T Jl i: O 11 U 1 T O F I 11 A .\ I' 3. <J7 



(A.c.O) = e sin cAp, 



(i.e. 1) = sin 

 (4.a.'2) = e cos 

 (6.c.2) = e s 

 when 



ty = (2'.:U - l".24-<) T+ <r.l37* 



I'litting in the above e\]ire.v>ions 



cosu = .0880 .0167 T t 

 sin u = -4- .9961 .0015 7*, 

 \vc liml 



(fc.c.O) = (()".!! (T.OG <) 7* 

 (6.U) = (0 .20 .ll)r O'.OoT* 

 (6.&1) = (2 .30 1 .24)7 7 + .127" 

 (6.*.2)= -0.017 



(i.c.2)= (0. 1 1 0.06;/) T. 



\\'i' have, finally, to consider the terms rf long period in ^ and <k which have 

 IMMMI omitted from thn periodic perturbations produced by Neptune, in computing 

 the terms ot' \ j on page 61, and which are as follows: 



^ = 1".43 cos (2f g) 0".39 sin (2f- /) 



- 2 .12 cos (4^ 2y) + 1 .00 sin (4/' 2g) 



+ .20 cos (6f 3</) .04 sin (6f 



-}- constant = 0".00 



Ue= 0*.80cos(2r g) 2". 28 sin (2f- 

 - 1 .06 cos (4f 2*7) ~ 1 .85 sin (4f 

 4- .04 cos (6f 3/) + .19 sin (Gf 

 -j- constant = 0*.364. 



For the period during which Uranus has been observed, these values of ^ and Ik 

 may be replaced by the following: 



& = + 0.277* 



which are to be multiplied by the factor 1 -}- u. The corresponding perturbation 



if the latitude will be 



$fi = sin v'; cos v[k. 



Tutting for v its approximate value 



v = rj -}- o -j- 2 sin g 

 and developing to quantities of the first order with respect to the eccentricities, 



we have 



sin v = sin (g -j- u) + sin (2g -\-u) e sin u 

 cos v = cos (0 + ") + e cos &9 + ") e cos "* 



13 Kr. 1873. 



