I20 
PHYSICS: L. PAGE 
Proc. N. a. S. 
system. If the dynamical equation for a charge e situated in the moving 
system is assumed to be 
dt' 
as measured in the units of this system, the relativity transformations give 
in the stationary system. This is the fifth and last of the electromagnetic 
equations. If the relativity transformations had not been made use of 
in deriving it, the term involving the magnetic intensity would have been 
absent But this term is the one that accounts for the current induced 
c 
FIG. 4 
in a wire moving through a steady magnetic field, and for the torque in 
a coil carrying a current which is placed in such a field. Therefore, the 
action of every generator and every motor used by industry in this age of 
electricity is incontrovertible evidence of the truth of the principle of 
relativity. 
In deriving expression (3) for the electric intensity due to a point charge, 
it has been tacitly assumed that the field does not rotate. If the sources 
of moving elements constituting the charge — the guns in the analogy 
previously used — are supposed to rotate with angular velocity co, the rate 
of change of c at the time r/c becomes 
^ = _L [(f X c) X c + {(co X c) X c} X c], 
dt 
for a charge which* is at rest relative to the observer at the time zero. 
This introduces into the expression (3) for E the additional term 
— I- {(co X c) X c} X c|, 
47rrV ) 
and E and H for a moving charge become 
