Spherical Motion. 
54i 
= 0 ; and when «- £,y=?f which is its value when * = o» 
as it ought to be, the track in this cafe, thfit is, when 
AS? is greater than CC% eroding AC and AB ; the bar m this 
cafe making only ofcillations and not revolutions. But if r 
now be made = - inftead of the bar will ftill make whole 
2 A 2-v. 
revolutions and as ^ : v/% :: the time of two whole revo- 
. y b (T 2 
lutions of the bar whofe centre of ofcillation is at — diftance 
from C : the time of one revolution of the body under Z. 
Thefe cafes may be otherwife refolved by finding the length 
SC = r, fuch that the bar may make two revolutions or ofcil- 
lations whilft the body makes one , thus, let ^-V, inftead ot 
being = u, be in a conftant ratio to it, or SV = /«, and 
lit _ Bi 
r 
B* 
t 2 zriu-Fii 4 ^ k~lu 2 \J ^ Zu 
X 
• u 
and comparing the homologous quan- 
i tV % / 
A 
rl 
lu 
tities, = ? r — s/IRgi 2r ? 
n m 
q z / z 2 Z ! 
, r = 
2C VlZg, s/l 
__ 2 C 4 c ° B y r 2CB q ^ cz 4C Bg — ; now, when 
r "“ 9 A A34 
fuch a bar makes whole revolutions, £ muft be greater than 
2r or than 1^, 2£ than unity, and CC 2 than A3h 
2r? 0 aa 4 a 2, 9 aa 2 
A bar therefore whofe centre of ofcillation is - diftant 
from the centre of motion, will make two whole revolutions 
whilft the whole track, WV'W'V moves once under Z 
