m 
CS = 0.25 
a 
Dr. Robertson’s expeditious methods of calculating 
Log- 9-3979400 
Log. 9-9954°3° 
Log. 9-3933 43o 
R° 
/ 
. 2473677 
. 2499627 = CMS 
.0025950=/ - Log. 7.4141374 
First term of the series. 
- Log. 1.7581226 
Log. 7.4141374 
(i + e) 
Num. • 14349 0 6 
2d term .0000429 
Sum o°. 1435335 
= SMN . CSM 
9.1722600 
Log. .0154366 
Log. 9.1568234 
= 8 , ..36 /, .72 
= 8i°..4o..4i .51 
CS = 0.25 
Log. 9-39794oo 
b Log. 9.1605669 
e = .0361832 Log. 8.55850 69 
1+0=1.0561832 Log. .0154366 
Second term of the series. 
Log. 1.7581226 
- Log. 93933 43° 
Log. 4.8282748 
15-9797404 
. - - Log. .3010300 
15.6787104 
( 1 + e ) 3 Log. .0463098 
Num. .0000429 Log. 5.6324006 
R° 
d 
r 
2 
ACE = 81 -49-- 18 * 2 3 
This also differs from M. Delambre’s conclusion only in 
the second place of decimals. 
Example III. 
Let us suppose ALP to be the orbit of the comet which 
appeared in 1682, and reappeared in 1759, according to the 
prediction of Dr. Halley ; that CE is equal to 18.07575, that 
that CS is equal to 17.49225, and that the mean anomaly is 
i79°-47 / -3 2,/,1 7’ ** ls rec l u i re d to find the excentric anomaly. 
•5835 
Here 
CM— CS 
CM + CS 35.568 
Log. tan. 89°..53'..46 // .o8 
83 ..41 ..34 .5 
Lon. tan. 
CSM = 
CMS = 
173 -35 -20 58 
6 ..12 ..11 58 : 
CMS 
- Log. 8.2149815 
12.741553 1 
10.9565346 
22331.58 Log. 4.3489194 
206264.8 Log. 5.3144251 
.1082666 Log. 9.0344943 
