352 



Mr DAVIES on the Equations of Loci 



or the curve passes through R and T ; and through R' and T', points equi- 

 distant from the opposite pole P'. 



2do, Let sin = 1 : then, 6 = ^1 IT, 



m 



and the equation becomes 



S j n _ cot L cot a {cosec 2 a 1 + cot 2 a cot 

 cosec 2 a 1 



_ cot L zh cosec L ^_ sin a (cos L -+- 1) 



cot a sin L cos a ' ' 



This gives two values of sin $, viz. 

 . , 2 sin a cos 2 ^ L 



; ^ _ ^ s i n a s ' 2 ? L 



in ^ L cos 5 L ct 



fco, Let sin 6 = I, or 6 = *'"~ A TT ; 



M 



then the equation becomes 



. , cot L cot a rt cot a cosec L rot L -4- cosec L sin a (cos L 31 1") 



sin = i . ', 



cosec 2 a 1 cot a sin L cos a 



This divides itself into 



9 sin a cos 2 i L , _ 



sin = -g = rrJ rr = cot i L tana (20.) 



2 cos a sm | L cos | L 



2 sin a sin 2 i L 



sin = JT-. r-f rr =tan^ L tan a (21.) 



r 2 sin i L cos ^ L cos a 



