Page 139 of 212

These last form the basis for the derivation of deductions from

the special theory of relativity, and in themselves they are

nothing more than the expression of the universal validity of the

law of transmission of light for all Galileian systems of

reference.

Minkowski found that the Lorentz transformations satisfy the

following simple conditions. Let us consider two neighbouring

events, the relative position of which in the four-dimensional

continuum is given with respect to a Galileian reference-body K

by the space co-ordinate differences dx, dy, dz and the

time-difference dt. With reference to a second Galileian system

we shall suppose that the corresponding differences for these two

events are dx′, dy′, dz′, dt′. Then these magnitudes always

fulfill the condition.[21]