's and their derivatives, can be developed (by means of algebraical and differential operations). This differential expression leads unambiguously, i.e. in only one possible way, to ten differential expressions in the
's. And now, in order to arrive at the required differential equations, Einstein puts these ten differential expressions proportional to the ten components of the stress-energy-tensor, regarding the latter ten as the quantities exciting the field. He inserts the gravitational constant as the constant of gravitation. These differential equations for the
's, together with the principle of motion given above, represent the fundamental laws of the new theory. To the first order they, in point of fact, lead to those forms of motion, with which Newton's theory has familiarized us (vide [Note 26]). More than this, without requiring the addition of any further hypothesis, they mathematically account for the only phenomenon in the theory of planetary motion which could not be explained on the Newtonian theory, viz. the occurrence of the remainder-term in the expression for the motion of Mercury's perihelion. Yet we must bear in mind that there is a certain arbitrariness in these hypotheses just as in that made for the fundamental law of motion. Only the careful elaboration of the new theory in all its consequences, and the experimental testing of it will decide whether the new laws have received their final forms.
Since the formulæ of the new theory are based upon a space-time-manifold, the line-element of which has the general form
all other physical laws, in order to bring the general theory of relativity to its logical conclusion, must receive (see p. 46) a form which, in agreement with the new measure-conditions, must be independent of the arbitrary choice of the four variables
