of the sun, when
he has left us.






96 ASTRONOMY.
T. You re right; do you ee those sveon tar
whieh are in the constellation of the Gree Beer I
some people have empposed their position will aptly
represent a plough; other say, that they are more
like awaggso and horses;-the four p
tarsrepresentingthebody ofawag-
gon, and the other three the horses,
and hence they are called by some a
the plough, and by others they are
called Charles's wain or waggon.
Here is a drawing of it ; abd re- b ,
present the four stars, and e B the A
other three. Fig. 1.
C. What is the star P t
T. That represents the polar star to which you
just now alluded; and you observe, that if a line
were drawn through the stars b and a, and produced
far enough, it would nearly toueh it.
J. Letme look at the heavens for it by thisguide.
There it is, I suppose ; it shines with a steady and
rather dead kidof light, and it appear to me that
it would be a little to the right of the line paying
though the stars and a.
T. It would, and these stars are generally know
by the name of the poiuter, because they point to
p, the north pole, which is situated a little more
than two degrees from the star i.
C. Is that star always in the same part of the
heavens I
T. It maybe considered a uniformly maintaining
its position, while the otherstars seem to moveround
it as a entire. We shall have occasion to refer to
this star again ; at present, I have directed your
attention to it, as a proper method of finding the
cardinal points by starlight.
J. Yes, I understand now, that if I look to the






OF TUN IaXBD fTAU. V7
north, by standing with my fee to that tar, the
south s at my back, on my right hand is the east
and the west on my left.
T. This is one important step in our astronomical
studies; and we can make use of these stars a a
kind of standard, in order to discover the names
and positions of others in the heavens.
C. In what way must we proceed in this businet
T. I will give you an example or two : conceive
a line drawn from the star (Fig. 1.) leaving n a
little to the left, and it will pw through that very
brilliant star near the horizon towards the west.
J. I se the star, but how am I to know its name 1
T. Look on the celestial globe for the stars, and
suppose the line drawn on the globe, as we eoneeived
it done in the heavens, and you will find the star,
and its name.
C. Here it is ;-its name is Areturus.
T. Take the figure, (Fig. 1.) and place Aretmar
at A, whichis its relative position, in repect to the
constellation of the Great Bear. Now, f you eon-
eeive a line drawn through the stars andb, and ex-
tended a good way to the right, it will pm jut above
another very brilliant tar. Examin the globe a
before, and find its name.
C. It is CisplJa, the go"t.
T. Now, weneveryou see any of thee you
will know where to look for the others without
hesitation.
J. But do they never move from their places I
T. With respectto us, they seemto move together
with the whole heavens. But they always remaining
the same relative position, with respect to each other.
Hence they are called lsd stars, in opposition to the
pleanst, which, likeourerth, are continually chang-
90 e




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