oes. . fm +4/m=(al — a)c’ 
Be ye mf (a! be]? 
ee (a, +b,)c,+(a’ — b’)c 
oe a 
tS s ; Computation of the Value of the Constant called x. 
“If we use Leverrier’s* mean distances and masses in his theory 
of Mercury, with the exception of Adams’st value 355 for the 
; mass of Uranns, and Hansen’s{ periods of rotation, we find by 
| condition (IV.) the following values of 
Qn 3 
= a? 
- 
' . Namely: 
* =15.179 by Venus. 
=14.811 by Earth. 
A =15.593 by Saturn. 
Whence, with double weight for Saturn: 
* =15.300= mean value adopted. 
x“ F 
If we form another constant k’= = we find 
By Venus, k’ = 1.9377 
Earth, =1.9054 
Saturn, =1.9772 
_ From which it appears that an approximate value for the rota- 
tion times might be obtained from 
tole 
a 
1=(55) 
But the other formula is preferable ; and we have 
0 2x 2 2 3 1 3 
ae ike 765" 
With this value of «, using the data above mentioned, interpo- 
ing the a, m, and 9 of the fifth or hypothetical planet, called 
Kirkwood, and three masses, viz. : of Mercury, Mars, and Uranus, 
the following normal elements of the primary system are obtain- 
ed, in which all of the above four fundamental conditions are 
fulfilled for each middle planet of five. For Neptune, Mr. W. 
had his own value of the mean distance, and Prof. Peirce’s 
mass from Bond’s measures of the elongation of the satellite. 
: The interpolated values are enclosed in parentheses. 
Saige || eR 3 
* Additions 4 la Connoissance des Temps, 1848, 17-26. 
i Proceedings R. A. Soc., vol. ix, pp. 159, 160. 
Schumacher’s Jahrbuch, 1837 
-°.. Eltamination of Kirkwood’s Analogy. 21° 
ae | 
