THEORY OF VOLCANIC ENERGY. 473 



some unexplained cause two contiguous areas have differed by as 

 much as one tenth in the amount of linear contraction throughout 

 (which is scarce]) 7 probable), it would require a thickness of crust of 

 400 miles to give occasion to one area being depressed one mile 

 below the other. This is much more than can be considered a thin 

 crust ; and by the time the crust had attained that thickness, or, 

 rather, the much greater thickness which would in reality correspond 

 to the assumed amount of contraction, tangential pressures must 

 have long ago come into play. 



We now approach the main question, viz. that regarding the cause 

 of volcanic heat. Mr. Mallet's " definition" is as follows : — 



" § 67. The heat from which terrestrial volcanic energy is at present 

 derived is produced locally within the solid shell of our globe by trans- 

 formation of the mechanical ivork of compression or of crushing of 

 portions of that shell, which compressions and crushings are themselves 

 produced by the more rapid contraction by cooling of the hotter mate- 

 rial of the nucleus beneath that shell, and the consequent more or less 

 free descent of the shell by gravitation, the vertical ivorlc of which is 

 resolved into tangential pressures and motion within the thickness of 

 the shells 



The only questions here raised which I wish to discuss are those 

 relating to the capability of the compression to give rise to volcanic 

 action. As regards the lateral compression itself, I had found in 

 1868* the same value for its maximum amount which Mr. Mallet 

 has arrived at. And, what is remarkable, in the MS. of my paper 

 I used the very same proposition relating to the tension of a flexible 

 vessel filled with fluid which he has used, in addition to the one 

 which I have printed. I was, however, advised to retain a single 

 proof as sufficient; and I retained the more elementary and indepen- 

 dent one — which I somewhat regret, because the proof which I dis- 

 carded (the same as Mr. Mallet's) answers an argument of Captain 

 Hutton's, and shows that where the curvature of the earth is greatest, 

 as at the poles, there the compressing force is proportionately in- 

 creased ; so that the compression theory is not encumbered with the 

 difficulty that it ought to give all the mountain-ranges about the 

 equatorial regions. 



The subject of § 85, respecting the horizontal or tangential pressure 

 within the earth, has regard to an inquiry which I made myself, and 

 in which I arrived at the following result : — The lateral pressure 

 within the earth, supposing any shell for a moment unsupported 

 by the matter beneath, but partially supporting that above it, will 

 be always greater than that at the surface (or than \gpU), until 

 some point is reached which cannot be further from the centre than 

 two fifths of the radius, and is probably much nearer to it. There 

 the internal horizontal pressure will be equal to that at the surface. 

 After that it becomes smaller, and eventually, near the centre, vanishes. 



No question can therefore be made that it will be sufficient, at 

 all such depths as we are concerned with, for any call that may 

 be made upon it for crushing the strata of the crust of the earth. 

 * Trans. Camb. Phil. Soc. vol. xi. pt. 3, p. 489. 



