﻿474 A NEW METHOD FOR CORRECTING A FLANET's ORBIT. 



And we thus finally form the equations in which Stf cos 6 is the known term, 8 z/j , 

 8 z/g the unknown quantities, and cos d D^j tf , cos d D^, rf the coefficients. 

 From normals 



II. — +0.40 + 0.0249 SJ,— 0.003G 5 J^ 

 IV. 27.96 0.0284 —0.1259 



V. 63.50 0.1145 —0.2672 



(41) 



From these equations were derived, by least squares, the values 



d Ji = —Gsm 1", 

 ^^^2 = +231. 2 sin 1", 



the weights being made proportional to the number of observations. 



By means of the previously computed partial differential coefficients, we are now 

 enabled to obtain the values 



nat p = —300.9 ) . , . , , ^ , . , 



, n„ „ Mil the sixth place of decimals. 

 logp = — 130.6 ) '■ 



d log nat p = — 300.9 

 .*. d com : 



logp = 0.452163, 

 8(p = 3' 37".4, 



(p = 7° 25' 34".2, hence, log cos <p 9.996342. 

 Sz=x — "°= —41' 26".6, ' 

 log a = 0.459479. 



Referring the previous, and still unchanged, node and inclination to the mean eclip- 

 tic and equinox of 1857.0, we find 



Jl° 4 28 34,7, 



a>° 309 47 34.0, 



i" 5 25.6. 



Hence, ^ = 313 34 42.1. 



From the value of D^^ *o =^, we obtain for 1857, Nov. 16.0, 



X- 



5z^=f,.SJ;! — —0.' 03328. 



7. . / 



Consequently, S Vi = d A^ — 3 ^ = „ . „ S Zi — 



This then gives us 5 v^ = — 28".2 — ^ ^ = +40' 58"!4. 



Then «s = 58° 52' 46".2, 



M = 46° 49' 58".7. 



Check, r, = — — ^ = r% (1 + d w,), 



1 + e COS r,'j ^ ' ■" 



which comes out exactly 0.424080 in both. 



From the equations (38) the values of S i ^ -]-ll".2, S S2 = — 16".l, were rather 

 roughly estimated ; whence n — % =^ ^ sin^ i i . 5 J2 = — 0".l. 



