THE EARTH’S MAGNETIC FIELD IN INTERNATIONAL UNITS. 
433 
constant, and C the current, then the axial component of the field at a point at a 
distance y from the centre, and at right angles to the axis is given by 
277 NC _p 2o>) 
+ ^ (4.x^ — a^) y® — ^ (8a;‘^ — 12xV + c&) y® 
— (See® — 136a;%^ + 159a;^a^‘ — 12a®) ?/ 
1 
+ -, ,, (Srr'^ — 12xW + a"^) y^ + etc- 1 > 
where + x^. 
Substituting in this expression the values for the various dimensions of the coils 
used in the experiments, we get 
27rNC {0'023653 — Q-Q^ 5 + O'Oe 11?/ - O'O^ 12/}. 
If we consider a point at a distance from the centre of the coils, in a direction at 
right angles to the axis, corresj^onding to the position of the pole of the longest 
magnet employed, which had a length of 6 centims., so that the distance between 
the poles was about 6 X f, or 4 centims., we get, putting y = 2, that the field at 
this jDoint is 
277 NC {0*023653 — O-O^ 5 + O'Oe 44 - 0*Oo 2}. 
It will he seen that for the purposes of this investigation we need on/ consider the 
first term, the field at the position occupied by the magnet being practically unifbini, 
so that the coil constant is given by the equation 
p 27rNfd 
~ (fd + a;2)5 ■ 
Differentiating this expression, we get 
rfF 2?;- — «“ da ox~ d.v 
F or + a fd + X ’ 
or for a = 30 centims., and for a; =15 centims.. 
dF 
F 
— 0*4 — 
a 
0*6 
dx 
Thus, if F is to he known to within one part in 10,000, we ought to know a and 
X each to within about 1 part in 10,000. That is the mean radius of the coils and 
the distance between their mean planes must each be known to within 0*003 centim. ; 
for a and 2a: are each 30 centimetres. 
3 K 
VOL. CXCVIII,—A. 
