ON ELECTRICAL THEORIES. 103 
Stefan’s Theory.' 
This resembles Ampére’s theory very closely, except that Stefan does 
not make the assumption that the force between two elements of current 
is along the line joining them: this difference leads to the introduction 
of two forces which Ampére neglects. 
We shall use the same notation as when we discussed Ampére’s 
theory, and consider, as before, the action of an element of current ds, 
on another element ds,. Stefan, like Ampere, assumes that we may 
replace an element of current by its component, so that we have to con- 
sider the action of the components (a, /3,) of ds, on the components 
(49, Bo, Y2) of ds). 
As in Ampére’s theory, the component a, is supposed to exert a force 
Aa) A 
v2 
on a», this force by symmetry must be along the line joining the 
elements. 
a, is supposed to exert a force on , equal to 
Ca Py 
ple 
along the axis of y. We can see that this force may exist, for it is 
conceivable that it should be in the same direction as }, when a, points 
from the middle of ds, to the middle of ds,, and in the opposite direction 
to , when «a, points in the opposite direction. Stefan assumes that a, 
exerts no force on (3, parallel to the axis of z, and no force at all on yp. 
{, is supposed to exert a force on ay parallel to the axis of y and 
equal to 
We may see, by the same reasoning as we used before for the force 
between /3, and a,, that it is conceivable that this force may exist. 3, is 
supposed to exert no force on a, parallel to the axis of z. 
As in Ampére’s theory, /3, is supposed to exert a force on /3, equal to 
2 1B a 
this force must by symmetry be along the line joining the elements; 3, 
is supposed to exert no force on yo. 
Thus the action of ds, on ds, consists of a force 
1 ae 
2 { Gad, + bP, \ 
along the line joining the elements, and a force 
fi 
ae { ca, 35 + dpyag \ 
at right angles to this line in the plane containing ds, and r. If we take 
1 Stefan, Wien. Sitzungsberichte, 59, p. 693, 1869, 
