[deville] abacus of THE POLE STAR 7 



Abacus of the Azimuth of the Pole Star. 



The azimuth of a star in terms of the latitude, hour augle^and polar 

 distance, is given by the formula : 



, tau P sec L sin t 



tan z = 



1 — tan F tan Jj cos t 



in which : 



z = Azimuth of the star 

 P = Polar distance of the star 



t = Hour angle of the star 

 X = Latitude. 



The azimuth and polar distance of the Pole Star are ho small that if 

 the above expression be developed in terms of the powers of 2 and P, the 

 terms containing powers above the second can, in the case of subdivision 

 surveys, be neglected. Expressing z and P in minutes of arc, we obtain : 



2C0S L = P 8int+ -2~ *^^ ^ ^'^ ^ ^ ^^^' ^' 



The surveys of Dominion Lands extend from the 49th parallel of 

 latitude to about township 84, in latitude 56^20', an interval of 7°20'. 



Substituting the values of the different lines, the equations become: 



Ô + X V 



hence 



— c 

 Adding up and dividing by 2 (5, we have : 



h + a 



-y{^) 



1 



y = 



b + a 



Subtracting the second equation from the first one gives : 



b — a 



Replacing y by its value and dividing by 2 



b — a 



g by 2: 



\ b + a y 



