GRAPHIC REDUCTION OF STAR PLACES.* 
BY 
Erasmus Darwin Preston. 
[Read before the Society January 4, 1896.] 
Introduction .—The reduction of stars from their mean 
places at the beginning of the }^ear, as given in the Catalogue, 
to their apparent places at any given time as found by ob¬ 
servation, forms a very considerable part of the astronomical 
calculations made in the Coast and Geodetic Survey Office. 
This work is especially heavy in the latitude computations, 
and the labor has been accentuated in recent years by the 
attention given to the subject of latitude variation. 
There are several ways of abridging the numerical calcu¬ 
lations, depending on the relation between the number of 
stars observed and the number of nights on which obser¬ 
vations are made. For example, if many stars are observed 
on two or three consecutive nights, differential formulae may 
be applied by means of which the position having been 
obtained on any one date, that on succeeding dates may be 
found in about one-third the time required to get the first 
one. This method is given in Appendix No. 13, Coast and 
Geodetic Survey Report for 1888. When, however, obser¬ 
vations are continued for a long time on the same stars, a 
condition that necessarily follows in researches on the varia¬ 
tions of latitude, the reductions can be very much facilitated 
by a method employed in Appendix No. 2, Report of Coast 
and Geodetic Survey for 1892. This method, which con- 
* Published by permission of the Superintendent of the United States 
Coast and Geodetic Survey. 
23—Bull. Phil. Soc., Wash., Vol. 13. 
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