1885.] 
Two Planets beyond Neptune. 
11 
concrete and dissolved in the most “ rigorous calculations,” 
— a remark illustrated by the following quotations. 
22. “All these” minor “differences between theory and 
observation may be very well put on account of the latter,” 
or may be accounted for by B. 
23. “ There will be no exception ” to the perfect agree- 
ment of theory and observation, “ but for equation (25) 
founded on the observations from 1824 to 1 ^> 2 7> the error, 
which remains almost always the same in the equation, 
whatsoever be the hypothesis, is from 5" to 6 ". ” 
Le Verrier abandoned for the owe planet the sound basis 
of his most “ rigorous calculations,” where in 1800 the two 
arcs with positive m' included the first one A, the second B, 
and had Neptune in the midst of their neighbouring ter- 
minals (189° 55'-t-263°8')+2 = 226° 31k He struck out for 
the periods and longitudes of greatest disturbances as those 
of probable conjunction of Uranus and the one planet, con- 
nected these periods by an ingenious combination, and ob- 
tained a success. 
The Predicted was not Neptune ; but Le Verrier has not 
only indicated the longitude of one planet out of three, but 
also that of A and B. 
Uranus. 
Neptune. 
Predicted, 
A. 
B. 
Solar distance 
— 19-18 
30-03 
36-156 
42 
76 
Perihelion 
— 167° 32' 
46° 6' 39" 
284-45° 
9 ° ? 
62°? 
Excentricity 
— o - oo 46 
0-0089 
0-1076 
0-0041 ? 
0-1156 ? 
Revolution years . . 
— 84-07 
166-6 
217 
272 
662 
Conjunction years .. 
— — 
171-4 
136-6 
121-34 
97 '3 
Longitude on January 1st: — 
Year. 
1778 
79 ' 3 ° 
— 79736 
e ’ 1800 
* 74 ° 
224-5° 
— 108-776° 
2 79’573 
Motion taken 1825 
280-84° 
279-308° 
— • 141-766° 
279 '573 
Circular for A and B .. 1847 
— 
327° 24' 
326° 32' — 
— 
1885 
— 
— 
— 221° 
3 * 4 ° 
1899 
2390 
or less. 
— 239-256° 
or more 
or less. 
The greatest differences observed during the 155 years, 
indicating positive in', fell in the period between 1824 to 
1827, and in 1690. After two failures to satisfy all observa- 
tions by the one planet, Le Verrier put the perihelion of an 
orbit into 284° 45', about the longitude of Uranus, on January 
1st, 1826. The time from 1690 to 1826 is 136 years, the 
