3 32 Dr. Robertson's expeditious methods of calculating 
e for d , and/ for e, in the series in the first method, we find 
EJfJL. R ° d /’J L ROg f3 4_ R°^ f3 R ° d 
2 (i+e) 3 OJ I 6fT4-e) 4 -' 2(i4-e\ 5 J 
J' + 
R°s 
si*+ 
6(1 
2(? +e) s - 
24(1 -fe) 5 
/* 
5R0 * /4 1 5ROfi3 -/ 4 -f &C. 
I2(i-fe) 6 ^ f" 8(i+e) ; 
I prefer this method to the first or second, and therefore I 
proceed to calculate by it. 
Example I. 
Let us suppose with M. Delambre* that the mean ano- 
maly is 135°, and the excentricity of the orbit 0.25, the mean 
distance from the sun being 1. 
CM— CS 
75 
Here CM +CS= 1.25, CM— CS— .75, and CM+CS — I 
the log. of which is to be used for any given mean anomaly 
in the orbit. 
TT S - - Lo S- 977 8l 5i3 
Log. tan. 6 7 0 .. 30' - 10-3827757 
Log. tan. 55 ..22. .49. 84 10.1609270 
CSM = 122 ..52. .49.84 
CMS = 
CMS is found by this 
proportion, 2o6264''.8 : 1 
: : CMS in seconds : its 
length in parts of the ra- 
dius. 
CS ===. 0.25 
a 
12.. 7. .10.16=43630" 16 
206264.8 
CMS = . 21 15249 
Log. 9-39794°° 
Log. 9 9241783 
d =. 2099511 Log. 9.3221183 
.2115249 = CMS 
,0015738=/, Log. 7.1969495 
CS 
b 
Log. 4.6297867 
Log. 5-3144251 
Log. 9.3253616 
Log. 9-39794°° 
Log. 3.7347108 
1357222 Log. 9.1326508. 
As CSM is obtuse, e is negative, 
l-f ^==^8642778 Log. 99366534. 
• Vol. II. page 28. 
