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Transformation of the fundamental equations.
§ 19. From now on it will be assumed that the bodies to be considered are moving at a steady velocity of translation $$\mathfrak{p}$$, under which we will have to understand in almost all applications, the speed of the earth in its motion around the sun. It would be interesting at first to further develop the theory for stationary bodies, but for brevity's sake let us immediately turn to the more general case. Besides, it may be still set $$\mathfrak{p}=0$$.

The treatment of the problems that are now coming into play is most simple, when instead of the co-ordinate system used above, we introduce another one which is rigidly connected with ponderable matter and therefore shares its displacement.

While the coordinates of a point with respect to the fixed system were called x, y, z, let those, which refer to the moving system and which I call the relative coordinates, denoted by (x), (y), (z) for the time being. Until now, all the variable parameters were seen as functions of x, y, z, t; furthermore $$\mathfrak{d}_{x}$$, $$\mathfrak{d}_{y}$$, etc. shall be seen as functions of (x) (y), (z) and t.

Under a fixed point, we now understand one point,