ian have been awakened into action is by the effort to
remove some glaring discrepancy between an imperfect theory and the
facts of observation. The genius of a Laplace or a Lagrange was
expended, and worthily expended, in efforts to show how one planet
acted on another planet, and produced irregularities in its orbit; the
genius of an Adams and a Leverrier was nobly applied to explain the
irregularities in the motion of Uranus, and to discover a cause of
those irregularities in the unseen Neptune. In all these cases, and in
many others which might be mentioned, the mathematician has been
stimulated by the laudable anxiety to clear away some blemish from the
theory of gravitation throughout the system. The blemish was seen to
exist before its removal was suggested. In that application of
mathematics with which we have been concerned in these lectures the
call for the mathematician has been of quite a different kind. A
certain familiar phenomenon on our sea-coasts has invited attention.
The tidal ripples murmur a secret, but not for every ear. To interpret
that secret fully, the hearer must be a mathematician. Even then the
interpretation can only be won after the profoundest efforts of
thought and attention, but at last the language has been made
intelligible. The labour has been gloriously rewarded, and an
interesting chapter of our earth's history has for the first time been
written.

In the progress of these lectures I have sought to interest you in
those profound investigations which the modern mathematician has made
in his efforts to explore the secrets of nature. He has felt that the
laws of motion, as we understand them, are bounded by no
considerations of space, are limited by no duration of time, and he
has commenced to speculate on the logical consequences of those laws
when time of indefinite duration is assumed to be at his disposal.
From the very nature of the case, observations for confirmation were
impossible. Phenomena that required millions of years for their
development cannot be submitted to the instruments in our
observatories. But this is perhaps one of the special reasons which
make such investigations of peculiar interest, and entitle us to speak
of the revelations of Time and Tide as a romance of modern science.

INDEX.

Aberdeen, tides at, 23
Action and reaction, 69
Adams, discoverer of Neptune, 186
Admiralty Manual of Scientific Inquiry, 30, 31, 34