282 Mathematical Theories of the Earth. — ^Yoodward. 
Time does not permit me to make anything but the briefest allusion 
to the comparatively new science of mathematical meteorology, with 
its already considerable list of well-defined theories pressing for 
acceptance or rejection. Nor need I say more with reference to th.)se 
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 mathe- 
matical theories of the earth already 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 astrono- 
mers, it may be permissible to offer, in closing, a single suggestion, 
which will perhaps help us to orient ourselves aright in our various 
fields of i-esearch. 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 improbable that the curve would show 
throughout some portions of its length a more 6r less definitely peri- 
odic 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 centuty ; and judging 
from the recent revival of geodesy and astronomy in Europe, and 
from the well-nigh general activity in mathematical and geological re- 
search, we may hope if not expect that the end of the present century 
will signalize a similar epoch of productive activity. The minima peri- 
ods which followed the of epochs Newton and Laplace are less defi- 
nitely 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 dimished 
energy, periods during which those who kept alive the spirit of inves- 
tigation were almost as conspicuous for their isolation as for their 
distinguished abilities. Many causes, of course, contributed to pro- 
duce these minima periods, and it would be an interesting study in 
philosophic history to trace out the tendency and efi'ect 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 immed- 
iately after the attainment of any marked success or advance. I refer 
