8 



ROYAL SOCIETY OF CANADA 



A. mean value of the latitude may therefore be adopted for the last term 

 of the above expression, which is always small.' Denoting by ig this 

 mean value, the equation may be written : 



p2 



P sin f + -^ tan L„ sin 2 t sin V 



2 



cos L = O 



now put 

 (10) 



F Bin t + — ^r tan L^ sin 2 t sin 1 = — 



(11) 



and the equation becomes : 



— cos L = 



(12) 



z /j 



+ 



L 



= o 



The value of ?/ is calculated by (10) for hour angle intervals of 10 

 minutes and laid out on the axis of u, A m, (Fig. 5), but the sidereal time 

 instead of the hour angle is marked opposite the divisions of the gradua- 

 tion. This time is equal to the sum of the hour angle and right ascen- 

 sion of the Star. The modulus l^ is ttie length of one minute of arc on 



Fig. 5. 



Au; it 18 selected arbitrarily so as to give suitab le proportions to the 

 figure. 



In the same way, the values of v or — cos Jj are laid out below B on 

 the axis of v, Bv, v being negative. The modulus l^ is the length of 

 cos 0° ; like the modulus /j, it is selected so as to give suitable propor- 



1 Designating by L^ and Li the extreme values of L, the value of L^ which 

 causes the least maximum error in the azimuth is given by the expression : 



. J tan 7>] cos Ln + tan X, cos L\ 



tan LiQ — -= — = 



cos Li + cos Li 



In the present case i^ = 53°17^. The error is a maximum for townships 



and 84 and for hour angles of 3 or 9 hours : it is then equal to 0.^22. 



