THERMODYNAMIC THEORY. 223 



to a period much longer than the whole of geological history. A measure- 

 ment of the actual shortening indicated by the crumpling of the strata 

 would allow an estimate of the length of time elapsed, or the "age of the 

 earth. " Near the beginning the shortening is roughly proportional to the 

 square of the time, and as an indication of the order of magnitude a graphic 

 integration from the same table gives about 100 miles in a billion years, the 

 time being, moreover, inversely proportional to the numerical value used 

 for the conductivity. 



There remains to be considered what is perhaps the principal point of 

 obscurity in the theory — the way in which the initial temperature is deter- 

 mined from the work of compression. This was done above through the 

 supposition that between these two there existed a definite proportionality 

 indicated by the specific heat, while the latter term was not sharply defined, 

 but for numerical illustration was assigned the value 0.2, an average value 

 of the ordinary specific heats of certain rocks. Now if e represent the work of 



de 

 compression per unit mass, the ratio -^ for any path of compression is of 



the nature of a specific heat in physical dimensions, but its identification 

 with o in any definite sense of the latter (except of course that which might 



de 

 be defined as -tk for the given path) amounts to a condition on the ther- 

 modynamic properties of the "working substance" whose import there is 

 need to determine. 



As concerns the relation of work and temperature, there may be con- 

 sidered to be two extreme cases conceivable, illustrated by the simple 

 mechanical example of a weight in frictional contact with a horizontal 

 plane and drawn by a spring. If the spring is very stiff it is only slightly 

 extended, and the greater part of the work of the impressed force is done 

 against the friction at the area of contact; if the spring is weak, the dis- 

 placement of the point of appUcation of the force comes largely from the 

 extension of the spring and the corresponding work is stored as elastic 

 energy. 



Corresponding to one extreme there is the fiction of a substance whose 

 resistance to compression is purely frictional, its transformation of energy 

 pure hysteresis — having at each density a certain critical pressure, the 

 maximum it could sustain without further crushing, and as a function of 

 the density to be used in formula (12) in computing the work of compres- 

 sion. Such a substance would show no tendency to restoration of volume 

 on relief of pressure; and though the manner of transformation be obscure 

 it seems natural to treat the heat derived from friction during compression 

 as equivalent to heat obtained by conduction or radiation, so that the ratio 

 of temperature to work would depend simply on the value, at the ultimate 

 density, of the specific heat in nearly the ordinary sense as related to con- 

 duction at constant volume or constant pressure, at least if the coefficient 

 of expansion be relatively small. 



Such an interpretation read into Parts I and II would give a more 

 definite and perhaps reasonably self -consistent theory; but the conditions 

 described would fail to represent the behavior of surface-rock under the 



