THEIR ARRANGEMENT'S AND FORMATION". 13 



which all the planetary masses at one time stood. It may 

 also be admitted that, when a ring broke up, it was possi- 

 ble that the fragments might spherify separately. Such 

 seems to be the actual history of the ring between Jupiter 

 and Mars, in whose place we now find four planets much 

 beneath the smallest of the rest in size, and moving nearly 

 at the same distance from the sun, though in orbits so el- 

 liptical, and of such different planes, that they keep apart. 



It has been seen that there are mathematical propor- 

 tions in the relative distances and revolutions of the pla- 

 nets of our system. It has also been suggested that the 

 periods in the condensation of the nebulous mass, at which 

 rings were disengaged, must have depended on some par- 

 ticular crisis in the condition of that mass, in connexion 

 with the laws of centrifugal force and attraction. M. 

 Comte, of Paris, has made some approach to the verifica- 

 tion of the hypothesis, by calculating what ought to have 

 been the rotation of the solar mass at the successive times 

 when its surface extended to the various planetary orbits. 

 He ascertained that that rotation corresponded in every 

 case with the actual sidereal revolution of the planets, and 

 that the rotation of the primary planets in like manner 

 corresponded with the orbitual periods of the secondaries. 

 The process by which he arrived at this conclusion is not 

 to be readily comprehended by the unlearned ; but those 

 who are otherwise, allow that it is a powerful support to 

 the present hypothesis of the formation of the globes of 

 space.* 



* M. Comte combined Huygens's theorems for the measures of cen- 

 trifugal force with the law of gravitation, and thus formed a sim- 

 ple fundamental equation between the duration of the rotation of 

 what he calls the producing star, and the distance of the star pro- 

 duced. The constants of this equation were the radius of the cen- 

 tral star, and the intensity of gravity at its surface which is a di- 

 rect consequence of its mass. It leads directly to the third law of 

 Kepler, which thus becomes susceptible of being conceived apri- 

 ori in a cosmogonical point of view. M. Comte first applied it to 

 the moon, and found, to his great delight, that the periodic time of 

 that satellite agrees within an hour or two with the duration which 

 the revolution of the earth ought to have had at the time when the 

 lunar distance formed the limit of the earth's atmosphere. He found 

 the coincidence less exact, but still very striking, in every other 

 case. In those of the planets he obtained for the duration of the 

 corresponding solar rotations a value always a little less than their 

 actual periodic times. " It is remarkable," says he, 11 that this 

 difference, though increasing as the planet is more distant, pre- 

 serves very nearly the same relation to the corresponding periodic? 



