FUNDAMENTAL PROBLEMS OF GEOLOGY 265 



likely to prove fruitless. A function of preliminary mathematical 

 inquiry is to discover productive fields, as well as desert tracts, 

 before serious and expensive cultivation is attempted. 



More specifically, Mr. I^unn has had under consideration the fol- 

 lowing problems : 



(a) The determination of the original distribution of temperature 

 in a solid earth where heat energy is supposed to have arisen from 

 gravitative compression, on various assumptions as to internal den- 

 sity and specific heat. The assumptions most closely related to the 

 Legendre-Ivaplace law of internal density have been given prece- 

 dence. The determinations, however, are given such forms that a 

 short computation is sufficient to reduce to numbers the results of 

 any assumed law likely to be entertained at any future time. 



(3) The determination of the total heat energy due to a merely 

 gravitative contraction of the earth mass, the assumptions in this 

 case corresponding to those under (a). The development involves 

 the proof of the consistency of the points of view assumed in (a) and 

 (d) relative, the one to the distribution of heat, the other to its 

 total amount. Comparison has also been instituted between the chief 

 bodies of the solar system, in these particulars, for the sake of the 

 collateral light they may throw on the earth problem. The imme- 

 diate inquiry does not contemplate more than first approximations, 

 but it is hoped that it will show the lines along which further and 

 more involved researches may best be attempted, by excluding barren 

 ground and narrowing the range of hopeful inquiry. 



(c) Postulating the previous determinations of the initial distribu- 

 tion of temperature, a theoretical determination of the history of the 

 cooling of the earth has been attempted, assuming various laws as 

 to conductivity. This has been found to offer very serious difficul- 

 ties, both in the analysis and construction of fonuulas, and in the 

 complexity of the computations. Enough has been done, however, 

 to show the probable validity of the conception, derived from pre- 

 liminary studies, that the initial stages of redistribution of heat in- 

 volved an actual increase of temperature in regions just below the 

 outer shell, and that this extended over some length of time from the 

 beginning of the process. 



(d) Some attention has been given to such collateral problems in 

 elasticity as were likely to throw light on the assumptions made in 

 the previous computations, especially those calculated to supplement 

 the meager experimental data. Mr. Lunn has also cooperated in the 

 informal discussion of other themes embraced in our joint studies. 



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