284 Prof. H. Hennessy on the Figures of the Planets. 



Q being the ratio of centrifugal force to gravity at its equator, 

 D the mean density of the planet, and D / the density at its 

 surface. This expression may be more simply written 



~2 Q (5D-3D7' 



But, on the hypothesis of primitive fluidity, we have 



, Q 



* = — *i, 

 Q 



where e l is the earth's polar compression, and q the ratio of 

 centrifugal force to gravity at the equator. Hence 



e_5e 1 P. 

 e'~2q5D-3D r 



For every planet in which the ratio of mean density to surface 

 density can be assumed to be like this ratio for the earth, we 



shall have jy = ^ — ^, and therefore 



£___70 fi_207 

 /~101g~303' 



after substituting the values of e\ and q. Thus, in such cases, 

 the compression resulting from superficial abrasion would be 

 sensibly less than that resulting from the hypothesis of 

 primitive fluidity. 



If we apply the formulae to the planets whose times of 

 rotation and mean density are most similar to those of the 

 earth, we obtain some remarkable results. 



For the planet Mercury, if we admit 8 6 700" for its time of 

 rotation, *075 for the ratio of its mass to that of the earth, and 

 •378 for the ratio of its diameter to the earth's mean diameter, 



we find Q = ; and if the planet were homogeneous, 



_J_ 



*~325* 

 With the same law of density as in the earth, on the fluid theory, 



_ 1 

 e ~413 ; 

 and on the theory of abrasion, 



1 

 e ~586* 

 These three results show that for Mercury no sensible com- 

 pression is likely to be observed. 



For Venus, if we adopt the values of the mass M, time of 



