Theory of Volcanic Energy. 311 



contraction, seeing that the points B, B' are not shifted upon 

 the nucleus, it follows that the compression of B B' is e B B'. 



Let /Li be the force which a unit in length of the crust would 

 just resist, so as under its action not to move over the nucleus. 

 Then, before motion commenced, ja would depend on the adhe- 

 sion — but after motion had commenced, on friction ; and /xAB 

 is the force which the length AB would just resist. Let, as 

 before, k be the thickness of the crust. In general jjl will not 

 be the same for BA and B'A; but we will suppose it so, in 

 which case BA and B'A will be equal. Hence, after compression 

 has taken place, we shall have for equilibrium, at sections passing 

 through B and B', 



and 



P X £ = ^AB' + P A £. 

 Adding 



2P X £=/*BB' + 2P A A-, 

 whence 



P^ — Pa 



BB'=2 x A k. 



Therefore the compression between B and B', which is supposed 

 to be localized at A, is eBB', or 



Px — Pa 



compression at A = 2 ek. 



Respecting the force which has acted at A to give rise to this 

 compression, we observe that it was P x & when the compression 

 began, and P A /c when it ceased. TV r e may therefore put it at 



P - -'- P 

 their mean, or — ^ — - k. Hence the work at A, which is the 



£ p 2 p 2 



product of these two quantities, = —k^e. 



Now our first object shall be to find a limit which must exceed 

 the greatest value that the above can reach. It is evident that 

 this will be given by assigning to P x the utmost value of the 

 compressing force, viz. P, and giving to P A the value zero. It 

 will be recollected that P is the weight of a column of rock 2000 

 miles high and 1 mile in sectional area, and of the density of the 

 crust. 



A superior limit to the whole work on a vertical section of the 

 strip of crust will therefore be 



P 2 



t-tfe; 



