THE THEORY OF FISHER. 191 



if the primitive temperature curve is given in the form 



d{r,Q)=d,F{x) (57) 



6q being the initial temperature at the center. 



To determine the form of this initial curve it is necessary to know in 

 what way the storage of the compressional and impact energy is mani- 

 fested in rise of temperature, which is again a matter of hypothesis. Fish- 

 er's third assumption, as stated above, implies that the energy stored in 

 unit-mass stands in a definite ratio to the increment of temperature. That 

 ratio is, then, of the nature of a specific heat, expressed in mechanical units, 

 but is subject to question as to its identification, as is tacitly done by Fisher, 

 with the specific heat in the ordinary sense, as relating to rise of tempera- 

 ture due to heat transferred by conduction or radiation. It will be shown 

 later, however, in connection with a detailed criticism, that the theory thus 

 developed may fairly be considered self-consistent, in the light of thermo- 

 dynamic laws, when associated with what appears as a certain extreme view 

 regarding the thermodynamic properties of the earth-substance. An effort 

 will then be made to develop an opposite extreme view, to permit comparison. 



For the present, then, the primitive temperature will be supposed de- 

 fined by 



e=-^ (58) 



where v is the fractional value of that part of the energy of impact which 

 remains after the loss by dissipation at the surface, and o is the specific heat 

 identical with that occurring in equation (52). A variation of a with the 

 density need not be excluded, but any possible variation with the tempera- 

 ture will be disregarded, not only because of the practical value of keeping 

 the linearity of equation (52), but also because any uncertainty from this 

 source would be bound up with the inevitable obscurity of the very notion 

 of temperature under circumstances so far beyond the range of laboratory 

 tests. 



The multiplier v may also vary for different portions of the mass, its 

 value depending on the rapidity of the accretion. It could be unity as one 

 extreme, for deposits made with such rapidity that each stratum is covered 

 up before its loss of heat by radiation is sensible; or zero as the other ex- 

 treme, for accretion so slow that the cooling of the momentary surface- 

 stratum by radiation is practically complete. 



^ One curious possibility may be noted in passing. With sufficient veloc- 

 ities of impact and appropriate values of v, it would be possible for the 

 expression e+ye^ to have the same value for all strata; if then o were like- 

 wise constant, this would indicate a primitive temperature uniform through- 

 out the body. For example, if e^ should be for each stratum that derived 

 from impact at the corresponding parabolic velocity, as listed in table 4, 

 and V should range from 0.38 for the central portions to 0.27 for the surface 

 layer, then e+ve^ would have everywhere the value 1.7X10" ergs per gram 

 mass, and for a = 0.2 this would give a primitive temperature of about 

 20,000°. Since this value of a may be too low, and it is practically certain 



