10 
MR. J. E. H. GORDON ON THE DETERMINATION OE 
through both, till there was no action on a small magnet suspended at a point O in a 
vertical plane perpendicular to and bisecting the common axis of the dynamometer and 
helix. Professor Maxwell found that when from O to centre was so great that the 
diameters of the coils could be neglected in comparison, the currents producing equili- 
brium had the ratio 
1 : 11-23. 
From these data another value of the area was calculated. In both cases the follow- 
ing reasoning was used : — 
Calculation of £(A), the sum of the areas of the windings of the Helix. 
We proceed as follows : — 
(1) We first obtain an expression for the force exerted at a point by one winding, 
at a certain distance and of a certain area, carrying a unit current. 
(2) We then, by calculation, find what the action of a certain standard coil of known 
area would be with a unit current. 
(3) We then, by experiment, find what that action is with a certain arbitrary cur- 
rent whose ratio to a second current is known. 
(4) We then, by experiment, find what the action of the helix is with this second 
current, adjusting the ratios till the actions are equal. 
(5) This eliminates the variations of the current, and enables us, by means of 
expression (1), to compare the areas acting in (3) and (4) ; one of these being 
known, we can obtain the other. 
To find an expression for the force exercised by a circular current in a given 
direction at a point, we must first find the potential at that point, and then differentiate 
along the given direction. 
For a winding carrying a current of strength i we may substitute a magnetic shell 
hounded by the winding and of strength i. But by Maxwell’s ‘ Electricity ’ (Art. 409), 
the potential at any point due to a magnetic shell is 
( 6 ) 
where $ is the strength of the shell and a the solid angle subtended by it at the point. 
We have therefore to find an expression for a. 
Now in Arts. 670 and 694 we find 
* = ( 7 ) 
for when unity, V=a», where radius of winding (which in this experimental case 
becomes a great circle) =c. r is the distance from the centre of the circle to -the point 
where the potential is to be found, and P the potential of a stratum of matter of surface 
