e cube of four,
and so on.

Beyond this no measures of parallax yet made will give us much
assistance. We can only infer that probably the same law holds for a
large number of spheres, though it is quite certain that it does not
hold indefinitely. For more light on the subject we must have recourse
to the proper motions. The latest words of astronomy on this subject
may be briefly summarized. As a rule, no star is at rest. Each is
moving through space with a speed which differs greatly with different
stars, but is nearly always swift, indeed, when measured by any
standard to which we are accustomed. Slow and halting, indeed, is that
star which does not make more than a mile a second. With two or three
exceptions, where the attraction of a companion comes in, the motion of
every star, so far as yet determined, takes place in a straight line.
In its outward motion the flying body deviates neither to the right nor
left. It is safe to say that, if any deviation is to take place,
thousands of years will be required for our terrestrial observers to
recognize it.

Rapid as the course of these objects is, the distances which we have
described are such that, in the great majority of cases, all the
observations yet made on the positions of the stars fail to show any
well-established motion. It is only in the case of the nearer of these
objects that we can expect any motion to be perceptible during the
period, in no case exceeding one hundred and fifty years, through which
accurate observations extend. The efforts of all the observatories
which engage in such work are, up to the present time, unequal to the
task of grappling with the motions of all the stars that can be seen
with the instruments, and reaching a decision as to the proper motion
in each particular case. As the question now stands, the aim of the
astronomer is to determine what stars have proper motions large enough
to be well established. To make our statement on this subject clear, it
must be understood that by this term the astronomer does not mean the
speed of a star in space, but its angular motion as he observes it on
the celestial sphere. A star moving forward with a given speed will
have a greater proper motion according as it is nearer to us. To avoid
all ambiguity, we shall use the term "speed" to express the velocity in
miles per second with which such a body moves through space, and the
term "proper motion" to express the apparent angular motion which t