1835. OccuUatlons of stars at Madras, 301 



the ans^le d a x (which we will call O) being the incliria- 

 tion of the star's apparent orbit to the circle of declinii- 

 ticij ; to compute it, we have 



tau O — eh 

 a b 



d 



a cos D 



© X being given ~ A' 

 X c n = O 



© n or n the neareast approach will be := ^ cos O 



And t the time describing • x n will be ^ — ^ 



a cos ^ 



for in the triangle c x n 

 X n = c X sin X c n 



= A sin O 

 a e : 1 : : A' sin O : t ' 

 t ' = A' sin O 



But a e = a ' cos D ' 

 cos O 



therefore t ' = A' cos O sin O n sin C) 



a cos D a cos D 



Nov/ the time of apparent cT in right ascension -|- t ' 

 (-j- when A ' and d ' are of like signs and — when con- 

 trary) = time of nearest approach, or the middle of the 

 occultation. 



If y represent the place of Immersion, the time of the 

 star describing n y will be the semi-duration, to deter- 

 mine which we have c y = S the Moon's semi-diameter 

 c n = n the nearest approach and l)y the 471 h of the Isb 



Book of Euclid v^'s^ — = y I s + n 1 . ! s — n i A 



