132 
Mr, Atwood's Investigations for determining 
- as th 2 is to it follows, that the time of a 
semivibration in the arc BO is to the time of a semivibration 
i — » » — * 1 o \~z± 
in the arc I O, as b 2 to c 2 , or as l to B 0 | • 
Suppose a watch to he adjusted to mean time when the semiarc 
of the balance's vibration is = B O (fig. 3.) and let this semiarc 
be afterwards diminished to I O ; the time shewn by the watch 
in any given portion of mean time t, when the semiarc of vi- 
bration is I O, will be = t x ; and if t is put = 2^, 
the alteration of the daily rate, in consequence of the dimi- 
V C ” + ‘-/+‘ X \/i-ZJ n+1 " 
x 
To find the proportion of the entire fluent of ^ i _ 7-1 n + j 
to the entire fluent of 1 _ 7.1 n + l 
then 
make x — — , so that when x zzo, y — o, and when x _ b, y _ c ; 
* fe y — 
c y/i — 2 _j ” + 1 * 
and the proportion of to _ r| »+ T wiU 156 e( * ual t0 that ° f 
by 
jt to 1, or of b to c; this being the constant proportion of the fluxions when x = — * 
c b 
the fluents will be in the same proportion, provided x = ; wherefore the entire fluent 
x y 
^/ === 1 ^.r+ T will be to the entire fluent of + , 1 ** g 1 ~t ~ 1 
of 
tO 
n+1 5 or as fy. 
C~~z~ 
to 
C 2 
