148 
This becomes 0 in two cases, 
(1) 1 — 5 sin 3 a = 0, sin 2 a = i, taira — | 
so that a is the angle whose tangent is 
This is the angle at which Dr. Joule has pointed out that 
it is best to work for accurate measurements. The first 
term (A) of the total correction will disappear, therefore, 
even though the centre of the magnetic needle may not be 
accurately in the plane of the coil, provided it is on a line 
perpendicular to the plane passing through the centre. 
When we work at any other angle the correction is 
3Z 2 E 
tail a 
(4e 2 — r) 
^(1 — 5 sin 2 a) 
87rr 2 (e 2 + r 2 )i 
The magnitude of the correction will depend therefore on 
that of the term 
(e 2 + r 2 f 
and will still become zero whatever be the value of 1 — 5 sin 2 a, 
provided 4e 2 — r 2 =0. 
The same accuracy is therefore secured by working at any 
angle with a needle whose centre is at a distance equal to 
half the radius of the coil from its centre, and along a line 
perpendicular to its plane. 
The next term of the correction becomes 
p 3 E 27Z 4 
1 — tail a-r^—J8e 4 - 
■1 2e 2 r 2 + r 4 ) 
2tt r 2 40jo 8 
for the angle a specified. For e—0 (needle at centre), 
this 
( P =d 
r 3 E tan a 27 1 4 
27rr 2 40 r 8 
r 4 - E tan a. 
27 1 4 
807rr 
For e it gives l 2 = e 2 + r 2 = 
97 
E.tan a~.|*4 x 
80?r p 8 
3r 2 
T' 
— E. tana. 
27 l 4 2 
80? r r 3 WJ5 
~¥~ 
- — E. tan a. 
27 
80 7T 
l l 48 
r 3 25 ^5 
