120 Mr. H. Hennessy on the Figure 



equator, and F(a') a function of tho radius, whoso form de- 

 ponds on the law of density in passing from the surface to 

 centre. 



If we denote by T' the time of rotation of the planet, by a! 

 its mean radius, and by W and g' its mass and intensity of 

 gravitating force at its surface, we shall have 





<?' = 



±tt 2 a' 

 ' T , 2 ^ 





9'= 



M' 



and therefore 





■ 4tt 2 a' 3 





q'= 



Z T /2 M / 



Similarly for the 



earth we 



have 



and also 



q= 



4:7r 2 a 



' T 2 9 

 M 





9 = 



z ^ ; 



hence M (ay 



and therefore 



(TV 2 a' a /T\W\*M 



o! 

 Astronomers generally admit that — = '54 nearly, T= 86164", 



and for T, 24 hours 37 minutes 22*7 seconds, or T'= 886427". 

 If we assume for the masses of the Earth and Mars the values 

 determined by M. Leverrier, we shall have 



M— q nr j M/ — 



324439 "2812526' 



we 



have 



and make \ 



? = 289' 



log (^) = -1 + 9753660 



+ 9379634 



log (^) = -1 + 1971814 



0-1105708 



log 289 = 2-4608978 

 -0-1105708 



log^ = 2-3503870 = 224-07. ^=224707' 



