1895. | NEW YORK ACADEMY OF SCIENCES. 69 
ceptional, and, so far as at present known, every catalogue of 
worth, as well as observations forwarded by various astronomers 
in manuscript have been utilized. A total of 13,762 observa- 
tions have been found, of which 543 were given zero weight, 
leaving an available average of 236 per star. These were taken 
from 134 separate catalogues or lists and 157 additional annual 
volumes, original records, etc., the average number of catalogues 
in which each star was found being 25. Since a determination 
of proper motion was in view, it was necessary to know the mean 
data of observation of the declination for any given catalogue; 
in order that a correction might be applied for the erroneous 
proper motion assumed by the observer in the reduction of the 
position at the time of observation to the epoch of the catalogue. 
Modern catalogues give this data, but for the earlier ones, 
Piazzi, Lalande, Taylor, Pond, Abo, and others, it had to be de- 
duced from the original record of the observations, by a careful 
search through all the many pages of records to find each par- 
ticular observation. 
A somewhat similar process was followed in the case of the 
declinations for all the volumes of annual results not yet re- 
duced to a determinate catalogue, the process followed being to 
find all the observations, then to reduce each one separately to 
the epoch 1875.0 and finally take the mean of all by weight pro- 
portional to the number of observations and regard this as a 
single determination of declination ; thus what will be printed 
in the final paper as one line was often the work of weeks of re- 
search and computation. Again, it was often necessary to re- 
duce in this manner (or otherwise by the aid of such tables as 
von Asten’s for Lalande, or Luther’s for Weisse-Bessel), even 
observations which have been already presented in catalogue 
form—this being the case on account of the inaccuracy of the 
catalogue-computers, or of the constants assumed in the re- 
duction. After all catalogues had been -reduced to the com- 
mon epoch 1875.0 and corrected for erroneous proper mo- 
tion, a further correction was applied to all to make each de- 
clination conform toa standard system of reduction (in this 
case to the Astronomische Gesellsschaft System of Auwers? 
