SriIKKICAL TRIGONOMF.TRY AND PLANE ASTRONOMY. 343 

 IGl'O. In a spherical triangle ABC, a+b + c = ir: prove that 



,A ,B ,C 

 sin* -r + sm f -r + sm = 1; 



_ 2 



* 



cos a = tan - tan - , <fec. ; 

 2i 2i 



A EC. 

 sin j = cos-^ cos sin a, tc. 



A 2i '- 



\ . In a spherical triangle, A = B + C: prove that 

 . ,a . ,b . ,c 



1621, If be the pole of the small circle circumscribing a 

 _ r le ABCy 



,b t c t a . b . c BOC 

 sin* ^ + sin f 2 - sin^sSsiii., Bin ., cos ^-; 



and, if P be any point on the circle, 



. " . PA . b . PB . c . PC 



., -fsm-sm 2 -+sm 2 sm T =,0, 



that arc c.f the three PA, PB t PC being reckom-d m-pitivo wliloh 

 crosses one of the sides. 



1623. Prove that when the Sun rises in the north east at a 



place in latitude /, tin- hour angle at sunrise is cot' 1 (- sin/). 



; latitud.- l.V 1 (1 ..... Wrv.-d time of transit of a 



!l til" rjll:it..r In' U li:i H'-'Ct rd 1 ,y tllC (M!lllilH'd rll'.vt 'f till' 



^ of level and deviation of the transit instrument, these 

 errors will be very nearly equal to each otli i. 



16. * be the ratio of the radius of the Earth's orbit to 



:<-t, n the ratio of their motions in longi- 



tude considered un, ion of a planet as seen fi. -m 



irth when the planet is stationary is tan'* 



