COEFFICIENT OF EXPANSION 59 



the theory, even when thus restricted, has been the 

 supposed position of the level of no strain, imagined 

 to occur not far from the existing surface of the 

 ground. 



It seems impossible to concede the validity of all the 

 reasoning on which this conclusion is based. The Eev. 

 O. Fisher* writes : - 



" Hence the condition that the shell at x is situated at 

 the level of no strain will be, since E = 30, 



3e dv dv 



It will be observed that the position of this level of no 

 strain does not depend on the coefficient of contraction, 

 which will divide out." 



The fallacy, as it appears to me, lies in the words I 

 have underlined. The statement is obviously true if the 

 coefficient e is the same on both sides of the equation, 

 i.e., if it is constant, but this it most certainly is not ; the 

 value of a coefficient of expansion depends on the tem- 

 perature, and is usually expressed by physicists according 

 to a formula e (1 + a t + j3 t 2 ), where a and |3 are 

 constants and t the temperature. Mr. Davison, taking 

 the effects of the first constant into consideration, has 

 shown how this will modify the result ; and if the second 

 term involving the square of the temperature be intro- 

 duced into the calculation still further modification must 

 follow. It may be objected that in the case of high 

 temperatures, approaching the fusing-point of basalt, the 

 application of such a formula as we have suggested 

 would be a very dangerous use of extrapolation. All 

 the more welcome, therefore, are the experiments of 



* " Physics of the Earth's Crust," by the Eev. Osmond Fisher, 

 London, 1889, p. 95. 



