into two sets—­one of 185 stars brighter, the other of 144 stars fainter than the eighth magnitude.  The first collection gave for the goal of solar translation a point about 4 deg. north of [alpha] Lyrae, in R.A. 280 deg., Decl. +43 deg.; the second, one some thirty-seven minutes of time to the west of [delta] Cygni, in R.A. 286 deg., Decl. +45 deg..  For a third and final solution, twenty-six stars moving 40"-100” were rejected, and the remaining 253 classed in a single series.  The upshot of their discussion was to shift the apex of movement to R.A. 289 deg., Decl. +51 deg..  So far as the difference from the previous pair of results is capable of interpretation, it would seem to imply a predominant set toward the northeast of the twenty-six swifter motions subsequently dismissed as prejudicial, but in truth the data employed were not accurate enough to warrant so definite an inference.  The Albany proper motions, as Prof.  Boss was careful to explain, depend for the most part upon the right ascensions of Bessel’s and Lalande’s zones, and are hence subject to large errors.  Their study must be regarded as suggestive rather than decisive.

A better quality and a larger quantity of material was disposed of by the latest and perhaps the most laborious investigator of this intricate problem.  M. Oscar Stumpe, of Bonn (Astr.  Nach., Nos. 2,999, 3,000), took his stars, to the number of 1,054, from various quarters, if chiefly from Auwers’ and Argelander’s lists, critically testing, however, the movement attributed to each of not less than 16” a century.  This he fixed as the limit of secure determination, unless for stars observed with exceptional constancy and care.  His discussion of them is instructive in more ways than one.  Adopting, the additional computative burden imposed by it notwithstanding, Schonfeld’s modification of Airy’s formulae, 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.       "      "               deg.               deg. 
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.