of them is instructive in more ways than one. Adopting, the additional
computative burden imposed by it notwithstanding, Schonfeld's
modification of Airy's formulæ, he introduced into his equations a
fifth unknown quantity expressive of a possible stellar drift in
galactic longitude. A negative result was obtained. No symptom came to
light of "rotation" in the plane of the Milky Way.

M. Stumpe's intrepid industry was further shown in disregard of
customary "scamping" subterfuges. Expedients for abbreviation vainly
spread their allurements; every one of his 2,108 equations was
separately and resolutely solved. A more important innovation was his
substitution of proper motion for magnitude as a criterion of
remoteness. Dividing his stars on this principle into four groups, he
obtained an apex for the sun's translation corresponding to each as
follows:

Number of Proper motion. Apex.
Group included stars. " " ° °
I. 551 0.16 to 0.32 R.A. 287.4 Decl. +42.
II. 340 0.32 to 0.64 " 279.7 " 40.5
III. 105 0.64 to 1.28 " 287.9 " 32.1
IV. 58 1.28 and upward " 285.2 " 30.4

Here again we find a marked and progressive descent of the apex toward
the equator with the increasing swiftness of the objects serving for
its determination, leading to the suspicion that the most northerly
may be the most genuine position, because the one least affected by
stellar individualities of movement.

By nearly all recent investigations, moreover, the solar _point de