Today we call Eq. 6.8 the FitzGerald-Lorentz contraction up to second order in
v/c. In order to interpret this result, Lorentz assumed that molecular forces, like
electromagnetic forces, 'act by means of an intervention of the aether' and that a
contraction effect O(v^2 /c^2 ) cannot be excluded on any known experimental
grounds.
These conclusions agree in remarkable detail with FitzGerald's earlier pro-
posal: save the aether by its dynamic intervention on the action of molecular forces.
In 1892, Lorentz was still unaware of FitzGerald's earlier paper, however.
The fall of 1894. Lorentz writes to FitzGerald, telling him that he has learned
of the latter's hypothesis via an 1893 paper by Lodge, informing FitzGerald that
he had arrived at the same idea in his own paper of 1892, and asking him where
he has published his ideas so that he can refer to them [LI4]. A few days later,
FitzGerald replies: His paper was sent to Science, 'but I do not know if they ever
published it. ... I am pretty sure that your publication is prior to any of my
printed publications'(l) [F5]. He also expresses his delight at hearing that Lorentz
agrees with him, 'for I have been rather laughed at for my view over here.'
From that time on, Lorentz used practically every occasion to point out that he
and FitzGerald had independently arrived at the contraction idea. In his memoir
of 1895, he wrote of 'a hypothesis ... which has also been arrived at by Mr
FitzGerald, as I found out later' [LI5]. This paper also marks the beginning of
Lorentz's road toward the Lorentz transformations, our next subject.
In the paper of 1895, Lorentz proved the following 'theorem of corresponding
states.' Consider a distribution of nonmagnetic substances described in a coordi-
nate system x,t at rest relative to the aether. Denote by E, H, D, the electric,
magnetic, and electric displacement fields, respectively. D = E + P; P is the
electric polarization. Consider a second coordinate system x',t' moving with veloc-
ity v relative to the (x,t) system. Then to first order in v/c, there is a correspond-
ing state in the second system in which E', H', P' are the same functions of x',t'
as E, H, P are of x,t, where
124 RELATIVITY, THE SPECIAL THEORYIt consists in the supposition that the line joining two points of a solid body, if at
first parallel to the direction of the earth's motion, does not keep the same length
when it is subsequently turned through 90°' [L13]. If this length be / in the latter
position, then, Lorentz notes, Fresnel's aether hypothesis can be maintained if the
length in the former position /' were