ASTRONOMY. 47 



C 3c 



'=tf COS 2 A'. 



~ D) 

 Hence c = 3 (cos 2 A -co* 2 A')' 



,c 2(D'~ D) 



a" 3D (cos 2 A cos 2 A')" 



Also, if = w, 



a = 



These formulas will be reduced to others, mote con- 

 venient for logarithmical calculation, by substitu- 

 ting for cos 2 A cos 2 A', its value, viz. 



2 sin (A+A') X sin (A' A); 



m (D' D) . 



= 3 sin (V + A) X sm(A'-A) 9 



^ , c_ D' D 



and a~ 3 D sin (A' + A) X sin (A' A)' 



When A is nothing, or when one of the degrees is at 

 the equator, A + A' and A' A, are each equal to 



^ so c = ^( p/ . D ). ; therefore the excess of the 

 3 sin* A 



degree. 



