312 C. Abbe on the Repsold Portable Circle. 
in which we have put 
36008 
sr i idereal ti =——_— 
g=hourly gain on sidereal time, _/f- 3600-49" 
C08 P cos 0 aba 
soaaaia yaa y=cot i. 
= f28=[6-25961] £28, 
= plgcer)=[9-0225] PG). 
ce. For the computation of the hour angle from the observed 
zenith distances in the prime vertical, we have the simple formula 
pc Vad lp beeeree Oe -—); 
ie} ae ay cos 6 ( cost} 
cosz 
the computation of which is sufficiently expeditious even with 
six-figure logarithms, if we are provided with the tables pre- 
viously mentioned. ‘The second approximation, using a correct 
zenith point, is made if necessary as before, by using the tabu- 
lar first differences. 
As the formula (A) shows the flexure of the tube to be not 
symmetrical with respect to the zenith, it is necessary for greater 
accuracy to correct the results given by each star of a pair, ac- 
cording to the formula 
J=6 sin(z+-B). 
The correction, f, is directly applicable to the zenith distances 
observed for latitude. 
For the time determination we have the differential formula 
pete sin Zz , 
(P) ~ ~~15 cos@ cose sin t * 
The application of these corrections is, especially for the lati- 
tude, necessary in order to entirely free the result from a pair 0 
Opponts stars from the influence of flexure. 
o the preceding sketch of the instrument and its formule 
may be added a few words as to the conduct of the field work, 
which may be carried on without inconvenience at a tempera 
ture of 15° or 20° Fahrenheit 
against — changes of temperature and disturbing jars. One 
or two 2 
eters .of Brauer’s construction haye been found to endure surpris- 
