332 Prof. J. J. Thomson on 
the system consisting of the field and the material systems 
in it, form a self-contained system the momentum of which 
remains constant in magnitude and direction. If we take 
the view that the effects in the electromagnetic field are to be 
explained on dynamical principles by the agency of a medium 
filling the field, the conception of momentum in this medium 
is as essential and as fundamental as that of energy. As 
the consideration of the momentum in the field throws a 
good deal of light on electromagnetic phenomena, and leads 
in a simple way to some of the most important laws of 
electromagnetic action; I have thought that a discussion of 
the application of the method to some simple cases might be 
useful, and also help students to get a better grasp of the 
principle and the methods of its application. A few such 
cases have already been given in my ‘ Electricity and Matter.’ 
Some of these are repeated here for the sake of completeness. 
The basis of the method is the result (Phil. Mag. xxxi. 
p. 149, 1891; ‘ Recent Researches,’ p. 9) that in the electro- 
magnetic field, there is at any point, an amount of momentum 
equal per unit volume to wHD sin 0, where H is the magnetic 
force at the point, D the electric polarization (Maxwell’s 
Electric Displacement), « the magnetic permeability of the 
medium, @ the angle between the directions of H and D: the 
direction of the momentum is at right angles to H and D, 
drawn according to the scheme on fig. 1. 
Fig. 1. 
Thus P, Q, R the components of the momentum parallel to 
the axes x, y, < are given by the equations 
Q =p(yf —ah), 
R=p(ag—A/). 
ee 
