Astronomical and Nautical Collections. 101 



Example II. 



January 1, 1825, in N. latitude, let the altitudes of Capellaand 

 Ursse Majoris, when on the same vertical, be respectively 70° 15' 

 and 11° 30', Required the latitude. 



O « // 



1. cosec. I = 0.063569 I =: 59 45 



1. cosin A = 9.528810 P = 44 11 20 



1. sin. J S+7= 9.971969 

 1. sin.^ S-|5= 9.750951 

 const, log. = 0.301030 

 N 413361 9.616329 



n. cos. P-Z 910403 A.S+p=69 38 7.5 



-N= 413361 J- . S-p=34 18 12.5 



Lat. = 29° 48' 13" 497042 = n. s. 



It is easy for a correct eye to determine when a line passing 

 through two stars is nearly perpendicular to the horizon ; and in 

 that part of the heavens towards the elevated pole, when this line 

 inclines a little to tlie right of the perpendicular, the stars will 

 shortly afterwards be on the same vertical. 



To take the altitudes, let the observer turn towards the elevated 

 pole, and select any two stars, not very near to each other, which 

 have nearly arrived at their vertical position. Let successive pairs 

 of altitudes be taken, till the stars have just passed the perpendi- 

 cular, and the differences be noted. These differences will gra- 

 dually increase till they attain a maximum, and afterwards decrease. 

 That pair of altitudes, the difference between which is the greatest, 

 is the pair to be made use of in the calculation, for the instant at 

 which the difference between the altitudes is greatest, is the instant 

 of their being on the same vertical. 



And since the apparent angular distance of the two stars at that 

 instant is always equal to the difference of their apparent altitudes ; 

 if these distances be taken at the same time with the altitudes, they 

 will afford a constant check upon the observations ; for the least of 



