!g2 Mr, Atwood’s Investigations for determining 
pL - as ^ is to r it follows, that the time of a 
^mivibmtion in the arc B O is to the time of a semivibration 
i — » 10I ini 
in the arc I O, as b~ to c * , or as 1 to -55 1 2 ■ 
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 = 24". 
the alteration of the daily rate, in consequence of the dimi- 
and v'i-Z|" + i 
To find the proportion of the entire fluent of y/ , _ > 
y 
to the entire fluent of y/ x _ 7.1 "+ 1 
snake x — — , so that when x = o, y = o, and when * = b, y = c ; 
± X ^ 
then 
v / 1 - 3 ” +1 
and 
, . r to / "" == will be equal to that of 
the proportion ot ~ — j n + t 10 y/j _ » + » 
i. to 1 , or of b to e ; this being the constant proportion of the fluxions when * = 7 * 
the fluents will be in the same proportion, provided x = ^i wherefore the entire fluent 
v y h - * 
of y/ b » P - wil1 be tQ the entire fluent 0 V c * + i -y i + Tas b’^ ° 
T+T ; eras b — to . 
