68 Intelligence and Miscellaneous Articles. 



" I propose in this memorandum to remove this objection [namely, 

 the objection to the hypothesis of the original fluidity of the planets 

 on the ground of the exceptional magnitude of the oblateness of the 

 planet Mars] by showing that geometers have not handled the pro- 

 blem of spheroids in such a general way as could be wished." And 

 after having indicated the method he employs, he says: — "This 

 calculation, made by the usual methods (that is to say, by employing 

 Laplace's functions and neglecting quantities of the second order), 

 leads me to the results which follow." 



Relatively to these points, I may be permitted to remark that I 

 have long ago investigated the same problem of spheroidal attrac- 

 tions and by precisely the same methods — that is, by the applica- 

 tion of Laplace's functions. At first I applied the result of my 

 calculations to the question of the figure of the Earth, with the aim 

 of thoroughly studying the theory which endeavours to explain its 

 spheroidal form by the attrition of its surface. This theory was 

 at first proposed by Playf air in his ' Illustrations of the Huttonian* 

 System ;' and it has been put forward afresh by Sir John Herschel 

 in his ' Outlines of Astronomy.' It also acquires some interest 

 because it has been cited by Sir Charles Lyell and serves as a foun- 

 dation for the opinion which he maintains in his ' Principles of 

 Geology,' as to the earth's figure. 



The results which I have obtained show that this theory cannot 

 be upheld ; for the greatest ellipticity which the earth could possess 

 from the action of attrition cannot exceed - 4 J T , a fraction which 

 differs considerably from that which is usually admitted as the 

 result of observations. 



In 1864 I had for the first time applied my calculations to the 

 question of Mars, in a communication to the British Association; 

 and a short extract of my paper was published. 



In February 1870 I published a memoir in ' Atlantis ' (No. ix., 

 8vo, London, February 1870) on the Configuration of the Planet 

 Mars ; and I applied to Mars the mathematical results of my pre- 

 vious investigations. I found (p. 178) an equation giving the 

 ellipticity as a function of the mean density D' and of the surface- 

 density D of the planet, 



„ 5 ? q. 



»-•« 2 H5) 



In the equation q is the ratio of the centrifugal force to gravity. 



Now, if we employ the notation of M. Amigues, q will be replaced 

 by <j>, and J)' by p , and D by p, which gives 



10-6^ 2(1-?^ 

 p \ 5 P J 



a formula which is precisely that given by M. Amigues. 



* In the Comptes Rendus "Hutton " is misprinted " Newton." 



