length of the pendulum vibrating seconds , 101 
reduced inertia % a?* P here consists of two portions : for the 
rod we may take the equivalent expression dlQ, which we 
may call axy, a being the weight of the bar (Q), x the distance 
(d) of the centre of gravity, andjy the equivalent length (/): for 
the ball we must employ the formula 2 #*P = + d*Q, 
and call tf P, u, and d 2 Q, bz\ b being the weight of the ball, 
and z the distance of its centre of gravity from the point of 
suspension : and in the same manner the force 2 (a?+ r ) P = 
{d+r) Q must be composed of the two portions a (a?+r) 
and b ( z -f r)', so that the equivalent length becomes 
• whir.h wp mav r a 1 1 
z+ w 
axy + u + bzz 
aTr + r) + b (z + r) 
axy + u 
— r~— nr ; which we may call __ 
ax -f- ar-\. br 5 J z-t- w 
The experiment being then performed in four different posi- 
tions of the weight, at the distances d! , d", and d'" , so that 
the second value of z may be z< — d' = z , the third z — d"=zz", 
and the fourth z — d!" = we must observe the times of 
vibration, and deduce from them the comparative lengths of 
the equivalent pendulum, t, n't, n"t, and n'"t : and hence the 
value of z, of v, and of t may be obtained, without deter- 
mining w, and of course without employing the quantity r. 
T" M -J-V 
First, — p- 
’ z+w 
/_ Z Z V ___ x. t v __ a t v ___ 
, z' A - VD 7 z" J- m ~ ” 7 z 111 let ' 
z'^+v 
+ V 
z' + w 7 z" + • 
Z ‘‘ + V I Z n + v 
Z + 
II, % + w== ^,tf +w== lgZ f + W = ^ 
z'" + w = z " ,z+v 
z'=d'i : 
n"'t. 
"* + v 
n"‘t . 
m, * 
IV, d' = 
d " ; z — z" ! — d"’. 
t 
z'^+v 
n't 
+ ® . lit 2*+V 
■> a — , 
n"t 
; d h 
z 2 +v 
t 
