154 ME. A. NORMAN SHAW: A DETERMINATION OF THE ELECTROMOTIVE 
We may take, therefore, 
(,_j if 
{a 2 +d 2 f\ 60 a 2 . 
and in a similar manner we have 
g ! = 7rN 2 a 2 + 3tj7rN 2 ^ 2 2 . 
In the case of G 5 , G 7 , g 5 , g 1 we may neglect the corrections due to the depth and 
breadth of the windings. 
(/>) The Expression for the Current Flowing through the Suspended Coils. 
Let the ratio of the current i 1 through the fixed coils, to the current i 2 through the 
suspended coils he r. If we assume that the magnetic azimuth of the planes of the 
fixed coils is zero, and that the angle which the axis of the suspended coils (in the 
undeflected position) makes with the planes of the fixed coils is also equal to zero,^ 
then it can be shown that 
. _ / B tan 0 / v 
' 2 V r(-4G^-4G^ 5 P' 5 -4G^ 7 F 7 ) •••••• 
where B sin 0 is the controlling couple due to the bifilar suspension, and tan 6 is the 
mean of four values tan 0 lf tan 0 2 , tan R>, tan where 
0 j is the deflection when i x is + and i 2 is + 
0 2 
0 3 
Oi 
+ 
+ . 
In this way the effect of the earth’s magnetic field is eliminated to a sufficient degree 
of accuracy. 
III. The Dimensions oe the Fixed Coils. 
(a) The Mean Radius of the Large Coils. 
The radii of the fixed coils had been determined by Mr. R. O. King. The following 
summary is taken from Prof. Callendar’s account of the measurement:— 
“ The mean radius of the pair of large coils was determined from the length of the 
copper tape with which they were wound. This method is not satisfactory with soft 
* If the axis of the suspended coils (in the undeflected position) makes an angle T with the planes of 
z 2 
the fixed coils, the above expression for i 2 is reduced to — , . The coils could, however, be 
V cos 
by optical methods with sufficient accuracy for us to neglect this factor. The choice of 01, 02, 03, 0 , 
eliminates the effect of small magnetic azimuth of the planes of the fixed coils. 
