early all recent investigations, moreover, the solar _point de
mire_ has been placed considerably further to the east and nearer to
the Milky Way than seemed admissible to their predecessors; so that
the constellation Lyra may now be said to have a stronger claim than
Hercules to include it; and the necessity has almost disappeared for
attributing to the solar orbit a high inclination to the medial
galactic plane.

From both the Albany and the Bonn discussions there emerged with
singular clearness a highly significant relation. The mean magnitudes
of the two groups into which Prof. Boss divided his 279 stars were
respectively 6.6 and 8.6, the corresponding mean proper motions 21".9
and 20".9. In other words, a set of stars on the whole six times
brighter than another set owned a scarcely larger sum total of
apparent displacement. And that this approximate equality of movement
really denoted approximate equality of mean distance was made manifest
by the further circumstance that the secular journey of the sun proved
to subtend nearly the same angle whichever of the groups was made the
standpoint for its survey. Indeed, the fainter collection actually
gave the larger angle (13".73 as against 12".39), and so far an
indication that the stars composing it were, on an average, nearer to
the earth than the much brighter ones considered apart.

A result similar in character was reached by M. Stumpe. Between the
mobility of his star groups, and the values derived from them for the
angular movement of the sun, the conformity proved so close as
materially to strengthen the inference that apparent movement measures
real distance. The mean brilliancy of his classified stars seemed, on
the contrary, quite independent of their mobility. Indeed, its changes
tended in an opposite direction. The mean magnitude of the slowest
group was 6.0, of the swiftest 6.5, of the intermediate pair 6.7 and
6.1. And these are not isolated facts. Comparisons of the same kind,
and leading to identical conclusions, were made by Prof. Eastman at
Washington in 1889 (Phil. Society Bulletin, vol. xii, p. 143;
Proceedings Amer. Association, 1889, p. 71).

What meaning can we attribute to them? Uncritically considered, they
seem to assert two things, one reasonable, the other palpably absurd.
The first--that the average angular velocity of the stars varies
inversely with their distance from ourselves--few will be disposed to
doubt; the second--that their ave