LATITUDE OF THE SYDNEY OBSERVATOBY. 95 



latitude, providing the position, on the circle, of the line 

 passing through the zenith is known. In order that the 

 observations, above noted, could be used for this object, 

 the nadir was observed each evening. Two observations 

 were taken, one before and another after the evening's 

 work, a mean of the two was generally adopted in the reduc- 

 tions to find the zenith distances from the circle readings. 



The fundamental equations used in these papers are 



Sn = $ + On + O 



K = 4> - (z s + n) 



If we put z to denote the zenith distance corrected for 

 refraction, then 



in which 5 n K have the same significance as previously 

 adopted, namely the distance from the equator measured 

 along a great circle at right angles thereto, positive 

 towards the north. 



From the foregoing equation, values of the latitude were 

 deduced and combined in a manner to be shown. It will 

 be noted that the latitude obtained from this equation is 

 independent of the absolute value of the refractions. The 

 error of the difference of the computed refractions for each 

 zenith distance, as determined from tables, still remains, 

 but if the difference z n — z' a is small, the error in this con- 

 nection can be neglected. The accuracy of the latitude 

 determined in this way depends in a large degree on the 

 exactness of the adopted declination of the stars observed. 

 In this investigation, the data have been taken from 

 Newcomb's " Catalogue of Fundamental Stars for 1875 

 and 1900, reduced to an Absolute System" and are 

 adopted as definitive. 



