ding
out into infinity, and finally, points in space as they are obtained
by repeatedly shifting that level spot a distance of a meter in the
direction perpendicular to it. If, consequently, one of the points
is chosen as an "original point" we can, proceeding from that point,
reach any other point through three steps in the common perpendicular
directions in which the points are arranged. The figures showing how
many meters are comprized in each of the steps may serve to indicate
the place reached and to distinguish it from any other; these are, as
is said, the "co-ordinates" of these places, comparable, for example,
with the numbers on a map giving the longitude and latitude. Let
us imagine that each point has noted upon it the three numbers that
give its position, then we have something comparable with a measure
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
velocity increases in equal degrees in equal consecutive divisions of
time at a rate that in this country gives the velocity a