104 
Mr. Christie on the mutual action of 
the ring, the points to which we may refer all the forces of 
the magnets, that is their poles, will not be at the same 
distance from their extremities as when the magnets were 
vertical ; and the errors which will arise from considering 
that these points continue fixed for different distances of the 
ring, will be increased when those distances are small, in 
consequence of the great obliquity of the direction in which 
some of the forces are exerted. The pole of the magnet will 
no longer be directly under the ring ; but if we call c the 
vertical distance of the middle section of the ring from the 
axis of the compound magnet, and e, as before, a constant 
horizontal distance from the pole, at either end, to a point 
behind it in the ring, then the formula ( 1 ) will be 
( 5 ). 
M 
a, 
l 
l c a + « a 
V 
5 
Putting, as before, a for ? and calling the values of a 
corresponding to the distances , c 
a a 
l m 
M = 
(c 7 -f c ) . (c, — ■ c ) 
v l “ m' W m' 
a* — a 
t m 
( 6 ')- 
Combining these observations in the same manner as those 
which precede, I obtain the mean values of M, and then the 
values of i from the separate observations, by means of the 
formula, 
e 2 = M a — r 
( 7 ) : 
or we may obtain e 2 independently of M from ( 5 ), then 
cf a • 
< m 
c' a, 
m I 
m 
c ; — c 2 ).a m 
- ( / m) 
£=- C 
or. 
( 8 ), 
