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 the astronomer measures upon the
celestial sphere.

Up to the present time, two stars have been found whose proper
motions are so large that, if continued, the bodies would make a
complete circuit of the heavens in less than 200,000 years. One of
these would require about 160,000; the other about 180,000 years