228 Mr. A. W. Flux on the 



.'. The new value of B ly 



cos 6 ,<, „ , . N /. sin 6 cos 6 



,r\i cos # /-. . /i j •\/i sin cos 0. ,\1 



=l 1 -^^( 1+tan ^* C0S ^ ) ( 1 ~7^^* C0S vJ' 



, r. COS "1 , COS 8 , , , n l~ s i n COS 01 



= rf 1 ^- — rf 3-icos^ tan d — — = — 5-3- , 



L yClCOSfc^J /icostv L/tcos-SjJ' 



s ,sin0(> 2 -l), 



^-sb* 008 * ( vi -> 



b0 \ sine' cos V J 



(5 + 2; cos — 6\ + s^/sin . cos ^), 



= # + <i> cos ^ -A-* — -r— ■ zr — — — ■ o/i tan Oj 



r T Lsm sin 6 sm 2 J 



■= x -^(bcos-dr (vii.) 



cos T 



t> = ?+=<«■- V), 



= y + (f>sm J (z + Zi) cos 6 = y + [z + g 3 ) <f> sin ^ . (viii.) 



Therefore 



& r 



A/= - (cos + sin . <f> cos ^r) # 2 + ?/ 2 



'^fe^ cos ^ +2 ^(^ +2r i) * sin ^J 



+ 2^ tan 2 6{z-z x cot 2 0) -?J??J fos + y*)"] 



cos v ^ y J 



to the 3rd order of small quantities, x, y, z, z 1 , <p being of the 

 1st order; 



= A* + -((> 2 + ?/ 2 ) sin 6-2xz\$ cos ty 



+ *>%(*■* 



= A + B </> cos -v/r + C . <£ sin i/r (say) (ix.) 



+ - . 2y (2 + ^) cos . $ sin i/r, 



