218 
MR. HEARN ON DISCREPANCIES OBSERVED 
The equation for angular motion is then 
+m 2 {d—u) — +n0), 
neglecting d 2 , &c., where n is a constant depending on the distance of the masses from 
the balls. 
Making rri 1 — this equation may be written 
Multiply by i the distance from the centre of motion to the scale =108 inches, and 
put iO=x, icc=b, then 
d 2 x 9 | ixEx* 
-jp-+lA 2 x = m 2 b-\ p — i 
in which the masses are in the positive position. 
The integral of the equation is 
m 2 b ixExi . . / j. \ x) \ 
x — + Y/jfi cos 
in which A and B are arbitrary constants depending on initial circumstances. 
Let e be the value of x for the ‘ resting point,’ or mean value of the above, 
m% t ixExi 
When the masses are in the negative position, the only alteration in the equation 
(still measuring x the same way) is in the sign of k; we have, therefore, for the nega- 
tive resting point, 
, m 2 b k x E x i 
Hence 
iv 
e — e' k 
xExi 
2 ~ 
F p* ' 
>n T=- 
1 2E i 
rji2 
k F7t 2 e — d 
It is then shown, on the hypothesis that k is the same for all substances, and on 
the law of universal gravitation, that &A = H, a constant depending on known quan- 
tities, so that we have 
Every division of the scale is ^th of an inch, so that if s and s' be the scale read- 
