1000000031

ue.

and conf:quently, the whole (paces areas [he fqu ares

of lhe t:lllo.!S, ur uf

,he lan acquired

veJociries.

r'or

,rht.: continucl.l ilddition of (he odd

AU Lnbers

yitlds

,he

fquares of all

num~ers

[rom un¡ty upwards. Thus,

is lhe

firn

odd nUnlher, and

,he

fqu are of

¡so

the (econd odJ number, and lhis added

makes 4,

,he

fqul rl! of 2;

IS lhe

thirJ odd number. which added

mAkcs

9, tbe

fqudre

of 3 ; and fa on for ever. Sioce,

thercfore, lhe times aad

velocities

procecd

evenly

aDd

con!bntlyas

1, 2,

3 4,

but ,he Cpaces deCcribed

io each equal time élre as

3, S'

Cc.

is e,·ident

thar ,he Cpaee deCcribed,

minute will be -

Cquare of

I n

mmu ,es - -

1+3=

Cqua« of

mlnu'es -

1+3+S=

C'luare of 3

In 4 minutes

1+3+5+7=16 =

Cquare of 4 &c_

A s heavy bodies are uniformly

accderated

lile power

of gravity in their

deCcent, it is plain

chac

they muO:

be uniformly rctarded by the fame power

their af–

cent. Thuefore, the velocity which a body acquires by

f,dling. is fufficient tO carry it up again tO lhe fame

h eigi: t (rom whence il felJ; alJowance beiog made for

the refil1ance of the air, or other medium in which lhe

body is moved_ Thus, Ihe body D (lig.

2_)

in rolling

dOWD

the inclined plane

AB,

will acquire fuch a velocity

lhe

time

arrlves al

wilI

carry it up to the io–

c1ined plane

BC,

almo!l to

aod would carry it quite

up 'o C, if the body and plane \Vere perfeétly Cmooth,

and the air gave no

reCil1ance.~So,

if a pendulum were put

into motioo in a rpace quite void of air and all other re·

fillance, aod had no fr¡étion on lhe paint of fufpenGon, it

would move for ever; for the vclocity it had acquired in

falJing through lht! dt!rcending part of the are, would be

llilJ fufficient

carry i, equalJyhigh in the afcending pan

thereof.

Th~

centre o/

gtavily

is that poinl of

body io which

the \Vhole force c.(its gravity or wc:ight is united. There–

fore, whatever fupports th.a point bectrs the wdght of the

whúle body; and whilfl i, is C"pponed, ,he body cannot

fati, becaufe all

pans are in a perfeét equilibriulIl

a·

bo"ut thac point.

An imaginary line drawn from the centre of gr;¡vity of

any hody towards the centre of ,he earth, is called the

fine

diu{li"" .

I n ¡his I¡ne all

he~vy

bodies deCcend,

oot

obllru!led_

Since the ",h oll! weight of a b'ody is united in its centre

of gravity, as thal centre aCcends or deCcends we mul1

Jook u'pon the whole bocly to do

too..

Rut

contrary tO the "at']fe o f heavy bodit!s tOafcend of thei r

own

aecord, or

nOl

deCccnd wheo they are pernlitted;

maybe rure: th;tt, unlefs the centre of gr;.tvity be rup.

ported, ,he whole body \ViII ,umble or f.11. Hence i, is,

that (¡odies

Ch.nd

upon (heir bares when the Ji"t: of d¡ree.

tion falls within lhe hafe; for i n this cafe the body can

not be m.&de tO fall without firl1 rai(jng the ('entre of gra–

vity higher lhan it

was

before. T hus, the incJining body

ASCO, (liR3 .)

wh~Ce

centre

gnvity is E, (I, nds firm–

on ilS baCe C D lK, becauCe ,he line of cjir<étion EF

f~lIs

\Vi,hin the baCe_ Hu, if a ",<iRh', as AllG H, be laid

1.1pnn (he tOr of the uod y. the c'!ntre of gravity of

th~

hole body aud wcight ,ogc,hcr is raifcd up

and

and !hen, as the line of direétian ID falls without the·

u;.tfe at

the centre of gravit)' I is OOl fupponed;

and·

lhe \IIhoJe bocly ao ...

wcight tumule down together .

The bro;¡der the baCe is, and lhe oe.Lrer the line of

d¡reélion is tO the middle o'r centre of il. the more.(irmly.

does the body llaod. On Ihe contrary, the narrower the

bafe, and lhe ne.Lrer Ibe Jine of direétion is

the fide of

it . the mOre eafily m3y the body

ovenhrown: a lef,

change of poCition being rufficient tO remove Ihe line o:

direétion out of the bafe io

lhe

Jan er cafe lhao

the

(armer. And hencc il

'SJ

that a fphere is fo eafily rolled'

upon a horiz.ontal plAne; and that il is fo difficult, if

no~

impoffibJe,

make things which are lharp pointed to

Hand upright on the point.-From what hath beeo raid,

plainly appears, that if rhe plaoe be inclined on which

the heavy body is placed, the body \ViII flide down upon

,he plane whiHl ,he line of direétion falls \V"hin the

b.Ce

;

bU(

will tumble or roll down wheo that line faJls Wilh–

out the baCe_ Thus, ,he body A (6g_ 4.) will only flide

down the inclined plaoe CD, whilfl Ihe body B roll.

down upon it.

When the line of direétion fans within ,he baCe of our·

(eet, we fiand ; and mofi fi rmly,

WQ<'l

it is in the middle:–

bUl

",hen

is OUt of that bafe, we irnmedialely

fall.

Aod lt is nOI ooly pleaGng, but even Curprifiog, to (e–

fleét upon Ihe various and uothought o( melhods and po–

fiurc::s which we

~fe,

to retain this pofition, or tO recover·

il when

is Jol1. For this pnrpofe, we bend our uody

forward when we rife (rom a chair, or when we go up.

fiairs : and for Ihis purpofe aman leaos fonvard when he

carries

burden on h-is back, and backward

\IIhen

he car–

ríes it

his brean, aod tO the nghl or lefl fide as he–

carries

on the oppofile fideo

The

quantíty of matter in all bodi€s

in exaét

proportion lO their weights, bulk for bulk.. Therefore•.

heavy bodies are as much more den{e Or compaét than líght

bodies

the Carne bulk, as theyexceed rhem in weight_

AII bodics are Cull of

~ore~,

or Cpaees void of maner :

.nd in gold, which is ,he heaviell of all known bodies,

there is perhaps a greater quarHity of {pace than of mat–

ter. For lhe particles of heal and magnelifm 6nd an

e~fy.

palf.ge

,hrough the pores of gold; and even water i,C:lf

has beeo forcc.:d through Ihem. Befides, if we confider

ho\V eafily the

ray~

oflight p'Cs ,hrough

Cohd a body as.

glafs, in alJ manDer

dire:étions,

\Ve

Chall

fiad

reafoD to

believe

thdt

bodies are exceedingly porous .

AII bodies are Come way or o,her affeétt d by hea, ;

and all metaJlic bodies ue expanded in lenglh , brea.dth,

and thicknefs Iheleby ,-The propon ion of the expan–

fion of feveral metals, according

th'e beH experiments,

i, nearly ,hus _ Iron .od glaC, as 3, neel 4, cúpper 4 and

one eighth, bra{s

tin

Jead

and one e:ighlh. An

iron rod

{eef long is about one 70th pan of an inch longer.

in fummer than in \ViOler.

The expaofioo

me,al. by he." ·is demonllrated by

,he foll owing nta,hine, called a pyrome,cr.

(fi g.

S.)

is a

fb,t picce of mahogony, io which art! fixcd (our brafs

llud!o

B,C,D,L;

and

lW·O

píos, one at F , and lhe othe"

H .

On the rin F lurns the: crooked ir.dcx El, and

upon lhe pin

,he

{l-r<!i~ht

indcx

GK;

;¡ga:nll which a

pieee of w.teh-Cprinc

bears gently, .nd

prclres i,

towart..h