224 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



first moderate increments of pressure, and though they might be more 

 closely followed under pressures beyond the observable crushing point, yet 

 the agreement, for instance, of the theoretical and empirical values of the 

 modulus of compression would be little more than coincidence. 



The other extreme corresponds to what may be taken as the definition 

 of a perfectly elastic substance in the thermodynamic sense, including for 

 the present purpose not only fluids but perfectly elastic solids, since the 

 work of shearing forces has been left out of account. Here the density 

 depends in a definite way on temperature and pressure, independently of 

 what series of changes the substance may have passed through; every path 

 of change is strictly reversible, and in any closed cycle the excess of mechan- 

 ical work is exactly accounted for by conduction and radiation, so that the 

 work of adiabatic compression may be considered as stored elastic energy. 



The actual materials composing the earth may be judged to partake to 

 some extent of the properties of both extremes. Observed cases of the 

 flowage of rocks would seem to be concerned chiefly with permanent change 

 of shape, with little change of volume, but it is known that the equilibrium 

 of a body as large as the earth could not be purely that of an elastic solid, 

 unless it should possess elastic moduli much greater than those of known 

 substances, so that most probably the violent pressures occurring even at 

 moderate depths would lead to some permanent diminution of volume, or 

 such as partly to persist in the event of removal of the pressure. On the 

 other hand, direct experiments on the compressibility of rocks, under what 

 must here be considered small ranges of pressure, show approximately per- 

 fect elasticity, with a relatively trivial amount of hysteresis. 



It may well be that both extremes could represent acceptably the be- 

 havior of the same substance under different circumstances; for instance, 

 according to the intervals of time involved. A bell made of pitch may 

 sustain well-developed vibrations counted by hundreds per second and yet 

 in a few hours flow into a permanently altered shape. Similarly the interior 

 of the earth may be capable of sustaining seismic tremors and tidal oscilla- 

 tions like an elastic solid, and yet under steady and long-continued stresses 

 3deld in such a way that the expenditure of energy must be counted almost 

 wholly dissipative. 



Thus in view of the great length of time which must be assumed for the 

 epoch of aggregation, the notion of compression with purely frictional re- 

 sistance, accompanied by the production of permanent set or non-reversible 

 diminution of volume, may be the appropriate one under the circumstances 

 postulated by the planetesimal hypothesis, and would seem to demand no 

 material modification in the essential features of the theory given in Parts 

 I and II. For example, under a steadily progressive compression the pres- 

 sure actually occurring with a given density at the corresponding depth 

 would be at every epoch the critical pressure for that density, so that the 

 density-curve for any epoch would necessarily, as was assumed without 

 comment by Fisher, determine the path of compression traversed by a defi- 

 nite element of the mass. 



It is likely that the phenomena of dynamical geology may themselves 

 ultimately furnish the material for the most satisfactory estimation of the- 



