Proceedings of the British Association. 101 



idea, we find the author first computing the time of rotation the 

 sun must have had about its axis, so that a planet situated on its sur- 

 face and forming a part of it should not press on that surface, and 

 should therefore be in a state of indifference as to its adhesion or 

 detachment — if we find him, in this computation, throwing overboard, 

 as troublesome, all those essential considerations of the law of cooling, 

 the change of spheroidical form, the internal distribution of density, 

 the probable non-circulation of the internal and external shells in the 

 same periodic time, on which alone it is possible to execute such 

 a calculation correctly; and avowedly, as a short cut to a result, 

 using as the basis of his calculation " the elementary Huyghenian 

 theorems for the evaluation of centripetal forces in combination with 

 the law of gravitation" ; — a combination which, I need not explain to 

 those who have read the first book of Newton, leads direct to Kep- 

 ler's law ; — and if we find him then gravely turning round upon us 

 and adducing the coincidence of the resulting periods compared 

 with the distance of the planets with this law of Kepler, as being 

 the numerical verification in question, — where, I would ask, is there 

 a student to be found who has graduated as a Senior Optime in 

 this University, who will not at once lay his finger on the fallacy 

 of such an argument,* and declare it a vicious circle? I really 



* M. Comte (< Philosophie Positive,' ii. 376, &c), the author of the reasoning 

 alluded to, assures us that his calculations lead to results agreeing only ap- 

 proximately with the exact periods, a difference to the amount of l/45, the 

 part more or less existing in all. As he gives neither the steps nor the data 

 of his calculations, it is impossible to trace the origin of this difference, — 

 which, however, must arise from error somewhere, if his fundamental princi- 

 ple be really what he states. For the Huyghenian measure of centrifu- 

 gal force ( FX ^) " combined" with "the law of gravitation" ( Fy — -J, re- 

 placing V by its equivalent,^ can result in no other relation between P and 

 R than what is expressed in the Keplerian law, and is incompatible with the 

 smallest deviation from it. 



Whether the sun threw off the planets or not, Kepler's law must be obeyed 

 by them when once fairly detached. How, then, can their actual observance 

 of this law be adduced in proof of their origin, one way or the other ? How 

 is it proved that the sun must have thrown off planets at those distances, and 

 at no others, where we find them, — no matter in what times revolving ? 

 That, indeed, would be a powerful presumptive argument ; but what geo - 



