6 MR. rumker's observations 



With these latitudes should be classed the 



This shows that the zenith distances have been observed too small ; and the 

 solstice moreover seems to indicate that the error increases with the zenith 

 distance. Without investigating the cause of this error, we may suppose 

 equal zenith distances on either side of the zenith equally influenced by it. 

 Calling therefore 5 and z the declination and observed zenith distance of the 

 northern, and B' and z' those of the southern star in his superior culmination, 

 and X the correction of the zenith distance, we have, if both stars have south 

 declination (in general if latitude and declination are of the same name) 



» + a^ + S = latitude 



and y — z* — x=. latitude 

 whence ''^ ~^ 



+ — ;:i — = latitude. 



2 ' 2 

 And thus the error x of the instrument is eliminated. 



• The solstices of 1821 and 1822 v^ere observed by Sir Thomas Brisbane and myself conjointly ; 

 those in 1823, by Sir Thomas Brisbane ; and the remainder by myself alone. 



