19 B THE MATHHMATICAL THEORIES OF THE EARTH. 



inecbanics of the ovoluticti of a solar system from a swarm of meteor- 

 ites, arc still far from l>eiii<;- clearly iiuule out. 



Time does not permit me to make anything but the briefest allusion 

 to the comitaratively new science of m:'.thematical meteorology with 

 its already considerable list of well-denned theories pressing for accept- 

 ance or rejection. Nor need I say more with reference to those older 

 mathematical questions of the tides and terrestial magnetism than that 

 they are still unsettled. These and many other questions, old and new, 

 might serve equally well to illustrate the principal /act that this address 

 has been designed to emphasize, namely, that the mathematical theories 

 of the earth already advanced and elaborated are by no means com- 

 plete, 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 sjieak to and for mathematicians and astronomers, 

 it may be permissible to offer, in closing, a single suggestion, which will 

 perhaps help us to orient ourselves aright in our various tields of re- 

 search. 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 min- 

 ima in its general tendency towards the limit of perfect knowledge ; and 

 it seems not improbable that the curve would show throughout some 

 portions of its length a more or less definitely i)eriodic 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 i)eriods 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 max- 

 imum of the epoch of Newton near the end of the seventeenth century, 

 with the equally marked nuiximum of the epoch of Laplace near the end 

 of the eighteenth century ; and, judging from the recent revival of geo- 

 desy 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 ])eriods which followed the epochs of Newton and 

 Laplace are less definitely marked but not less noteworthy and instruct- 

 ive. 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 

 l)roduce these minima periods, and it would be an interesting study in 

 philosophir history to trace out the tendency and efiect 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, 



