Theory of Volcanic Energy. 317 



In this case the work on a square mile of section, viz. 



Px "~* A * ke, will be expressed by 10(P x +Pa)&?. 



The superior limiting case will be when the compressing force 

 has the maximum value P assigned to it, and when P A has like- 

 wise the same value. In that case, however, /^ = 0, or there is 

 no action between the crust and nucleus, and, because P A = P X , 

 no relief given at the weak plane A. This is therefore an 

 impossible case. If, however, we were to suppose it to occur, 

 we should have the work 



=20Pfo?. 



This would be only five times as great as the work was found to 

 be in the superior limiting case with a solid earth, and conse- 

 quently would not afford 500 units of heat to a square foot of 

 vertical section. 



Again, if we make the other supposition made before, that 

 P x = 400 and P A — 200, we have ^ = 20; and the coefficient 



analogous to that of friction being y, would be y 1 ^, which seems 



a not improbable value as between the solid crust and a viscous 

 layer. The work on a square mile of section in this case would 

 be 



10 x 600 x Ice, 



which is g 9 ^ of the work in the superior limiting case as found 

 for a solid earth, and would afford only 45 units of heat per 

 square foot of section. This last may be looked upon as a not 

 improbable estimate of the circumstances affecting the develop- 

 ment of heat along a vertical section of the earth's crust upon 

 the supposition that it rests upon a viscous layer ; and we see 

 that it would be quite incompetent to produce volcanic pheno- 

 mena ; at the same time the limiting case shows that no con- 

 ceivable larger value of the compressing force would raise the 

 amount of heat sufficiently for that purpose ; so that in this case, 

 as well as in that of a solid earth, we conclude that the theory is 

 untenable. 



If the work of descent of the crust is not transformed into 

 the heat of volcanic energy, it may be asked what becomes of 

 it ? The answer is, it is transformed 



(1) into heat within the nucleus, 



(2) into work of relative elevation in the crust, 



(3) into heat within the crust. 



This last is the only portion which can be appealed to for vol- 

 canic energy. The amount of it is probably too small (being 

 on the most extravagant supposition only y^ of the whole) to 



