PROCEEDINGS. 
593 
Mr. H. Farquhar read a paper entitled Systematic Differ¬ 
ences of Proper Motions in Declination Catalogues. The follow¬ 
ing is an abstract: 
[Abstract.] 
The “ Fundamental-Catalog ” of the Berlin Jahrbuch (Astr. Gesellsch. 
Pubs. 14 and 17, Dr. A. Auwers) and that of the American Ephemeris 
(Report of Northern Boundary Commission, Appx. H, Prof. L. Boss) con¬ 
tain 303 stars in common. Boss gives, along with his proper motion in 
declination, an estimate of its probable error; and the probable error- 
square of the difference between his proper motion and Auwers’ is taken 
proportional to the square of this estimate plus a constant (e| + .000008), 
the differences being weighted accordingly from 1 to 4. The stars were 
first taken in zones between parallels 5° apart, then within limits of an 
hour of right ascension. The former only of these comparisons is shown 
in the table. Though the differences in order of right ascension show 
some uniformities of sign, they are not well satisfied by a formula in sine 
and cosine of a, while the smallness of the means and the wide range of 
the individual residuals throw doubt on their significance/ 
The first column of the table gives the declination, the next two the 
number of + and — residuals within the zone in the direction Boss- 
Auwers, the fourth the sum of the weights, as just explained; the fifth 
the mean difference of proper motion in declination in seconds per cen¬ 
tury ; the sixth the same difference, smoothed by taking five times the 
means of successive values. This is adopted as the systematic difference 
of the two catalogues in proper motion. It is so applied to the next 
column, five times the reduction of the Pulkowa ’45 to the Pulkowa ’65 
catalogue or the systematic difference between Auwers’ system of proper 
motions and those to be obtained from a comparison of these two, column 
8 giving the same difference for Boss. The uniformity of sign is signifi¬ 
cant. If this column, 8, were corrected by the rate of change of latitude, 
f 7/ per century, deduced from observations of Polaris at Pulkowa, but not 
included in the declinations, the residuals, except near the southern limit, 
would all become very small. Column 10 gives the systematic difference 
between the proper motions of Boss and those to be deduced from com¬ 
parison of six Greenwich catalogues, 1840 to 1872, all reduced to the same 
refractions. It is derived from the table of systematic corrections to each 
of these catalogues. Column 9 = No. 10 — 6 gives a similar difference for 
Auwers. Considering northern stars only, the closer agreement of the 
Boss system is noteworthy, but the effect of those south of the equator is 
materially to weaken the argument from these catalogues. Column 11 is 
from the Berliner Jahrbuch for 1884, and shows the systematic difference 
in declination between the Jahrbuch and the American Ephemeris for 
1883 as found by Dr. Auwers. No. 13 gives the difference of the funda¬ 
mental catalogues themselves (Epoch 1875) found by me in 1886 [see Bull. 
7G—Bull. Phil. Soc., Wash., Vol, 11. 
