Rotation of the Primary Planets, 167 



Mr Kirkwood then modestly concludes : — 



'* The foregoing is submitted to your inspection with much diffi- 

 dence. An author, you know, can hardly be expected to form a 

 proper estimate of his own performance. When it is considered, 

 however, that my formula involves the distances, masses, annual re- 

 Tolutions, and axial rotations of all the primary planets in the sys- 

 tem, I must confess I find it difficult to resist the conclusion, that 

 the law is founded in nature." 



After this letter had been read, Mr Walker said, that, induced by 

 the importance of the subject, he had at once proceeded to verify 

 the data and conclusions of Mr Kirkwood, and had found that there 

 was nothing in them requiring modification, except, perhaps, the 

 substitution of some more recent values for the masses of Mercury 

 and Uranus. This theory and that of Laplace, with reference to 

 nebulae, mutually strengthen each other ; although the latter has 

 been a mere supposition, while the former rests upon a mathematical 

 basis. In a later letter, which was also read, Mr Kirkwood says 

 that he has pursued this subject for the last ten years, it having 

 been first suggested to him by the nebular hypothesis, which he 

 thought could be established by some law of rotation. 



Mr Walker then entered into a lengthened examination of the data 

 on which the law rests, and seemed to come to the conclusion, that, 

 as far as we know at present, everything is in favour of the truth of 

 the law, except that it requires the assumption of another planet be- 

 tween Jupiter and Mars. 



Mr Walker closed his examination by saying, *' We may, there- 

 fore, conclude, that, whether Kirkwood^s analogy is or is not the ex- 

 pression of a physical law, it is, at least, that of a physical fact in 

 the mechanism of the universe. The quantity on which the analogy 

 is based has such immediate dependence upon the nebular hypothesis, 

 that it lends strength to the latter, and gives new plausibility to the 

 presumption that this, also, is a fact in the past history of the solar 

 system. 



" Such, then, is the present state of the question. Thirty-six 

 elements of nine planets (four being hypothetical) appear to har- 

 monize with Kirkwood's analogy in all the four fundamental equa- 

 tions of condition for each planet. 



" To suppose that so many independent variable quantities should 

 harmonize together by accident, is a more strained construction of 

 the premises than the frank admission that they follow a law of 

 nature. 



•* If, in the course of time, the hypotheses of Laplace and Kirk- 

 wood should be found to be the laws of nature, they will throw new 

 light on the internal organization of the planets in their present, 

 and in any more primitive, state through which they may have 

 passed. 



" For instance, we may compute the distance from the centre at 



