﻿.5) 

 ^2> 



A NEW METHOD FOR CORRECTING A PLANET's ORBIT. 473 



As we do not wish E here, we can apply a method like the simpler well-known forms 

 of converting right-ascension and declination into latitude and longitude. 

 From the elements 



log (Z; v'/'°) = 8.461728; 



and from what has been previously obtained, 



log r V y) 



Sept. 17.5 0.413888 43 50.G7 85° 2l'.16 



Nov. 16.0 0.423901 58 11.80 84 10.36 



From (32) and (33) are now derived, 



log/. logy. 



For t: — Sept. 17.5 +0.45230 +9.58475 



4 = Nov. 16.0 —1.47254 +9.56672 



The equations (36) for detennining D^^, log p, &c. become, subtracting the second 



of them from the first, and also those with the same coefficients for finding D^^ log p, 



&c. if we make B^^ log p = h, D^^ log^ = 4» Da, cp = m^, D^^ q) = m^, I)^^ % =" ^*i' 



(1.) (2.) 



+2.833 +29.685 = (1.9.5061) /— (1.83514) m — (1.03991) «; 



+0.38437 0.00000 = (0.00000) ^ — (9.81607) w — (8.91004) ?i ; I (39) 



0.00000 + 0.36874 — (0.00000) I — (9.68983) m — (9.00885) n ; 



of which the solutions are, 



log (Da, log natp) = +9.8222 ; log (D^, 9) = ^9.9737; log (Da, x) = +1.0423 ; 



log (Daj log nat j9) = —9.4000 ; log (D^^ 9) = +9.9620 ; log {T>^^x) = —1.0199. 



When z/i is changed, the value of s for t^ remains unchanged, and vice versa ; so 

 that, for any time. 



Da, 2 = Da, {z — z,) ; (40) 



But z — ^2 does not contain L , so that we shall have 



Da, s = Diogp (z — z,) Da, cos jo + D, (2 — z,) Da, 9 + D^ (s — z,) Da x- (40') 



Similarly, Da, z = Da, (z — z,). (41) 



Nor does S iv contain S L^. 



We now find for the times of normals II., IV., and V., by formulae (11), (19')) as 

 modified in (40), (41), 



Da, s Da, M' Da, s Da, w 



n. — 4.373 +.1645 — 11.33 +.2108 



IV. +37.39 —.3285 — 96.07 +.6848 



V. +72.52 —.4890 —146.44 +.8395 



