which perform this transition to another system, must not alter the analytical expression for the physical law under consideration.
This leads us to set up a principle of relativity which will be called the general principle of relativity in the sequel. It demands the invariance of physical laws with respect to arbitrary continuous substitutions of the four variables. Moreover, the line-element that occurs in it must preserve its form when subjected to any arbitrary transformations whatsoever. This condition is fully satisfied by the line-element
in which no restrictive reservations of any description are made as to what the co-ordinates
,
,
are to signify. The Euclidean line-element