sphere of three or four thousand stars is a task practicable only
under certain conditions. To begin with, the proper motions
investigated must be established with _general_ exactitude. The errors
inevitably affecting them must be such as pretty nearly, in the total
upshot, to neutralize one another. For should they run mainly in one
direction, the result will be falsified in a degree enormously
disproportionate to their magnitude. The adoption, for instance, of
system of declinations as much as 1" of arc astray might displace to
the extent of 10° north or south the point fixed upon as the apex of
the sun's way (see L. Boss _Astr. Jour._, No. 213). Risks on this
score, however, will become less formidable with the further advance
of practical astronomy along a track definable as an asymptote of
ideal perfection.

Besides this obstacle to be overcome, there is another which it will
soon be possible to evade. Hitherto, inquiries into the solar movement
have been hampered by the necessity for preliminary assumptions of
some kind as to the relative distances of classes of stars. But all
such assumptions, especially when applied to selected lists, are
highly insecure; and any fabric reared upon them must be considered to
stand upon treacherous ground. The spectrographic method, however,
here fortunately comes into play. "Proper motions" are only angular
velocities. They tell nothing as to the value of the perspective
element they may be supposed to include, or as to the real rate of
going of the bodies they are attributed to, until the size of the
sphere upon which they are measured has been otherwise ascertained.
But the displacement of lines in stellar spectra give directly the
actual velocities relative to the earth of the observed stars. The
question of their distances is, therefore, at once eliminated. Now the
radial component of stellar motion is mixed up, precisely in the same