contraction when moving. He introduced new variables for the moving system defined by the following set of equations.
x^1 = β(x - ut), y^1 = y, z^1 = z, t^1 = β(t - (u/c^2)·x)
and for velocities, used
v_{x}^1 = β^2v_{x} + u, v_{y}^1 = βv_{y}, v_{z}^1 = βv_{z} and ρ^1 = ρ/β.
With the help of the above set of equations, which is known as the Lorentz transformation, he succeeded in showing how the Fitzgerald contraction results as a consequence of "fortuitous compensation of opposing effects." It should be observed that the Lorentz transformation is not identical with the Einstein transformation. The Einsteinian addition of velocities is quite different as also the expression for the "relative" density of electricity. It is true that the Maxwell-Lorentz field equations remain practically unchanged by the Lorentz transformation, but they are changed to some slight extent. One marked advantage of the Einstein transformation consists in the fact that the field equations of a moving system preserve exactly the same form as those of a stationary system. It should also be noted that the Fresnelian convection coefficient comes out in the theory of relativity as a direct consequence of Einstein's addition of velocities and is quite independent of any electrical theory of matter.
[P. C. M.]
Note 3.
See Lorentz, Theory of Electrons (English edition), § 181, page 213.
