86 TRANSACTIONS OF THE [MAR. 2, 
ON THE CALCULATION OF STAR-PLACES FOR ZENITH TELESCOPE 
OBSERVATIONS. 
BY HAROLD JACOBY. 
(Abstract. ) 
In determining the latitude from zenith telescope observations 
it is not necessary to compute the ‘‘reduction from mean to 
apparent place” of every stamobserved. or the stars are ob- 
served in pairs; and to obtain the latitude we need to know 
the mean of the apparent declinations of the two stars of any 
pair. It follows, therefore, that we only require the mean of 
the corresponding reductions for the two stars.‘ This mean 
can be arrived at by a single computation, which may be effected 
nearly as quickly as the reduction of either star could be sepa- 
rately computed. 
Let 
a,, 0,, be the right ascension and declination of the Southern 
Star, 
a,, 0,, the same quantities for the Northern Star, 
and put: | 
t 
ay 
4(Q@2 — &) aS 
4 (Q2 + a) Ooo= 
The correction which must be added to the latitude, computed 
simply with the mean declinations for the beginning of the year,. 
is then given by the following equations: ° 
Ag = ix + Thy + g cos (G + a) cos f+ hm cos (H+ a. + kt) cos f 
k =cotgtan€ 
oe) COSI COS) G 
Me = sin 6,Ccos ft 
k, x, and m, are auxiliary quantities, having constant values for 
any particular pair of stars. The other letters have their usual 
significance (see American Hphemeris), and 4, is the mean of the 
proper motions of the two stars in declination. 
In applying this method it will be expedient to tabulate a, &,. 
and log m, (which are always positive) for the latitude of the ob 
serving station. The formation of such a table requires but a 
very few minutes, as will be seen from the following example: 
1 See also a paper by Prof. T. H. Safford, Pro. Am. Ac. Arts and 
Sciences, 1875, Vol. XI., p. 167. 
2 For a demonstration of these formule, see Astronomical Journal, 
No. 288. 
