C. Abbe on the Repsold Portable Circle, 311 
these or similar special ones the observer loses no time in select- 
ing the pair of stars to be observed. The latitude stars are of 
course observed on the meridian as nearly as possible, excepting: 
the polars, which are observed at any hour angle. 
n the accurate computation of the results, the following form- 
ul are used by Mr. Déllen, following Struve’s habit of sepa- 
rately reducing each observation. 
a. For the polars, all observed zenith distances are reduced to 
the upper culmination. The formula (C) may be written 
2it 
(L) sin}(z—t)—=cos y cosd ae oy 
or approximately ; 
2cos cos : 
7 - f— i ci hp ce 214 
(J.) Fee ft bo een sin y sin$(z-+£) sin 24. YY 
where psig 8, 
cos =cos 2-+-2cos cos) sin? fi, 
using of course convenient tables for sin?4¢ and Zech’s tables 
for addition. vi 
- For other stars than the polars observed near the meridian, 
the direct computation of logr by means of the following series 
will be found convenient. We have from (C) 
cosgcosd , 
(K.) sin7r-+-2sin24r cot f= 2 . sin? 4t; 
whence 
2 1 cospeosd , _¢t 
L. os in 1’ —= r3 sin21”, &e,—2——__—___ sin? ~. 
(L.) aa cott sin 1”- g7> sin 1”, &e. rae z 
Regarding the second member as a first approximation to r, and 
developing the sin?4¢, we obtain the following, which is due to 
Mr. Dé len, 
) logr=log( pt?) ~ 9¢? 
