160 MR. A. NORMAN SHAW: A DETERMINATION OF THE ELECTROMOTIVE 
Let us first find the couple on the magnets tending to decrease 6, due to a current 
Ii in the large coils. If the magnetic system is small, it can be shown that this 
couple is given by 
— 2l x sin 6 [yiGjP'i + y 3 G 3 P' 3 + y 5 G 5 P' 5 +...] 
where G 1; G 2 , G 3 , &c., have the same significance as before; 
P' d [ P ( C °s9 )] nd M; y 3 = ML 2 ; y 5 = MX* .... 
a (cos 0) 
where M is the magnetic moment of the suspended magnets, L is their “ equivalent 
length,” and X is a length differing slightly from L. Now we have 6 = - and G 3 = 0, 
2 
hence our required couple can be taken as 
— 21] [y) Gj + -;/ 1 yr,G-] • 
In the same way it can be shown that the couple due to a current I 2 (in the opposite 
direction) in the small coils with their centres at a distance x from the centre of the 
magnetic system, is given by 
-I 2 [y 1 P 1 + 1 #y 5 P s ], 
where lfi, T 5 , are constants for the two small coils added together. It should be noted 
that Tj and V 5 are not derived in the same way as g x and g 5 . In this case, the 
calculation of y corresponds to that for g, and the method of calculating T is 
analogous to that for determining 2G for the large coils. It can be shown that 
where 
and 
A 
B = 
X | i. J 2 15 ( X ~ S Y I + i ( 4 (x—S) 2 —a. 2 
241 - 2 {a. 2 + {x-S) 2 Y\ ^ 8 \{ a . 2 + {x-S) 2 } 2( ^’ 
a 
[ 2 
l+^l4-15 
la 
( X + S) 2 \ ^ T ( 4(x + d) 2 —a 3 \ 2 
'+{x+syy! ^ 8 1{a 2 + (x +<^) 2 } 2 j % ' 
l a 
When the currents are such that there is no deflection in the magnetometer 
that is, when 6 = - ) we have 
2 / 
and therefore 
2 li [yiG 1 + J g fL y 5 G 6 ] = I 2 [yiPi+ J #y 5 r5] 5 
I 2 _ 2G] f 15 y 5 /G 5 T 6 \\ 
fjj. (0) 
The magnetic system consisted of fourteen small magnets made from hair springs 
and each about 1 cm. in length, seven being placed on either side of a mica strip such 
that the system of magnets occupied a space about 1 cm. broad and 1’5 cm. high. It 
