with numbered subdivisions; only we now have to do, one might say,
with a good many imaginary measures in three common perpendicular
directions. In this "system of co-ordinates" the numbers that fix
the position of one or the other of the bodies may now be read off
at any moment.

This is the means which the astronomers and their mathematical
assistants have always used in dealing with the movement of the
heavenly bodies. At a determined moment the position of each body
is fixed by its three co-ordinates. If these are given, then one
knows also the common distances, as well as the angles formed by the
connecting lines, and the movement of a planet is to be known as soon
as one knows how its co-ordinates are changing from one moment to
the other. Thus the picture that one forms of the phenomena stands
there as if it were sketched on the canvas of the motionless ether.



EINSTEIN'S DEPARTURE

Since Einstein has cut loose from the ether, he lacks this canvas, and
therewith, at the first glance, also loses the possibility of fixing
the positions of the heavenly bodies and mathematically describing
their movement--i.e., by giving comparisons that define the positions
at every moment. How Einstein has overcome this difficulty may be
somewhat elucidated through a simple illustration.

On the surface of the earth the attraction of gravitation causes
all bodies to fall along vertical lines, and, indeed, when one omits
the resistance of the air, with an equally accelerated movement; the