142 REPORT—1885. 
or with our notation 
[fee (w (@—f) +0 (y—n)+u'(@- )) de dy di 
74 
+ f[2*2e Ww @—8) +0! yn) +w (0) a, 
where w’, v’, w’ are the components of the current at the point ££; 
so that in addition to Ampére’s forces we have additional forces 
wherever P and = have finite values. From the above expressions we see 
that any element where P has a finite value exerts a repulsive force equal 
per unit of volame to 
eo 
—zicos8, 
, 
tending from the element; where r is the distance of the element from 
the point at which the force is reckoned, 7 the intensity of the current at 
this point, and 6 the angle between the direction of the current and r. 
Any element of surface where has a finite value exerts a repulsive 
force equal per unit of surface to 
Dt as 
— 2008 0, 
r 
where the notation is the same as before. Of course none of these forces 
exist in Maxwell’s theory. They could be most easily detected in cases 
where the part of the forces given by Ampére’s theory vanishes as it 
would for the case of an endless solenoid. In this case, though the 
Amperian forces vanish, the forces due to the discontinuity in the current 
do not, so that if the endless solenoid were to move under the action of 
external currents it would denote the existence of discontinuity in the 
current. An experiment of this kind has been made by Schiller; we 
shall discuss the results of it later. ; 
To sum up, the differences between the most general theory which 
takes into account the action of the dielectric, and Maxwell’s, are— 
1. The existence of a normal wave in the general theory, but not in 
Maxwell’s, 
2. The difference in the velocity of propagation of the transverse 
wave. 
3. The difference in the relation between electric currents and mag- 
netic force. 
4, The forces which arise from discontinuity in the currents. 
The Experimental Evidence as to the Truth of the various Theories. 
The theories we have considered may be divided into two great classes, 
according as they do or do not take into account the action of the dielec- 
tric surrounding the various conductors in the field. The first thing, 
therefore, that we have to do is to see whether experiment throws any 
light on this point. 
When a dielectric is in an electric field it experiences a change in its 
structure ; this is rendered evident by the alterations in its volume and 
elasticity observed by Quincke, by the change in its optical properties 
