MECHANICAL STATE OF THE ISOSTATIC SHELL 263 



bv Adams, 6,4-1:8,000. If the compression followed Hooke's law, it Avould 

 then be expressed by the straight line which is so designated. Since, how- 

 ever, it is more probable that the rate of compression diminishes with 

 increased state of compression and higher pressures, the actual amount 

 of cubical compression is presumably more nearly that indicated by the 

 curve OLM. This curve represents compression at surface temperatures. 



The expansion of volume due to rise of temperature, under a pressure 

 of one atmosphere, may be represented by plotting the three values 

 determined by Du Long and Petit for 100, 200, and 300 degrees centi- 

 grade. The resulting curve, arbitrarily prolonged, gives the line ONP. 



The curve OLM, representing compression, is concave downward, 

 whereas OXP, representing expansion, is concave upward. The former 

 is minus, the latter is plus. The difference of their abscissas, as NL, 

 would represent the resultant effect. Down to 40 miles they are, as drawn, 

 divergent, but they would converge at some greater depth. Their diver- 

 gence indicates increasing density,, and the convergence tbe opposite. 

 Hence the density and strength of rock would become less after passing 

 a certain maximum. 



"We are thus landed in a conclusion which contradicts the unquestion- 

 able fact that density increases continuously with depth, and the contra- 

 diction is directly due to the assumption that the effects of pressure and 

 heat are independent. It is clear that pressure, the dominant force under 

 the conditions of gravitation and heating in the lithosphere, controls 

 thermal expansion. The curve ONP may be flattened to the straight OQ, 

 or more probably may be reversed to the curve OR. The latter is neces- 

 sary under normal relations, if we accept the results reached by Lunn^^ 

 for the increases of pressure, density, and temperature on the assumption 

 that the increase of density varies as the square root of the increase of 

 pressure, as postulated by Laplace. 



While it is thus clear that compression controls and limits thermal 

 expansion under normal relations of pressure and heat in the lithosphere, 

 it is equally evident that temperature affects the degree of compression. 



Assuming that the curves OLM and OE indicate respectively the degree 

 of compression and expansion, their difference, OST, represents the 

 resultant of the two. The actual degree of compression or expansion of 

 any mass in the lithosphere is thus that state which is determined by 

 the equilibrium of the effects of pressure and heat at any instant. The 

 forces of pressure and heat are all-pervading, ever present, and constantly 



" A. r. Lunn : Geophysical theory under the planetesimal hypothesis. Carnegie In- 

 stitution of Washington. Publication 106, 1908, p. 200. Also in Chamberlin and Salis- 

 bury's Geology, Am. Scl. series, advance course, vol. i, 1909, pp. 564-566. 



XVITT— Bull. Gkol. Soc. Am., Vol. 31, 1919 



