97 



lar opinion, that the prevalence of Cholera is owing to a pe- 

 culiar condition of the atmosphere. 



Dr. Franklin Bache made some observations on the pre- 

 sumed electrical condition of the atmosphere as connected with 

 Cholera, and doubted the influence ascribed to this condition 

 in some recent publications. 



Mr. Sears C. Walker communicated to the Society the dis- 

 covery of a new analogy in relation to the periods of rotation 

 of the primary planets, recently made by Mr. Daniel Kirk- 

 wood, of Pottsville, Pa. 



Mr. W. remarked at length on the nature of the analogy, and gave 

 his opinion, based on careful computations, made for the purpose of 

 testing the hypothesis, that it deserves to rank at least with Kepler's 

 harmonies, and that its close agreement with the elements of all the 

 primary planets, justifies the remark, " that it is difficult to resist the 

 conclusion that it is a law of nature." 



This analogy may be thus expressed : " The square of the num- 

 ber of a planet's days in its year, is as the cube of Laplace's diameter 

 of the planets sphere of attraction in the nebular hypothesis." 



Mr. W. expressed a belief, that Mr. Kirkwood's analogy would 

 tend to throw light on the present internal organization of the planets, 

 and perhaps, also, on their more primitive condition, as assumed by 

 Laplace in his nebular hypothesis. 



Whatever may have been in a more primitive state, that quantity 

 of motion which is now the momentum of rotation of the planets, we 

 know that it must have been a constant. While, therefore, each 

 planet now preserves this constant momentum of rotation, it has taken 

 such a diameter, such a mean density, and such a decrease of density, 

 from centre to surface, as to give it that angular velocity of rotation, 

 which has, towards the ratio of the mean distance, and primitive di- 

 ameter of the sphere of attraction, the very simple relation first dis- 

 covered by Mr. Kirkwood. If either the diameter, mass or law of 

 decrease of density, from centre to surface, for any one of the planets 

 were different from its present state, Kirkwood's analogy would fail 

 for that planet. 



We may also remark, that a great change in the quantity of caloric 

 of a planet, or in the law of its distribution in the interior of it, or in 

 the calorific repulsion of any two adjacent particles, at a given tem- 

 perature and given distance from each other, would impair the pre- 

 cision of the analogy. Since no.such defect is noticed in the applica- 

 VOL. v. — o 



