166 On the Figure of Equilibrium of a Planet, SfG. [Dec. 13, 



a = 







i a. 



h a. 



4 a. 



a. 



(Laplace) 



e 



t ~ 







•812 



•844 



•902 



1-000 



(Constant 

 compress.) 



e 

 t 







•459 



•693 



•851 



1-000 



Thus tlie Laplacian solution attributes much higher ellipticity to 

 the internal strata. The solution with constant compressibility iri 

 fact gives so large a proportion of the mass in the central region, that 

 attraction has a greater influence compared with rotation, than in the 

 solution of Laplace. 



[P.S. — If, as is not improbable, the increase of density in the interior 

 of the earth is due rather to the heavier materials failing down to the 

 centre than to great pressure compressing the material until it has a 

 high density, then the determination of a modulus of compressibility 

 would be fallacious, and it would be more logical to leave the 

 expressions for the pressure and the density both as functions of the 

 radius, without proceeding to eliminate the radius and to form an 

 expression for the modulus of compressibility. I owe this suggestion 

 to a conversation with Sir William Thomson. — December 19, 1883.] 



