152 
MR. A. NORMAN SHAW: A DETERMINATION OF THE ELECTROMOTIVE 
where 0 is the angle of deflection from the position in which the suspended coils are 
at right angles to the fixed coils, then the couple acting on the suspended coils and 
dW 
tending to increase 6 is 
d<p 
The mutual potential energy, W, is equal to the sum of the four mutual potential 
energies of each fixed coil with each suspended coil. In fig. 1 a section of the coils 
is represented for <p — 0. If we call the coils I, II, III, IV, as 
marked in the figure, then 
r 
u 
n 
nr 
U 
w 
n 
nr 
w = w (I , m) +w am +w 
(I, IV) ■ 
(II, III) 
+w 
(II, IV) J 
( 1 ) 
n 
IV 
a where the suffixes indicate the pairs of coils considered. 
If we take 0 as the origin, a' a. as the radii of the large and 
small coils, and d, $ their distances from the origin respectively, 
then it can be shown that 
W(n,i V ) = i 1 i 2 [GIiStPi (cos 0) -fG^P, (cos <f>) 
+... + G„pqP„ (cos 0 ) +...], 
n 
where G 2 , G 2 , G 3 , ... are constants depending on “a,” “ d,” 
f~h and the sectional dimensions of the winding, g ly g 2y g 3 , ... 
depending on a, 3 (and the sectional dimensions of the wind¬ 
ing), and Pj (cos 0), P 2 (cos0), P 3 (cos0), ... are surface Zonal 
Harmonics of orders 1, 2, 3, .... 
It is obvious from the symmetry of the dynamometer that 
FIG. 1 
and also 
W (IIiIV ) — Wa.no 
W. 
(i, iv) — W (II , xjd, 
but in the latter case we must have 7 r + 0 for 0 , and the sign of either i x or i 2 must be 
reversed, hence 
W (I , IV) = W (II> In) = hi 2 [Gi^Pj (cos 0 ) - G 2 (/ 2 P 2 (cos 0 ) + G : ^ 3 P 3 (cos 0 ) - G 4 gr 4 P 4 (cos 0 ) +...]. 
It follows, therefore, from (l), that 
W = 4 i x i 2 [GxgxP, (cos 0 ) + G^ 3 P 3 (cos 0 ) + G^ 5 P 5 (cos 0 ) +...], . . 
( 2 ) 
and hence the required couple is equal to 
where 
- 4 i x i 2 sin 0 [G^F, + G^'s -h G^P'g +...], . 
p/ = d\V n (cos 0 )] 
" d (cos 0 ) ' 
( 3 ) 
We shall require to evaluate this couple in terms of i 1 , i 2 , a, d, a, S, and 0. 
