212 D. Kirkwood on Certain Analogies in the Solar System. 
his observations in 1848. The resulting diameter of Saturn’s 
sphere of attraction is 
D=8 618608, é 
and the corresponding value of the constant of rotation is . 
ae Fo 2 
‘ n 
* —, =C=972°929, 
Dp? * 
where n= the number of axial rotations performed during one 
revolution round the sun. The values of D for the other planets 
whose periods of rotation are known, are then determined from 
the formula . as 
2 
_ bog. D=3 (log. n — log.C). 
If we assume that the adopted values of m for Jupiter, Saturn 
and Uranus are entirely correct, the received masses of Mercury, 
Venus, and Mars will not perfectly harmonize with my analogy. 
y tabular masses of the two latter differ from the received 
masses by about one-seventeenth of their values. That of Mer- 
cury differs from Leverrier’s mass by about one-fiftieth. Are 
these interpolated masses admissible ? 
It is distinctly stated by Humboldt that these elements for the 
three planets mentioned probably need correction.* “ The masses 
of Mercury and Venus,” says Captain Smyth,t “are still subject 
to discussion, since the question is surrounded by every difficulty, 
as neither of them has a satellite.” In regard to Mars, Mr. Hind 
remarks, that ‘in the absence of a satellite to afford us a more 
exact value, we can only be said to have approximated to the 
mass of the planet.”{ It is unnecessary to quote other authori- 
ties. That the received mass of each of these planets may 
in error to the amount of one-seventeenth of its value, will hardly 
be called in question. 
o interpolate the elements of. the asteroid-planet, we have 
the equations :— 
pe Sern 
2 Re agree: ‘ (2) 
u m 
92 pe bale ia>?% uw ape 
a == G48, . (3) 
@ dered se cee ee 
whence 
Se r4a/M 
eT (0 EO 
* Cosmos, vol. iv, pp. 445, 472, 508. ; : 
$ Oycle of Celestial Objects, vol. i, p. 106. + Hind’s Solar System, p. 78: 
ae 
