to K are given ? The relations must be so chosen that the law of the
transmission of light in vacuo is satisfied for one and the same ray
of light (and of course for every ray) with respect to K and K1. For
the relative orientation in space of the co-ordinate systems indicated
in the diagram ([7]Fig. 2), this problem is solved by means of the
equations :

eq. 1: file eq01.gif

y1 = y
z1 = z

eq. 2: file eq02.gif

This system of equations is known as the " Lorentz transformation." *

If in place of the law of transmission of light we had taken as our
basis the tacit assumptions of the older mechanics as to the absolute
character of times and lengths, then instead of the above we should
have obtained the following equations:

x1 = x - vt
y1 = y
z1 = z
t1 = t

This system of equations is often termed the " Galilei
transformation." The Galilei transformation can be obtained from the
Lorentz transformation by substituting an infinitely large value for
the velocity of light c in the latter transformation.