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SCIENCE. 



[Vol. XIV. No. 344 



atures, and carefully considered most of the troublesome details 

 which lay between his theory and its application. While he ad- 

 mitted the nebular hypothesis and an initial fluid state of the earth, 

 he rejected the notion that the observed increase of underground 

 temperature is due to a primitive store of heat. If the earth was 

 originally fluid by reason of its heat, a supposition which Poisson 

 regarded quite gratuitous, he conceived that it must cool and con- 

 solidate from the centre outwards ; so that according to this view 

 the crust of our planet arrived at a condition of stability only after 

 the supply of heat had been exhausted. But Poisson was not at a 

 loss to account for the observed temperature gradient in the earth's 

 crust. Always fertile in hypotheses, he advanced the idea that 

 there exist, by reason of interstellar radiations, great variations in 

 the temperature of space, some vast regions being comparatively 

 cool and others intensely hot, and that the present store of terres- 

 trial heat was acquired by a journey of the solar system through 

 one of the hotter regions. " Such is," he says, " in my opinion, the 

 true cause of the augmentation of temperature which occurs as we 

 descend below the surface of the globe." This hypothesis was the 

 result of Poisson's mature reflection, and as such is well worthy of 

 attention. The notion that there exist hot foci in space was ad- 

 vanced also in another form in 1852 by Rankine, in his interesting 

 speculation on the re-concentration of energy. But whatever we 

 may think of the hypothesis as a whole, it does not appear to be 

 adequate to the case of the earth unless we suppose the epoch of 

 transit through the hot region exceedingly remote and the temper- 

 ature of that region exceedingly high. The continuity of geolog- 

 ical and paleontological phenomena is much better satisfied by the 

 Leibnitzian view of an earth long subject to comparatively constant 

 surface conditions but still active with the energy of its primitive heat. 

 Notwithstanding the indefatigable and admirable labors of Fou- 

 rier and Poisson in this field, it must be admitted that they accom- 

 plished little more than the preparation of the machinery with 

 which their successors have sought and are still seeking to reap 

 the harvest. The difficulties which lay in their way were not 

 mathematical but physical. Had they been able to make out the 

 true conditions of the earth's store of heat, they would undoubtedly 

 have reached a high grade of perfection in the treatment of the 

 problem. The theory as they left it was much in advance of obser- 

 vation, and the labors of their successors have therefore neces- 

 sarily been directed largely towards the determination of the 

 thermal properties of the earth's crust and mass. 



Of those who in the present generation have contributed to our 

 knowledge and stimulated the investigation of this subject, it is 

 hardly necessary to say that we owe most to Sir William Thomson. 

 He has made the question of terrestrial temperatures highly at- 

 tractive and instructive to astronomers and mathematicians, and 

 not less warmly interesting to geologists and paleontologists. 

 Whether we are prepared to accept his conclusions or not, we 

 must all acknowledge our indebtedness to the contributions of his 

 master hand in this field as well as in most other fields of terres- 

 trial physics. The contribution of special interest to us in this 

 connection is his remarkable memoir on the secular cooling of the 

 earth. In this memoir he adopts the simple hypothesis of a solid 

 sphere whose thermal properties remain invariable while it cools 

 by conduction from an initial state of uniform temperature, and 

 draws therefrom certain striking limitations on geologic time. 

 Many geologists were startled by these limitations, and geologic 

 thought and opinion have since been widely influenced by them. 

 It will be of interest, therefore, to state a little more fully and 

 clearly the grounds from which his arguments proceed. Conceive 

 a sphere having a uniform temperature initially, to cool in a medium 

 which instantly dissipates all heat brought by conduction to its 

 surface, thus keeping the surface at a constant temperature. Sup- 

 pose we have given the initial excess of the sphere's temperature 

 over that of the medium. Suppose also that the capacity of the 

 mass of the sphere for diffusion of heat is known, and known to 

 remain invariable during the process of cooling. This capacity is 

 called diffusivity, and is a constant which can be observed. Then 

 from these data the distribution of temperature at any future time 

 can be assigned, and hence also the rate of temperature increase, 

 or the temperature gradient, from the surface towards the centre 

 of the sphere can be computed. It is tolerably certain that the 



heat conducted from the interior to the surface of the earth does 

 not set up any reaction which in any sensible degree retards the 

 process of cooling. It escapes so freely that, for practical pur- 

 poses, we may say it is instantly dissipated. Hence if we can as- 

 sume that the earth had a specified uniform temperature at the 

 initial epoch, and can assume its diffusivity to remain constant, 

 the whole history of cooling is known as soon as we determine the 

 diffusivity and the temperature gradient at any point. Now Sir 

 William Thomson determined a value for the diffusivity from 

 measurements of the seasonal variations of underground tempera- 

 tures, and numerous observations of the increase of temperature 

 with depth below the earth's surface gave an average value for the 

 temperature gradient. From these elements and from an assumed 

 initial temperature of 7,000°, he infers that geologic time is limited 

 to something between twenty million and four hundred million years. 

 He says : " We must allow very wide limits in such an estimate 

 as I have attempted to make ; but I think we may with much proba- 

 bility say that the consolidation cannot have taken place less than 

 twenty million years ago, or we should have more underground 

 heat than we actually have, 'nor more than four hundred million 

 years ago, or we should not have so much as the least observed 

 underground increment of temperature. That is to say, I conclude 

 that Leibnitz's epoch of emergence of the conszstenizor status 

 was probably between those dates." These conclusions were an- 

 nounced twenty-seven years ago, and were republished without 

 modification in 1883. 



Recently, also, Professor Tait, reasoning from the same basis, 

 has insisted with equal confidence on cutting down the upper limit 

 of geologic time to some such figures as ten million or fifteen mil- 

 lion years. As mathematicians and astronomers, we must all 

 confess to a deep interest in these conclusions and the hypothesis 

 from which they flow. They are very important if true. But 

 what are the probabilities ? Having been at some pains to look 

 into this matter, I feel bound to state that, although the hypothesis 

 appears to be the best which can be formulated at present, the odds are 

 against its correctness. Its weak links are the unverified assumptions 

 of an initial uniform temperature and a constant diffusivity. Very 

 likely these are approximations, but of what order we cannot decide. 

 Furthermore, if we accept the hypothesis the odds appear to be 

 against the present attainment of trustworthy numerical results, 

 since the data for calculation obtained mostly from observations 

 on continental areas are far too meagre to give satisfactory average 

 values for the entire mass of the earth. In short, this phase of the 

 case seems to stand about where it did twenty years ago, when 

 Huxley warned us that the perfection of our mathematical mill is 

 no guaranty of the quality of the grist, adding that, " as the grand- 

 est mill will not extract wheat-flour from peas-cods, so pages of 

 formula will not get a definite result out of loose data." 



When we pass from the restricted domain of quantitative results 

 concerning geologic time to the freer domain of qualitative results 

 of a general character, the contractional theory of the earth may be 

 said to still lead all others, though it seems destined to require 

 more or less modification, if not to be relegated to a place of sec- 

 ondary importance. Old as is the notion that the great surface 

 irregularities of the earth are but the outward evidence of a crump- 

 ling crust, it is only recently that this notion has been subjected to 

 mathematical analysis on any thing like a rational basis. About 

 three years ago Mr. T. Mellard Reade announced the doctrine that 

 the earth's crust, from the joint effect of its heat and gravitation, 

 should behave in a way somewhat analagous to a bent beam, and 

 should possess at a certain depth a " level of no strain," corre- 

 sponding to the neutral surface in a beam. Above the level of no 

 strain, according to this doctrine, the strata will be subjected to 

 compression, and will undergo crumpling, while below that level 

 the tendency of the strata to crack and part is overcome by pres- 

 sure which produces what Reade calls " compressive extension," 

 thus keeping the nucleus compact and continuous. A little later 

 the same idea was worked out independently by Mr. Charles Dav- 

 ison, and it has since received elaborate mathematical treatment at 

 the hands of Darwin, Fisher, and others. The doctrine requires 

 for its application a competent theory of cooling, and hence cannot 

 be depended on at present to give anything better than a general 

 idea of the mechanics of crumpling and a rough estimate of the 



