FUNDAMENTAL PROBLEMS OF GEOLOGY. 257 



subsequent cooling were determined, on several assumptions as to 

 conductivity and internal density. I have not thought it worth 

 while to regard the specific heat as other than constant, because of 

 the uncertainty attending (i) the application of Fourier's equations 

 at such high temperatures, and (2) the very definition of tempera- 

 ture under these conditions. 



This much is practically read}-- for publication, except the round- 

 ing' off of the mode of presentation. I think it would hardly pay 

 to attempt more in this direction just now, and I plan to offer this, 

 with a critique of the assumptions, as part i of the paper to be sent 

 in shortly. 



The energy so generated is, however, not the entire amount of 

 gravitational energy, though perhaps in any ordinary case the major 

 portion. The reason is that — assuming, as we have done, that the 

 pressure depends only on the density — a dynamic equilibrium is 

 possible only in the final state of the mass ; consequently the pas- 

 sage from the homogeneous to the compressed condition must be 

 accompanied by the generation, in addition to the strictly compres- 

 sional energy, of the kinetic energy of a more or less oscillatory 

 motion, which would be transformed to heat by the internal fric- 

 tion due to the viscosity of the mass. The problem of determining 

 how this portion of the energy is localized is a very puzzling one. 

 The exact determination of every phase of this motion is hardly to 

 be expected, since even the analogous problem for a globe of perfect 

 gas leads to equations of whose solution practically nothing is 

 known. However, the features of the solution in certain analo- 

 gous, though much simpler, cases of damped acoustic and electro- 

 magnetic vibrations suggest that the ' ' asymptotic ' ' case for infinite 

 coefficient of viscosity can be made more easily accessible, and this 

 result would probably be useful, since the viscosity of lava is actu- 

 ally so great. I am hopeful of success in this direction, but have 

 nothing complete to offer yet. 



The theory needs to be completed in another respect before I can 

 be satisfied with it. The contraction due to cooling makes the gen- 

 eration of heat proceed parallel with its conduction. On account of 

 the small coefficient of expansion, the heat thus added is negligible 

 in a small bod}-, but becomes an important portion of the whole in 

 a mass as large as the earth. Hence to follow the process strictl}^ 

 it would be necessary to consider the conduction and contraction as 

 simultaneous, following the initial compression. The difficulties in 

 the way here are serious. 



