Theory of Volcanic Energy. 307 



cooling of the nucleus, from which it passes through the crust. 

 Consequently he assumes for the coefficient of contraction a 

 mean of those higher values which he has shown experimentally 

 to obtain for exalted temperatures. In passing, it may be 

 remarked that this seems to be opposed to Sir W. Thomson's 

 conclusions in his paper "On the Secular Cooling of the Earth"*, 

 in which his diagram shows that, if no convection-currents 

 exist within the nucleus, the heat in the deep interior of 

 the earth has scarcely decreased at all since it was all melted, 

 but that the loss has taken place chiefly from the outer portions, 

 and continues to do so still. Hence it is doubtful whether Mr. 

 Mallet's mode of estimating the contraction is admissible, and 

 whether he has not consequently made the annual descent of 

 the surface too great. 



Having in this manner estimated the annual descent of the 

 shell, he calculates the amount of volume by which the shell 

 will, after its descent, be found too large to fit the contracted 

 nucleus; and he supposes that the superabundant matter is 

 crushed and extruded, giving forth the amount of heat ap- 

 propriate to its volume, as estimated from the experiments 

 discussed in his original paper. He then compares this amount 

 with the amount of heat estimated to be sufficient to maintain 

 volcanic energy for a year, and finds it somewhat greater than 

 sufficient if the shell be 400 miles thick. 



Now it is obvious that this mode of arguing assumes the 

 numerical correctness of the experimental results and their 

 applicability to the case of deeply buried rocks. But it seems 

 that the whole subject will be placed on a more intelligible basis 

 if some comparisons be made which may be independent of this 

 particular assumption. 



With a crust 400 miles thick Mr. Mallet reckons that the 

 annual radial contraction would be 0*00000000928 mile, or 

 0-00058995 inch. 



We will then proceed to find the number of units of heat due 

 to the annual descent of the crust on these suppositions : — 



R, r the external and internal radii of the crust, 

 d its descent, 

 p its density. 



Then the work of descent is approximately equal to 



4ffg?R fl (R-r)£ 



* Trans. Roy. Soc. Edinburgh, vol. xxiii. pt. i. p. 157. Phil. Mag, 

 4 th levies, vol. xxv. Also Thomson andTait's Nat. Phil., App. D. 



X 2 



