ADAMS— THE EINSTEIN THEORY. 181 



time except at a definite position in space. It was Minkowski who 

 first clearly stated that to define an event four generalized co- 

 ordinates are needed — three to define its place in space and one to 

 define its time. The universe thus becomes, in Riemann's sense, 

 a four-dimensional continuum. 



The expression for the square of the line element in this gen- 

 eralized space is a quadratic differential form with ten terms. The 

 coefficients in this expression determine the departure of this gen- 

 eralized space from Euclidean space. In order to satisfy the con- 

 dition for the complete relativity of physical phenomena it is neces- 

 sary that this line element shall have the same value in whatever 

 system of coordinates it is measured. Now in Einstein's theory 

 these coefficients have more than a purely geometrical significance. 

 They have a dynamical meaning in that they determine the gravita- 

 tional field. Or to put it in another way, the curvature of space 

 is determined by the presence of matter. At a great distance from 

 all matter this four-dimensional space is Euclidean. The presence 

 of matter gives to space its curvature. We can now see how, for 

 gravitational forces, the goal of the Hertzian mechanics is attained, 

 although in a wholly different way from that contemplated by Hertz. 

 Gravitational forces, according to Einstein, do not exist. Hertz's 

 law of the straightest path has universal validity in this system, 

 but the straightest path may appear to be a curved path because 

 it must be drawn in space which is curved. In the two-dimensional 

 analogue the straightest path between two points on a curved sur- 

 face is not the straight line connecting the two points, for that 

 line would take us out of our space. The straightest path is the 

 geodesic drawn on the surface between the two points. And so 

 light rays passing close to the sun are not attracted by the sun, but 

 the space through which they pass being curved under the influence 

 of the mass of the sun, the rays follow a curved path in reaching 

 the earth. 



Now any theory of this kind to be at all complete cannot stop 

 with explaining away gravitational forces. Electric and magnetic 

 forces, which we have seen differ in their nature from gravitational 

 forces, must also be considered. I can only mention a remarkable 



PROC. AMER. PHIL. SOC, VOL. LIX, L, JULY 23, 192O. 



