THE THEORY OF FISHER. 197 



The zone of rising temperature, which would be narrowed down and 

 finally disappear as the conduction progressed, extends at the start from 

 the surface to a depth of about 700 miles. The total rise of temperature 

 would be trivial near the extremes of this zone, but more marked toward 

 its interior. According to the residuals in column 6, table 5, the rise may 

 be expected to be most significant in the neighborhood of a depth of about 

 400 miles, reaching in that region, with allowance for even a considerable 

 percentage of decline in the first component, a value of probably at least two 

 one-hundredths of the central temperature, or 400°, which is the increase 

 over initial temperatures ranging about 1,200°. Such a change might 

 carry the substance through its temperature of fusion, even under the high 

 pressures there sustained. 



The foregoing sketch of the thermal process lacks, of course, the pre- 

 cision which could be reached through a computation extended to include 

 all components of sensible influence; this also would alone suffice to yield 

 an accurate estimate of the time-intervals implied, which would probably 

 be counted in billions of years for the epoch during which rising tempera- 

 tures occur. It must be noted also that a small outstanding portion of the 

 energy of impact might alter the features of the thermal process seriously, 

 especially in the strata near the surface, where the very fact of the oc- 

 currence of the rising temperatures may be said to be due to that relative 

 deficiency in the heat from the purely compressional source which is rep- 

 resented by the upward concavity of the initial temperature-curve. 



It is desirable, however, to know more precisely the result of the complete 

 computation, under at least one set of reasonable assumptions, which, in 

 the absence of experimental information, may fairly be conditioned by the 

 practicability of the calculations; for instance, through the use of a suitable 

 alternative hypothesis regarding the specific heat. This has thus far been 

 treated as a constant, but there would seem to be some reason, under a 

 molecular theory, for supposing it to decrease with increase of density, since 

 the consequent diminution of the intermolecular spaces might tend to throw 

 more of the energy into the " unordered " kinetic or thermal form, by inter- 

 fering with the " ordered " movements which have been conceived by Hertz 

 and others to account for the storage of energy apparently in latent or 

 potential form. It will be of interest to see how far the thermal process 

 described above is modified by supposing the specific heat thus variable. 



A simple supposition on this point, hardly more arbitrary than any other 

 that could be made and having at least the merit of yielding tractable form- 

 ulas, is that o is inversely proportional to p, or op = o^^. With constant 

 " calorimetric " conductivity X this makes the " thermometric " conductivity 



— also constant, and reduces equation (55) to the form: 

 op 



giving for the fundamental functions: 



^ sin nnx (67) 



^" rntx 



