: 
. 
“From | rett by the force of this acceleration through 
GYRATION. 
i¢ follows alfo that the angular velocity of the fyftem is 
iain accelerated, beeaufe the a velocity of any 
a given diltance from the of motion is as the 
mylar velocity of that fy ftem, id gra of the 
Viele Ly tke 
: i * manifett that it is of no confequence whe- 
ther lye » Kee pies in the fame or m dif- 
ee is obvious alfo, that changing the pofition of | 
the iin A; B, and C in the fame plane will not affect the 
force which accelerates the fyitem, prov — their refpective 
: thus, with 
be deferibed ; ; if Bis transferred to 4, or C toc, the worng 
force, which aéts on thefe bodies refpectively, will no 
, and confequently the mafles moved being likewile 
conttant, the accelerating force will be the fame. 
~ 7—Alfo the propofitions concerning rotation will 
be oot = whatever es by “which the an- 
metion $ generated, Abort a it be conftant ; or if 
variable, ould - action be confidered for an evaneicent 
fms wees 
plied at a fingl 
the axis. ‘Thus, eae a treoling ee to confift 
the bodies A, B, C o nefcent magnitudes, and equal 
to each other in. quantity. —Let a weight P cn to 
ey by means of a line, going 
Moreover, le 
th 25 a8 4 SC = 4, and let it be required 
nd ~ 
to a the force which accelerates the defcent of the — 
ae to the rule, we have the force a 
SD*x.P 
“AXAD PBRBS +@x CS a eT a6 
= ~ 3p which is the true accelerating ferce, when the 
=e moving Seige mvold of i inertia 5 sbuti in the reac ma the force 
and'as P_ moves with the fame dea as the point D, ss 
its inertia will be eftimated es fappeing a maf of 
ter. = P to be colleéted into the € point - en 
‘s moving a Some P, and the mafs iowa’ se 
ee ee 
ra’ pets ge Ss 
force tet Sees the defcent of P will be 
S a x P 
= Ei i line saa of sc es bersiae | 
account. Tt follows, therefore, that the weight will defcend 
nee 
Teeter in oon ‘and in cea dilincet inde if 
of Aw ASi+B x BS4+ Cx CS 7 
Thus puttin Boe 8 Be 
puns DISD PAX AS 4+Bx BST CxCS" 
=F, /= 193 inches, f = the fpace defcribed by P from 
es the velocity gre as by P will be , “4lF / F finches 
a fecond, and i in the fame manner, havin ng 
city acquired, the other two may be determined. 
Ina fyftem of bodies A, B, C, (jig. 3.)- revolving round 
axis which paffes through S ; having g given the quantities of 
a er contained in A, B, C, ad the « dflancess A, 5B,5C, 
tis required to diteraine SR, 
of gyration from the axis of motion. 
Let any force P be applied to oa ihe fyfiem at any 
given diftance from the axis S he force which acce- 
lerates n point D be the Naps in any two cafes, the 
abfolats: aoe of that point, generated ina gine? time, mult 
be the fame, and confequently the angular velocity generated 
in the {yftem equal in both cafes, the; force aEAt, accelerates 
iftance of the centre 
P 
AxAS?+BxBS*4Cx es” 
let A+B+C coincide with R, and the foree which 
‘gteaied, 2 
accelerates D will RESO: ore 
mult fe equal by the hypothefis; making, ite, 
Px of AP P «x &i)* 
the point D = 
x § 
: : the’e forces 
A+B+4+4CxSR 
we fhall have S ie? xAS'+B aBS +£2.58 
ees 
and the diftance of the centre of gyration required = 
pAx AS? + Bx BS'+CxCS* 
ihe WA 
Cor. 1.-—Let A + B+ C= W. , and fince A x AS*+ 
S*=SR’*x W,i it follows, that § R* 
: wherefore the diftance of the centre of 
gyration is a mean proportional between the diftances of 
the centres of gravity and olfcillation from Oe axis 
see 
~ Every thing remaining, the angu I Fe 
seme in na fyftem will | be the fame, whether the = W is 
placed at a a SR=VSO x 8G, oz whether the 
ornare mine DP 2 ae 
‘et 
“* 
male eye 
ae A ee ee 
-Let 
~ Cor 
and Seek an axis which pafles ee the centre of gravity 
“AXGA'+B x GB BG 9 CORe. 
Ay BC: 
diftance of the centre of. Woe the ‘ais of 
andlet GQ'= J 
‘be 
motion ; ‘ o* the si £0 mea it appears, that G ey = 
°C 
ie 
ved 
cies 4—Let A BC dD Feira arly pendulous body, 
moveable a round an axis of motion H 1, which paffes through 
S, and let any impaét be imprefied on the point D, — 
the ovata th is at aie ign in an lane ABCD. direction 
ean sa 
