204 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



in which are put 



A=^KkpQ^r^ 



z=- 



Po 



Zl = l—C 



The constants p^, c may be determined by assigned values of the mean 

 and surface densities, which will here be supposed to be in the ratio 2:1, 

 giving c = -^, whence results 



,00 = 9.653 |0, = 2.758 Hi = 3A5XlO'' 



^ = 3.110X10^8 (l>= 2.426X103' 



and for the quantities p, p, H at various depths the values listed in table 9, 

 which for the present density-formula replaces the corresponding columns 

 in tables 1 and 2. This value of c is somewhat less than that used by Roche, 

 which seems to give rather too small an estimate for the surface-density, 

 when the more modern determinations of p^ are used. 



Comparison with the tables of Part I shows that the range of values in 

 density, pressure, and specific compressional energy is in each case some- 

 what less than under the previous conditions, but that the modulus of com- 

 pression, while somewhat less at the lower densities, is decidedly greater at 

 the higher, showing that the departures of formula (74) from (25), which it 

 replaces, have qualitatively the character shown to be needed. Of the 

 energy-totals, 0^ is necessarily the same as before, while (P and E are respec- 

 tively 1.2 per cent and 14.1 per cent less than their former values, so that 

 relatively more of the primitive energy is transformed by impact and lost 

 by radiation. This is obviously due to the greater mass of the nucleus, at 

 a given radius, and the correspondingly larger velocity of impact in this as 

 compared with the former case. 



Table 9. 



