396 On the Law of Rotation of the Primary Planets. 
exceeds that of Prof. Loomis. “The singular irregularities in 
the form of Saturn, and the great compression of Mars,” says a 
distinguished writer, “ prove the internal structure of these two 
planets to be very far from uniform.” 
While, then, the compression of a planet may be regarded as 
denoting in general the fact of its rotation, it is by no means a 
reliable indication of its angular velocity. In all probability, a 
variety of modifying causes, which cannot at present be reache 
by our analysis, have coéperated in producing the actual forms 
of the heavenly bodies. 
If the planets have undergone a progressive contraction from a 
state of vapor, their oblateness at former epochs must have been 
indefinitely greater than at present, and must have varied during 
the entire process of condensation. ‘The question then naturally 
presents itself whether the ratio of a planet’s diameter to that 0 
its sphere of attraction may not have some connection with its 
present polar compression. Perhaps it may not be improper to 
rernark that these ratios in the case of Mars and Uranus are about 
equal, and each very much greater than in any other planet. 
I shall now consider the objection that my analogy assigns in- 
admissible elements to the hypothetical planet between Mars and 
Jupiter. And first in regard to the mass. Thirteen supposed 
admitted to be extremely uncertain. ‘The apparent diameters of 
only four,—Vesta, Juno, Ceres, and Pallas,—have been taken ; 
and in regard to these, the measurements of Herschel, Schroeter, 
and Madler are very discordant. According to the determination 
of Schreeter the sum of their volumes is more than equal to one- 
fourth that of Mars. Adopting this estimate, therefore, and assum- 
ing that their average magnitude is equal to that of the remain- 
ing nine, the thirteen already discovered would be nearly equal to 
It may not be improper to remark in this connection that 
the apparent brilliancy of the asteroids does not always seem to 
increase with the magnitude. Pallas, which according to both ~ | 
Madler and Schreeter, is very much larger than Vesta, appears aS __ 
a star of the eighth magnitude, while the latter is of the sixth, 
and has been seen by the naked eye. eee. ee 
But the objection to the mass of the hypothetical planet, even 
adopting Madler’s values, does not appear to me very important. — 
What is there improbable in the supposition that hundreds or even 
thousands of asteroids, too small to be detected by our telescopes, — 
‘May revolve in this mysterious cluster? Indeed, if we may judge 
from the receut success which has attended the researches, Of as 
tronomers, it would seem by no means unreasonable -to suppose — 
_ that a number meh greater than has yet been observed, may D@- 
overec oe See 
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