86 TRANSACTIONS OF THE [MAR. 2, 



ON THE CALCULATION OF STAR-PLACES FOR ZENITH TELESCOPE 



OBSERVATIONS. 



BY HAROLD JACOBY. 



(Abstract.) 



Ill determining the latitude from zenith telescope observations 

 it is not necessary to compute the *' reduction from mean to 

 apparent place '' of every star observed. For 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^, d^, be the right ascension and declination of the Southern 



Star, 

 a„, 6„, the same quantities for the Northern Star, 

 and put: 



t = i (a^ - «i) C = i (-52 — 5i) 

 a,, = I (as 4- ^i) 5o = 5 {Si + 8i) 



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: ' 



Jq) = ix + t).iq + g cos ((r + rto) cos t + limo cos (iJ + ao + M) cos ? 

 k = cot q) tan ? 

 X = cos q) cos C 

 m» = sin (5ocos t 



Jc, X, and ?»„ are auxiliary quantities, having constant values for 

 any particular pair of stars. The other letters have their usual 

 significance (see American Ephemeris), and //, is the mean of the 

 proper motions of the two stars in declination. 



In applying this method it will be expedient to tabulate x, h, 

 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: 



^ See also a paper by Prof. T. H. Saflford, Pro. Am, Ac. Arts and 

 Sciences, 1875, Vol. XL, p. 167. 



' For a demonstration of these formulae, see Astronomical Journal, 

 No. 238. -. 



