﻿FkzGerald Loreniz Contraction. 87 



formulated " as that of the determination of the natural 

 sequence of changes in the configuration of the system." In 

 § 51, and in Chapter x. of e iEther and Matter/ the general 

 outline of the method is sketched. The essential point is, 

 that a complete basis for the explanation of all the pheno- 

 mena involved is to be found in the electromagnetic equa- 

 tions, which give the time rates of change of the setherial 

 displacement /, g, A, and the magnetic induction a, b, c, in 

 equations of the type 



. B/"_ck ~db sK ,m-ic^_d/i "dg n , 



*t By d^' v ; 3* ^ B: yj 



where C is the velocity of light. 



The electron is a singular point in the aether, near which 

 the setherial displacement increases indefinitely. The past, 

 present, and subsequent history of the electrons in a piece 

 of matter, and indeed of the whole universe, are completely 

 determined when we have /, g, h and a, b, c given as 

 functions of #, y, z and t, satisfying the electromagnetic 

 equations ; indeed, it is sufficient to know the values of 

 /, g, h, and of the special derivatives of/, g, h, a, b, c, at ono 

 instant, to determine the whole history of the svstem. The 

 equations implicitly involve the condition that, if 



w + a? + ^ h 



B^ "dy B~ 



is zero at any point and time, it shall be for ever zero at that 

 point, so that it is necessary to postulate that the equations 

 need not hold at a singularity, as otherwise we should restrict 

 our electrons to remain permanently at rest. The electrons 

 are then the places where 



B/* , ~dg , BA 

 'dx ~dy ~dz 



is not zero, this being in fact the analytical criterion for 

 finding their motions. 



As an example, suppose that we were given/, g } h, a, b, c, 

 as functions of the form 



m/; * *)= b{x _^+ f+z >fi> { <*-*>' y> z - } 



0, b. c) = t-7 { ^—« ^ (o. -re, rv. \ 



where e ' — 1— . ,-., . 



