the intensity of magnetic forces y ^c. 7 
first terms, and we shall in these cases thus obtain a much 
more convenient equation for computation. Since 
1 + ~ . a cos. (p 4 - a® cos.^ (p -j- ^ ‘ ^ ‘4 cos.^(p 
^ “T .4 2 # ^ • O 
(i— a cos.p) 
and 
1 
(i 4- <z cos. Ip) 
3 
2 
2.4 ' '2.4 
3 • 5 • 7 • 9 ^4 
+ 
2 . 4 . 6 . 8 
a* cos.*(p + See. 
+ 
(i — a cos. p) (i 4- a cos. ip) 
So that the equation ( B) will become 
. a cos. (p 4 - — ^ cos.® 0 — ^ ^ ■ 4 a^ cos.^0 
^’2.4 2.4.0 
+ ^ a ' Q ^^*OOS.'^(p + 
' 2 . 4 . 6 . 8 
3 = 2 + (f COS.®<f + a* cos.’* Ip 
+ &c. 
r 
— F . 
7 ^ r-L' I 2 + 3 • 5 • ■ S . cos.’ p ) 
J_, (2+3.3. 3.cos.’p) 
»4- t 2 I ) rR I 
- (R+/>) 
5 • -7 
I (R +p)’ 
^ = 0 
‘ 4 r^J j 
neglecting the terms which contain the fourth and higher 
powers of cos. <p, 
Taking one of the cases which I investigated, and from 
which the others do not differ very considerably, the values 
of the co-efficients of cos. 0 in the denominators of the frac- 
tions in the equation (B) are .25691 and .15951 ; so that 
the greatest of the terms neglected would be 
X (.25691 )^ cos. > and x ( .15951 )" cos.>. 
Now, supposing that 0 is 70°, if these terms are employed 
in determining the value of F, it will be 218.7705 . M, and 
218.8184 . M, if they are neglected; making a difference of 
.0479 M, or only affecting the fifth figure in this extreme 
