THE THEORY OF FISHER. 



183 



~ In table 1, fifth column, / (x) stands for (l-^x^, tabulated for com- 

 parison because of its occurrence in an approximate formula for the density- 

 used later. The maximum value of g occurs at a; = 0.8411, or about 630 



miles below the surface. 



Table 2. 



The second and fourth columns give the values of the pressure and bulk- 

 modulus in milHons of atmospheres, an atmosphere being taken as one 

 megadyne per sq. cm., while the seventh column gives the specific com- 

 pressional energy in biUions of ergs per gram. The last column is added 

 for the sake of vividness of interpretation in terms of temperature, being 

 the measure of the thermal equivalent of e in centigrade degrees, under 

 specific heat one-fifth that of water. 



Of the total store of potential energy <P, it appears that 72 per cent is 

 accounted for by (!>„, which would be the energy exhausted if a system of 

 planetesimals, originally infinitely dispersed, united to form a homogeneous 

 sphere of density p^; this portion is to be thought of as energy of impact. 

 Of the remaining portion (^—0^, the compressional energy E accounts for 



53 per cent. . 



It remains to be determined whether the excess oiO-O^ over E is also 

 to be ascribed to energy of impact. That a part at least must be so con- 

 sidered follows from the assumed character of the actual aggregation. For 

 when a given particle impinges on the momentary surface, the mass already 

 gathered has condensed, under its own gravity, to smaller dimensions than 

 it would occupy in the homogeneous sphere; the radius being smaller, the 

 velocity of impact is greater than would be the case under the attraction of 

 the same mass in homogeneous form with the minimum density p^ For a 

 particle having any assigned position in the completed planet the attracting 

 mass within can be computed by (26). But the velocity of impact depends 

 also on the momentary radius of that mass, before it has been further con- 



