Theory of Volcanic Energy. 313 



= 76908; 

 ,\ Heat per square foot = — - =99 units. 



The corresponding value for BB' will be 5333 miles. 



Now, according to Mr. Mallet's results in his original memoir, 



§ 133, (1) and (6), we are informed that 6472 units of heat 



would fuse 0*108 cubic foot of mean rock previously at 300° F., 



taking 2000° as the melting temperature. Hence with a solid 



earth, according to our calculation, a limit greater than the greatest 



possible gives 0*0015 cubic foot of mean rock that could be fused 



annually for each square foot of the plane of vertical section. 



With this value it would take a thousand years to fuse one 



vertical slice of a foot and a half thickness within the range 



of crust defined by the distance BB ; , or 5333 miles^ on a great 



circle of the sphere. But the place of weakness cannot but 



have a considerable thickness throughout which the heat would 



be distributed. If, then, it were, say, a mile thick, the number 



99 

 of units of heat to each cubic foot would be ,,^ ~ . or about 0*02 



5280 



unit. 



The force of compression, besides the work at A where the 

 yielding takes place, also does work over the plane of shearing 

 in overcoming adhesion and friction. Let the whole force ex- 

 pended in overcoming adhesion and friction along BB' be 

 /u/BB'. The space moved over increases from nothing at B and 



BB' 

 B ; to eAB and cAB' at A. The mean is — -. Hence the work 



along this plane is 



mm BB ' 

 fM'BB' x e -jr- 



o i *x — Ba / , Px — Pa 7 



= 2u! k x e k. 



And making the same suppositions as before for a superior limit, 

 this becomes on the whole plane 



P 2 



2a'— eh 



f* 



"We took ix at the value | of the weight for friction. We will 

 take it as equal to the weight for the adhesion, since that is 

 probably greater than the friction, although its ratio to the fric- 



