ii6 
PHYSICS: L. PAGE 
Proc. N. a. S. 
The electrodynamic equations are five in number : four of these specify 
the electric and magnetic fields in terms of the distribution of charge and 
current throughout space, and the fifth specifies the force on charged matter 
due to the strength of the electric and magnetic fields in which it is moving. 
First will be taken up the kinematical interpretation of the two equations 
— Coulomb's law and Ampere's law — which do not involve the space tirrie 
transformations, and hence are not dependent on the principle of relativity. 
In the representation to be employed, each charged particle e is to be 
considered as a source of moving elements projected outward uniformly 
in all directions with the velocity of light c. A line of force is a curve 
drawn through the moving elements which have been projected in a given 
direction. Perhaps a better picture of the method by which the field 
is produced may be obtained by imagining a very large number of guns 
to be stationed at e, pointing outward in all directions. Suppose each 
gun to be provided with a long, perfectly elastic cord on which shot are 
strung. Let these shot be fired from the gun at regular but very short 
intervals with the velocity of light. Then the shot constitute the moving 
elements emanating from the charge, and the elastic cord connecting them 
marks the line of force diverging in the particular direction under con- 
sideration. 
The number of lines of force diverging from a charge de will be supposed 
to be very large, no matter how small de may be. For convenience in 
making numerical calculations, these lines will be grouped into bundles 
or tubes of M lines each, where M is a large number so chosen as to make 
the number of tubes diverging from any charge equal numerically to the 
magnitude of the charge. This convention is tantamount to measuring 
electric charges in Heaviside-Lorentz rational units. 
If the electric intensity E is defined as the number dN of tubes per unit 
cross section, the component of the intensity normal to the small vSurface 
dcF is 
According to Gauss' theorem, the average divergence of E over a small 
volume dr surrounded by the closed surface cr is given by 
V-Et/r = \^'d(T 
Now the part of this sum due to charges outside the region dr vanishes, 
while the part due to the charge de inside this region is equal to de itself. 
Hence, if p is the density of charge at the point in question. 
dN 
a 
V-E = p. 
(1) 
This is Coulomb's law. 
