September 6, 1889.] 



SCIENCE 



171 



magnitudes of the resulting effects. Using Thomson's hypothesis, 

 it appears that the stratum of no strain moves downward from the 

 surface of the earth at a nearly constant rate during the earlier 

 stages of cooling, but more slowly during later stages. Its depth 

 is independent of the initial temperature of the earth ; and if we 

 adopt Thomson's value of the diffusivity, it will be about two and 

 a third miles below the surface in a hundred million years from the 

 beginning of cooling, and a little more than fourteen miles below 

 the surface in seven hundred million years. The most important 

 inference from this theory is that the geological effects of secular 

 cooling will be confined for a very long time to a comparatively thin 

 crust. Thus, if the earth is a hundred million years old, crump- 

 ling should not extend much deeper than two miles. A test to 

 which the theory has been subjected, and one which some consider 

 crucial against it, is the volumetric amount of crumpling shown by 

 the earth at the present time. This is a difficult quantity to esti- 

 mate, but it appears to be much greater than the theory alone can 

 account for. 



The opponents of the contractional theory of the earth, believ- 

 ing it quantitatively insufficient, have recently revived and elabo- 

 rated an idea first suggested by Babbage and Herschel in explana- 

 tion of the greater folds and movements of the crust. This idea 

 figures the crust as being in a state bordering on hydrostatic equi- 

 librium, which cannot be greatly disturbed without a readjustment 

 and consequent movement of the masses involved. According to 

 this view, the transfer of any considerable load from one area to 

 another is followed sooner or later by a depression over the loaded 

 area and a corresponding elevation over the unloaded one ; and in 

 a general way it is inferred that the elevation of continental areas 

 tends to keep pace with erosion. The process by which this bal- 

 ance is maintained has been called " isostacy," and the crust is said 

 to be in an isostatic state. The dynamics of the superficial strata 

 with the attendant phenomena of folding and faulting, are thus re- 

 ferred to gravitation alone, or to gravitation and whatever oppos- 

 ing force the rigidity of the strata may offer. In a mathematical 

 sense, however, the theory of isostacy is in a less satisfactory state 

 than the theory of contraction. As yet we can see only that isos- 

 tacy is an efficient cause if once set in action ; but how it is started 

 and to what extent it is adequate remains to be determined. 

 Moreover, isostacy alone does not seem to meet the requirements 

 of geological continuity, for it tends rapidly towards stable equilib- 

 rium, and the crust ought therefore to reach a state of repose early 

 in geologic time. But there is no evidence that such a state has 

 been attained, and but little if any evidence of diminished activity 

 in crustal movements during recent geologic time. Hence we in- 

 fer that isostacy is competent only on the supposition that it is kept 

 in action by some other cause tending constantly to disturb the 

 equilibrium which would otherwise result. Such a cause is found 

 in secular contraction, and it is not improbable that these two 

 seemingly divergent theories are really supplementary. 



Closely related to the questions of secular contraction and the 

 mechanics of crust movements are those vexed questions of earth- 

 quakes, volcanism, the liquidity or solidity of the interior, and the 

 rigidity of the earth's mass as a whole, — all questions of the great- 

 est interest but still lingering on the battle-fields of scientific opin- 

 ion. Many of the " thrice slain " combatants in these contests 

 would fain risk being slain again ; and whether our foundation be 

 liquid or solid, or to speak more precisely, whether the earth may 

 not be at once highly plastic under the action of long continued 

 forces and highly rigid under the action of periodic forces of short 

 period, it is pretty certain that some years must elapse before the 

 arguments will be convincing to all concerned. The difficulties 

 appear to be due principally to our profound ignorance of the prop- 

 erties of matter subject to the joint action of great pressure and 

 great heat. The conditions which exist a few miles beneath the 

 surface of the earth are quite beyond the reach of laboratory tests 

 as hitherto developed, but it is not clear how our knowledge is to 

 be improved without resort to experiments of a scale in some de- 

 gree comparable with the facts to be explained. In the meantime, 

 therefore, we may expect to go on theorizing, adding to the long 

 list of dead theories which mark the progress of scientific thought, 

 with the hope of attaining the truth not so much by direct discov- 

 ery as by the laborious process of eliminating error. 



When we take a more comprehensive view of the problems pre- 

 sented by the earth, and look for light on their solution in theories 

 of cosmogony, the difficulties which beset us are no less numerous 

 and formidable than those encountered along special lines of at- 

 tack. Much progress has recently been made, however, in the 

 elaboration of such theories. Roche, Darwin, and others have 

 done much to remove the nebulosity of Laplace's nebular hypothe- 

 sis. Poincare and Darwin have gone far towards bridging the 

 gaps which have long rendered the theory of rotating fluid masses 

 incomplete. Pioncare has in fact shown us how a homogeneous 

 rotating mass might, through loss of heat and consequent contrac- 

 tion, pass from the spheroidal form to the Jacobian ellipsoidal form, 

 and thence, by reason of its increasing speed of rotation, separate 

 into two unequal masses. Darwin, starting with a swarm of me- 

 teorites and gravitation as a basis, has reached many interesting 

 and instructive results in the endeavor to trace out the laws of 

 evolution of a planetary system. But notwithstanding the splendid 

 researches of these and other investigators in this field, it must be 

 said that the real case of the solar system, of the earth and moon, 

 still defies analysis ; and that the m^echanics of the segregation of 

 a planet from the sun or of a satellite from a planet, if such an event 

 has ever happened, or of the mechanics of the evolution of a solar 

 system from a swarm of meteorites, are still far from being clearly 

 made out. 



Time does not permit me to make anything but the briefest al- 

 lusion to the comparatively new science of mathematical meteor- 

 ology, with its already considerable list of well-defined theories 

 pressing for acceptance or rejection. Nor need I say more with 

 reference to those older mathematical questions of the tides and 

 terrestrial magnetism than that they are still unsettled. These 

 and many other questions, old and new, might serve equally well 

 to illustrate the principal fact this address has been designed to 

 emphasize, namely, that the mathematical theories of the earth al- 

 ready advanced and elaborated are by no means complete, and that no 

 mathematical Alexander need yet pine for other worlds to conquer. 

 Speculations concerning the course and progress of science are 

 usually untrustworthy if not altogether fallacious. But, being dele- 

 gated for the hour to speak to and for mathematicians and astron- 

 omers, it may be permissible to offer, in closing, a single sugges- 

 tion, which will perhaps help us to orient ourselves aright in our 

 various fields of research. If the curve of scientific progress in 

 any domain of thought could be drawn, there is every reason to 

 believe that it would exhibit considerable irregularities. There 

 would be marked maxima and minima in its general tendency 

 towards the limit of perfect knowledge ; and it seems not improb- 

 able that the curve would show throughout some portions of its 

 length a more or less definitely periodic succession of maxima and 

 minima. Races and communities as well as individuals, the armies 

 in pursuit of truth as well as those in pursuit of plunder, have their 

 periods of culminating activity and their periods of placid repose. 

 It is a curious fact that the history of the mathematical theories of 

 the earth presents some such periodicity. We have the marked 

 maximum of the epoch of Newton near the end of the seventeenth 

 century, with the equally marked maximum of the epoch of Laplace 

 near the end of the eighteenth century ; and, judging from the re- 

 cent revival of geodesy and astronomy in Europe, and from the 

 well-nigh general activity in mathematical and geological research, 

 we may hope if not expect that the end of the present century will 

 signalize a similar epoch of productive activity. The minima 

 periods which followed the epochs of Newton and Laplace are 

 less definitely marked but not less noteworthy and instructive. 

 They were not periods of placid repose ; to find such one must go 

 back into the night of the middle ages ; but they were periods of 

 greatly diminished energy, periods during which those who kept 

 alive the spirit of investigation were almost as conspicuous for 

 their isolation as for their distinguished abilities. Many causes, of 

 course, contributed to produce these minima periods, and it would 

 be an interesting study in philosophic history to trace out the ten- 

 dency and effect of each cause. It is desired here, however, to 

 call attention to only one cause which contributed to the somewhat 

 general apathy of the periods mentioned, and which always 

 threatens to dampen the ardor of research immediately after the 

 attainment of any marked success or advance. I refer to the im- 



