228 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



V <l> 



2 



ad-f" (150) 



Ka=a'^ H=^{aAc + a) (151) 



« = 1+^^' (152) 



o 



Since the pressure-density curve at the close of the epoch of compression is 

 supposed to be an adiabatic hne, the variation at different depths of all the 

 magnitudes concerned, for a planet of definite mass, will be determined in 

 terms of the constants introduced, when a value is assigned for the entropy, 

 which may as well be taken equal to zero, since the level of reckoning is 

 arbitrary. The various surface-values are then fixed by the condition pi = 0, 

 with ej = 0, so that the constants are subject to the conditions: 



, oA+a /IKON 



e,=— + Bv,+C (154) 



^^^=A. B (155) 



^'=^oB+b (156) 



If then Kj, Vi, ^1, ttj, a( are considered to be obtained by direct measure- 

 ment, a and H^ may be computed from 



a=a^-K^v^e^a^ (157) 



if,=K,|l+^^'| (158) 



and then the solution of (153) to (156) gives 



j^A_K^ (159) 



V{ a 



a=tL^-aA (160) 



h==^-aB (161) 



C=d.- — -Bv^ (162) 



leaving the single parameter A undetermined. The Laplacian constant 



^^^ h=H,v'' (163) 



in terms of which the distribution of pressure and density are still given by 

 (21) and (25), while the excess of intrinsic energy and of temperature over 

 their surface-values are 



