226 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



In addition to special hypotheses as to the form of the functions p, e, 

 it would be necessary to specify the exact path of the compression in order 

 to determine the rise of temperature produced by a given amount of me- 

 chanical work. It has, however, been assumed from the beginning that in 

 view of the low conductivity of rock the compression might be considered 

 as relatively instantaneous and therefore adiabatic; under this condition 

 the path of compression would be a curve of constant entropy, and the 

 ratio of mechanical work to rise of temperature would be determined by 



de\ _de p 



ddj, dd , de (140) 



dv 



de \ 

 Comparison of this with (135) shows that -^ j , which was treated pre- 

 viously as a specific heat, can be identified with the specific heat at constant 



de 

 volume only at points where — = 0. This latter condition is satisfied 



identically by a perfect gas, which the substance might perhaps resemble 



in this respect, while differing widely in the relation between pressure, 



density, and temperature. 



de 

 If, however, -^==0 is satisfied everywhere, so that the intrinsic energy 



is a function of the temperature only, equation (137) shows that p would 

 have the form p = 6V and consequently by (136) that Ka=V; where V 

 is some function of v only. Since at the surface the pressure vanishes, V 

 would be zero for the argument v^, hence the surface material would have 

 to be either isothermally incompressible or have a zero coefficient of expan- 

 sion. Now the observed compressibility and expansion of surface rock are 

 enormously less than for gases, but the existence of an appreciable value 

 for both of these is a necessary element in the application to dynamical 

 geology, so that a correction is called for if the above be taken as the mean- 

 ing of the specific heat used in equation (58). Though there is nothing to 

 impose this special interpretation, the result still suggests one way in which 

 a coherent theory can be constructed, as a modification of the previous one, 

 but such as to take account of the measured values of all the thermal and 

 dynamical coefficients. 



Let it be supposed that the specific heat o at constant volume is a con- 

 stant, understood henceforth as measured in mechanical units; that the 

 intrinsic energy, instead of depending on the temperature only, has the form 



e=od + <p(v) (141) 



where <p{v) is a function of v to be determined; and that the isentropic lines 

 have the form . 



P =/i (^) ^ +/2 (^) (142) 



The latter condition results from the Laplacian equation (21) by treating 

 h and p^ as functions of the entropy, and is suggested as a condition in view 

 of (the assumption hitherto made, that the path of compression is deter- 



