THEORY OF ELECTROMAGNETISM. 
735 
Rowland and Mr. Hutchinson describe the experiments by which they have proved 
that a moving charged body acts on surrounding bodies as it should on the convection 
current theory. Now, this can be shown accurately to follow from equation (23) if 
we make the double assumption (I) that the medium in contact with the moving 
conductor is at rest, and (2) that the slipping which thus takes place may be regarded 
as the limit of a rapid shear ; and approximately to follow without the assumption. 
First, then, assume there is no slipping. Let the motion be steady. If the moving 
dielectric be itself charged, we see by the term — p'SV'd' in c' that the effect of its 
motion is to cause the current due on the convection current theory to its charge. Since 
the motion is steady, dd'/dt — 0. To take account of the remaining term VV'Vd'p' of c', 
consider the current through a strip of surface constructed thus :—Take an elementary 
line PQ in the surface of the conductor. Through all points of PQ draw the lines of 
electrostatic induction (lines at every point of which the tangent is parallel to d'). 
Bound the strip of surface thus obtained at any distance from PQ by another element 
pq. In fig. 1 the arrows indicate (l) the direction of motion of the conductor, (2) the 
Fig. 1. 
positive direction (PQqy>) round the strip when the positive direction through it is 
that of the motion at PQ. The current through PQgy? = — jjSc'c/2' taken over the 
strip. The part contributed to this by the term YVYd'p of c is 
by equation (3), § 5. The parts contributed to the line integral by the lines of 
induction pV, Qq are zero. Hence the current through the strip 
= - SFQd>' + S pqXp 
where PQ, pq stand as usual for the vectors PQ, pq. The first of these terms is the 
rate of flow in the direction of motion of electrostatic charge through the element 
