262 B. WILLIS DISCOIDAL STRUCTURE OF THE LITHOSPHERE 



vidual minerals, and the difference between quartz and hornblende is 

 such as to show that the modulus for granite, for instance, would depend 

 largely upon the predominance of one or another mineral. To this must 

 be added the well known fact that the moduli of linear expansion of 

 cr3^stals vary greatly in different directions, and consequently the expan- 

 sion of a granite or gneiss would depend on the orientation of the crystals. 

 Thus, in approaching the general problem of thermal expansion in the 

 lithosphere, we are obliged to accept an average modulus, and with the 

 available data it seems that the best approximation to the general fact 

 will be reached by taking the modulus of expansion of glass, which we 

 can compare with the modulus of compression of the same substance. In 

 making this comparison I am not unaware that the expansion of fused 

 silica, silica glass, is exceedingly small, while that of crystalline quartz is 

 high; and by analogy it may be that the expansion of glass is notably 

 lower than that of crystalline silicates. But this possibility does not ap- 

 pear to offset the advantage of comparing the expansion and compression 

 of one and the same substance. 



Du Long and Petit determined the cubical expansion of glass as fol- 

 lows : 



to 100 centigrade 0000258 



100 to 200 centigrade .0000275 



200 to 300 centigrade 0000307 



These results indicate an increasing rate of free expansion with rising 

 temperature. By free expansion we mean expansion under atmospheric 

 pressure. A similar increase was determined by Fizeau for the linear 

 expansion of quartz, measured successively at 10 degree intervals from 

 20 to 50 degrees centigrade, and both parallel to and perpendicular to 

 the major axis. It seems reasonable, therefore, to assume that the three 

 determinations given above for glass represent a change in rate, which 

 continues with further rise in temperature. We proceed according to this 

 suggestion, although clearly the rate of increase of the modulus of 

 expansion is indeterminate and extrapolation is no better than guessing 

 in the right direction. 



The effects of cubical compression and cubical expansion of plate-glass 

 are represented in plate 9 under the conditions of pressure and tempera- 

 ture existing in the lithosphere to a depth of 40 miles, using the data just 

 recited and extrapolating arbitrarily beyond them. The curves are hypo- 

 thetical and the resultant has only a suggestive qualitative value. 



D, the modulus of cubical compression, whose reciprocal gives the 

 decrease in volume of a cubic inch of material for a pressure of one pound 

 per square inch applied on every side, is taken at the value determined 



