THE ELECTEIC AHD LUMINIFEROUS MEDIUM. 
229 
Now change the time variable from t to t', equal to t — vxjd^, so that 
didx + vj&. djdt becomes djdx, and djdt becomes djdt', and these equations assume 
the form of an electric scheme for a crystalline medium at rest. Finally write x^ for 
xe, for for/'e“q dt^ for df:'e~% keeping the other variables unchanged, and 
the system comes back to its original isotropic form for free tether. Thus the final 
variables g^, /q) and {a^, h^, c^) will represent the aethereal field for a correlative 
system of electrons forming the molecules of another material system at rest in the 
aether, of the form of the original one pulled out uniformly in the ratio e" along its 
direction of movement; the electric disjDlacements through corresponding areas 
in the two systems ai'e not equal, but their molecules are composed of equal electrons 
and are situated at corresponding points, and the individual electrons describe corre¬ 
sponding parts of their orbits in times shorter for the latter system in the i-atio 
or (1 — while those less advanced in the direction of v are also relatively 
very slightly further on in their orbits on account of the difierence of time-reckonino’. 
o 
Thus we have here two correlative systems each governed by the circuital relations 
of the free eether : (i) a system in which the electric and magnetic displacements are 
{f> 9’ ^^^cl (a, h, c), moving steadily with uniform velocity v parallel to the axis 
of X, (ii) the same system expanded in the direction of a; in the ratio and at rest, the 
displacements at the corresponding points being (e~y, g — vclind, h -fi vh/inQ^) and 
(e~%, h — AttvIi, c + Airvg), and the molecules being situated in the corresponding 
positions with due regard to the varying time-origin. Inasmuch as the circuital 
relations form a difibrential scheme of the first order which determines step by steji 
the subsequent stages of a system when its initial state is given, it follows that if 
these two rethereal systems are set free at any instant in corresponding states, 
they will be in corresponding states at each subsequent instant, their electrons or 
singularities being at corresponding points. If then the latter collocation represent 
a fixed solid body, the former will represent the same body in uniform motion ; one 
consequence of the motion thus being that the body is shrunk in the direction of its 
velocity v in the ratio e““ or 1 — It may be observed that there is here no 
question of verifying that the mechanical forces acting on the single electrons in the 
two cases are such as to maintain this correspondence ; for in the present complete 
survey of the individual atoms there is no such entity as mechanical force, any more 
than there is on a fi’ee vortex ring in fluid; the notion of mechanical forces enters at 
a subsequent stage when we are treating of molecular aggregates considered as con¬ 
tinuous bodies, and are examining the relations between the different groups into 
which our senses analyze their Interactions (§ 48). 
If this argument is valid, it will confirm the hyjDothesis of FitzGerald and 
Lorentz, to which they were led as the ultimate resource for the explanation of the 
negative result of Michelson’s optical experiments; and conversely it will involve 
evidence that the constitution of a molecule is wholly electric, as here represented. 
