T11K OH BIT OF UUANUS. 1G1 



"We h;ive next to express the values of ^?. and fp in terms of the corrections to 

 the rlrnK'iits. Differentiating the expressions 



X = / + (2e Je 3 ) sin (/ n) + |e* sin (21 2*) + \$e? sin e 3 sin (3/ Sn) + etc. 

 p = -D + | 3 + ( e + %<?) cos (I n) |e 2 cos (2/ "frr) etc., 



with rc-jicct to /, c, and TT, and reducing the coefficients to numbers, we find 

 ^ = 1 + 0.0939 cos y + 0.0055 cos 2y 



|^ = 1 .999 sin y + 0.1 1 7 sin 2<j + 0.007 sin Zg 



fft 

 - = 2.000 cos g 0.1 17 cos 2y 0.007 cos 3y 



O7t 



Wr have here put I for the mean longitude, or 



I = nt + e 

 whence 



Also, from the expression for p 



v = Jc (1 Ic 1 ) cos 7 |e cos 2y etc. 



s 



^ ^P A 

 <9w ~ o 1 ? 3n 



The values of these coefficients which depend only on g are shown in the following 

 table : 



21 May, 1873. 



