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We can state this general principle of relativity in still

another form, which renders it yet more clearly intelligible than

it is when in the form of the natural extension of the special

principle of relativity. According to the special theory of

relativity, the equations which express the general laws of

nature pass over into equations of the same form when, by making

use of the Lorentz transformation, we replace the space-time

variables x, y, z, t, of a (Galileian) reference-body K by the

space-time variables _x′, y′, z′, t′, of a new reference-body

K′_. According to the general theory of relativity, on the other

hand, by application of _arbitrary substitutions of the Gauss

variables x1, x2, x3, x_4, the equations must pass over into

equations of the same form; for every transformation (not only

the Lorentz transformation) corresponds to the transition of one

Gauss co-ordinate system into another.