﻿deduced from the Electrical Theory of Matter. 65 



points of interest have been brought to light in the exami- 

 nation of the question, one of the most curious of which is 

 the conception of local time. These ideas originally found 

 their basis in the fact that the electromagnetic equations when 

 transformed to a system of moving axes, reverted to the type 

 for a system at rest. The reasoning is somewhat of an 

 abstract nature, and it seems desirable for deeper insight into 

 the matter, to deduce the contraction, together with the other 

 results associated with it, by a method which follows more 

 closely our ordinary concrete methods of reasoning. It is 

 with this object that the present paper has been written. 



On the electromagnetic view, a piece of matter consists 

 entirely of an assemblage of positive and negative electrons, 

 in a state of stationary motion, and while the electrons may 

 be collected into groups and sub-groups which we call 

 molecules and atoms, they nevertheless as a whole form one 

 complete system. 



The resulting effects produced by imparting a uniform 

 translatory motion are most easily arrived at for the particular 

 kind of system in which all the electrons are at rest, when 

 the system as a whole is at rest, i. e. the electrons in the 

 system at rest are considered absolutely devoid of motion, but 

 difficulty here arises owing to the impossibility of such a 

 system being in equilibrium, unless constraints are applied at 

 the boundary ; we shall, however, consider this case first, and 

 shall overcome our scruples with regard to the equilibrium of 

 the system by stating the problem to be proved as follows. 



"If the electrons of a system are absolutely at rest, and 

 are in equilibrium, constraints being applied to the electrons 

 at the boundary to prevent the system from collapsing, then 

 when this system is set in motion parallel to the axis of x 

 with velocity v, it can again assume a state of equilibrium, if 

 suitable constraints are applied at the boundary, by shrinking 

 parallel to the axis of x so that the difference of the x 

 coordinates of any pair of electrons is reduced in the ratio 



0-5)'" 



Now it is a well-known fact that a point charge of strength 

 e when moving with velocity v parallel to the axis of x pro- 

 duces on unit charge at rest in the rcther, a force whose 

 components X, Y, Z are given by 



(X, Y, Z)=(X„, Y„ + r 7 , Z - t y3) 



where a, /3, 7 is the magnetic force due to the motion of the 

 Phil Mag, S, 6. Vol, 23. No. 13.°). Jan. 1912. F 



