298 COMPUTATION OF THE VALUES OF LOG ff" 



r> sin 2 + (l-e 2 ) 2 cos 2 1 - 2e" cos 2 + e< cos 2 



Q I c A - 



a 2 sin 2 + (1 - e 2 ) cos 2 1 - e 2 cos 2 



r . n, sin sin 



- sin (r = -T= 



. 

 ./l-e 2 cos 2 



r a ,_ (l-e a )cos(9 _(l-e 2 )cos<? 

 cos t/ ^~ ._-.- j ~ . 



N/l-e 2 cos 2 



and tan & - - ; tan 6. 



le- 



These formulae give the radius vector and the geocentric colatitude in 

 terms of the geographical colatitude. 



2. NOW a _, 



and ? - sin (ff -0)= ^^_ {1 - (l - <?)} = e ] sln g COS . 



a VI - e j cos 2 l Vl - e 2 cos 2 



/af m cos 2 0' + (l-e 2 )sin 2 ^ 

 Also cos(^' 6} = -j--~ 



>7cos 2 6' / + (l-e 2 ) 2 sin 2 (9' 



1 - e- sin 2 ^ 



j in> a\ e'sm cos 



and sin (0' 0)= , a .- 



Also 



sn 



.v (l e 2 ) cos 



cos ^ = -; -- v ; 



Also we get, taking t/ as the angle of the vertical, i.e. (ff-ff), 



l-e'cos-0 



cos / = cos (0' &) = 



7l-e'(2-e 2 )cos 2 0' 



, t ni n\ e * s i n cos 



sm \li = sin (0' 0) = . . 



/l-e 2 (2-e 2 )cos 2 



