AZIMUTH IN TRIGONOMETRICAL OPERATIONS. 



95 



reference to first principles, but have the subject in a complete state be- 

 fore them ; and this must be my apology, should it be objected to me that 

 I have presumed to intrude on the Society with propositions strictly 

 elementary. 



In any spherical triangle ABC if the sides 

 h and c are constant, the sines of the angles B 

 and C will attain their greatest values contempo- 

 raneously. 



C 



h 



For the general equation is 



-vm h 



sin Bzz sin C. --- 

 in which the term sin B is obviously a maximum when sin C is a maxi- 

 mum ; i. e. when C—^ov 90°. 



If, therefore, A represent the Pole, B the Zenith, and C the place 

 of a circumpolar star ; when the Azimuth which is represented by the 

 angle 2? is a maximum, the angle of position at C will be a right angle : 

 in that case, therefore, we have 



1st. Cos A — Ian h. cot c (a) 



2nd. sin B —^JUlA (f3) 



SlU c 



3rd. Cos a (r) 



cos b 



But A represents tlic hour anulc, or ])(ir(ion of sidereal space passed 

 through between the iustiiuL ul' irausiUuid thai of maximum Azumith ; 



