PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 511 
Now if the current instead of being variable from the centre to the circumference of 
the section of the wire had been the same throughout, the value of F would have been 
F=T+ W (l-Q, 
where y is the current in the wire at any instant, and the total countercurrent would 
have been 
Hence 
ff 
IdF l 
-2 %rdr— 
§ 
a„.„_ K (T.-iy-! ( .|EO=— 
L'C 
!-> sa y- 
L=L'-fcfcZ, 
or the value of L which must be used in calculating the self-induction of a wire for 
variable currents is less than that which is deduced from the supposition of the current 
being constant throughout the section of the wire by +/+ where l is the length of the 
wire, and [Jj is the coefficient of magnetic induction for the substance of the wire. 
(116) The dimensions of the coil used by the Committee of the British Association 
in their experiments at King’s College in 1864 were as follows : — 
metre. 
Mean radius ....... =«=T58194 
Depth of each coil =§ = -01608 
Breadth of each coil .... = c = - 01841 
Distance between the coils . . . =-02010 
Number of windings .... ^=313 
Diameter of wire =-00126 
The value of L derived from the first term of the expression is 437440 metres. 
The correction depending on the radius not being infinitely great compared with the 
section of the coil as found from the second term is — 7345 metres. 
The correction depending on the diameter of the wire is 1 . 
. \ & . + -44997 
per unit oi length J 
Correction of eight neighbouring wires +-0236 
For sixteen wires next to these +-0008 
Correction for variation of current in different parts of section — -2500 
Total correction per unit of length -22437 
Length 311-236 metres. 
Sum of corrections of this kind 70 „ 
Final value of L by calculation 430165 „ 
This value of L was employed in reducing the observations, according to the method 
explained in the Report of the Committee*. The correction depending on L varies 
as the square of the velocity. The results of sixteen experiments to which this correc- 
tion had been applied, and in which the velocity varied from 100 revolutions in 
seventeen seconds to 100 in seventy-seven seconds, were compared by the method of 
* British Association Reports, 1863, p. 169. 
