252 Prof. Challis on Theories of Magnetism 
called g being in this case insignificant. Now, whatever be the 
phases of the several component functions, the non-periodie part 
of the square of their sum is equal to the sum of the non-periodic 
parts of the squares of the separate functions. In the case of 
attractive action, according to the investigation given in the 
Mathematical Theory of Attractive Forces contained in the Phi- 
losophical Magazine for November 1859, the motion of trans- 
lation depends on the value of g, and on the product of W and 
d?W 
dt? * 
assigned, the non-periodic part of the product for the sum of 
the terms is the sum of the non-periodic parts of the products 
for the component terms taken separately, independently of 
their phases. In short, as we are only concerned with squares 
of circular functions, the mutual interferences by difference of 
phase do not come under consideration. On this account the 
dynamical effects of two series of undulations from separate 
sources, take place independently of each other, and combine 
according to the laws of the composition of accclerative forces. 
To the additional objection, that, ‘‘if the series of undulations be 
allowed to proceed, they diverge from each other without any 
mutual action,” I can make no reply, because I do not under- 
stand it. I can only conclude that it was written under some 
misapprehension. 
Professor Maxwell goes on to assert that “the mathematical 
laws of attractions are not analogous in any respect to those of 
undulations.” In making this assertion he must surely have 
overlooked the very remarkable analogies exhibited by the facts, 
that undulations, like central forces, diverge from a centre, and 
diminish in intensity according to some law of the distance. 
Each body in the universe on which a series of undulations is 
incident, becomes a centre of minor undulations, just as when 
waves on the surface of water encounter an insulated obstacle, 
the obstacle becomes a centre of subordinate waves. The con- 
tinuous generation of subordmate undulations corresponds to 
- the maintenance of the gravitating power of the body. 
Perhaps, however, the assertion, although it is not limited, 
was intended to apply only to such attractions as are observed 
in a magnetic field. If so, it is in accordance with my general 
theory, which makes a distinction between attractions and repul- 
sions by means of undulations, and attractions and repulsions due 
to currents. Electric, galvanic, and magnetic forces are of the 
latter kind. But, while it is admitted that the laws of these 
forces “have remarkable analogies with those of currents,” I 
should not say that they are analogous “to the laws of the con- 
duction of heat and electricity, and of elastic bodies,” because, 
But it is easily seen that if W have the form above 
