136 Mr. C. Davison on the Straining of the 



supposition that the coefficient of dilatation is constant, i. e., 

 an inferior limit to the depth if the coefficient of dilatation 

 increases with the temperature. This agrees of course with 

 the first approximation obtained by Prof. Gr. H. Darwin and 

 the Rev. 0. Fisher*. 



Putting ft equal to zero, t. e., e'/e to infinity, we get 



9 3*/2^r a 



or 



# = . 



/ 18tt* ; 



)% ; (?) 



which gives a superior limit to the depth of the surface of 

 no strain so long as the coefficient of dilatation increases 

 with the temperature. 



In Fizeau's table of coefficients of dilatation t> eighteen 

 determinations for non-crystallized bodies are given as especi- 

 ally trustworthy. Making use of these only, and taking V 

 at 7000° F., the average value of /3 is *1. With this value, 

 the depth of the surface of no strain after 100 million years 

 is 7*79 miles. At the same time, with a constant coefficient 

 of dilatation, it would be 2*17 miles. 



It is evident from equation (4) or (5) that there is no simple 

 relation between the depth of the surface of no strain and 

 the time. If e'/e be small, the depth varies nearly as t: if 

 eVe be large, the depth varies nearly as t*. 



Volume of Folded Hock above the Surface of No Strain, — 

 Since k and e are both small fractions, the volume of that 

 part of the shell of radius r and thickness Br which is stretched 

 or folded in unit time is 



47r6Y . r 1 — 4:7r8r(r Q + 2r . kr) = $tt(c— a)8x . kr, 



where kr is given by the expression (1) or (2). Denoting 

 this by SU, we have 



dU _ IQeYs/JTTic) 

 dy /3{c-atf)y/(tyW)> 



* Phil. Trans. 1887 A, p. 246 ; Phil. Mag. vol. xxv. 1888, p. 14. 

 f Jamin's Cours de Physique, vol. ii. 1878, pp. 80-81. 



