Page:DeSitterGravitation.djvu/9

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396
Prof. de Sitter, On the bearing of the Principle
LXXI. 5,

Similarly we have for the force acting on from ,

(15)

We will now introduce simultaneous coordinates. Let these be for time

and

In the equations of motion of , i.e. in the expression (14), we must use the coordinates and velocities of for the time defined by

and we have

In (15) we must use the coordinates and velocities of for the time defined by

and we have

Further, we have for use in (14)—

and in (15)—

The expression for is the same in both cases.

We find then,

(16)

This form of the equations is not unique. We can multiply by any power of , or make more complicated alterations, for which the reader is referred to Poincaré.

Multiplying by we get—

(17)