Theory of Volcanic Energy. 309 



be no resistance, and if absolutely rigid no movement, so that 

 in cither of these extreme cases no heat would be developed in the 

 crust. 



It is easy to see that the whole work which can be obtained 

 out of the lateral compression is the same thing as the whole 

 work of subsidence ; for let ds, dd be the edges of a rectangular 

 element of the shell, k its thickness, e the coefficient of com- 

 pression, which is evidently the same as that of radial contraction 

 under the suppositions made above, P the mean pressure on a 

 unit of area of a vertical section of the crust ; then P k ds is the 

 pressure on a face of the element. 



And J*kdsx eels' is the work of compression of that element 

 in the direction perpendicular to ds. 



Similarly, Ykds x eds is the work in the orthogonal direction. 

 And the sum of these will be the whole work on the element. 



Hence the entire work on the crust will be 

 2?ke$dsds ! . 



Or work of lateral compression = 8Vke 7rR 2 . 



R* 



Now, if we give P its full value, viz. gp— , we get 



work = 4 irpg eH 3 k. 



Comparing this expression with that for the whole work of 

 descent of the shell, and observing that cH = d and # = R— r } 

 we perceive the two to be identical. 



In nature, however, P is not likely to be ever so great as this. 

 But the fact that the utmost annual amount of energy which can 

 be got out of subsidence of a crust 400 miles thick on a very 

 favourable supposition is only one fifteenth of the energy dis- 

 sipated from the globe, shows how large a store of heat there 

 must be within the nucleus. 



"We will suppose, then, that the rocks are of such a character, 

 and under such conditions, that an amount of heat sufficient, and 

 more than sufficient, to account " quantitatively" for all volcanic 

 phenomena is capable of being developed. 



I accept Professor Hilgard's challenge to prove its "qualitative" 

 insufficiency, by which I understand that it cannot be localized 

 under such conditions as to produce the volcanic phenomena 

 wn to occur. 



Let us thus then survey the conditions of the problem. A, 

 contracting globe induces in its enveloping crust a state of com- 

 pression, which owes its existence to the gravitation of the whole 



* See the author's paper " On the Elevation of Mountains by Lateral 

 Pressure," Trans. Camb. Phil. Soc. vol. xi. pt. iii. p. 4JJ2 (1868). Also 

 Mr. Mallet on Volcanic Energy, Phil. Trans. 1873, p. 173, § S3. 



