of the Planet Mars. 121 



For the Earth, 



e- 



gV(a) ; 



and if F(a) has the same value in Mars, or, in other words, if 

 the law of density in going from its surface to its centre is the 

 same as in the Earth, 



e ' 9.' j q r 

 - = ±- or €f——e. 



e q' q 



But the latest determination for e gives g= q» ,p *. Now 

 log 293-46 = 2-4676969; and as log ^ = 0-1105108, by sub- 

 tracting this from the foregoing we have 



log- =2-3571861 = 227-61. 

 Hence 



As the planet Mars presents evidence of the existence of an 

 aqueous fluid on its surface, a theory sometimes invoked for 

 explaining the earth's spheroidal figure might be appealed to 

 in order to account for the figure of Mars. This is the theory 

 of superficial abrasion and denudation, combined with the cen- 

 trifugal force resulting from rotation around the planet's axis. 

 This theory has been prominently put forward by Sir Charles 

 Lyell in various successive editions of his ' Principles of Geo- 

 logy ;' and although it has been shown to be discordant with 

 the results of mathematical investigation, it seems to hold a 

 place in connexion with the view of some geologists in 

 England and Scotland. It was originally propounded in the 

 latter country by Playfair, whose authority as a mathematician 

 gave it considerable currency. (See Illustration of the Hutto- 

 nian Theory, Playfair's Works, vol. i. p. 480.) 



On the theory of surface-abrasion or surface-moulding of 

 any planet by the action of water, I have found for the ellip- 

 ticity of the liquid coating, 



5?D + 6(D-1)E 

 2(5D-3) ? 



where E is the ellipticity of the solid surface, D the mean 

 density, and D y the surface-density of its solid materials. The 



* See Colonel Clarke's paper, Phil. Mag. August 1878, and the recently 

 published ' Geodesy' by the same author. 



Phil Mag. S. 5, Vol. 10. No, 60. Aug. 1880, K 



