An introduction to mathematics, by A. N. Whitehead.

TRIGONOMETRY 193
duced. We leave out of account the exceptional influence of winds which cannot be
foreseen. The general problem of the harmonic analysis of the tides is to find sets of
terms like those in the expression on page
191 above, such that each set will give with
approximate accuracy the contribution of
the tide-generating influences of one "period"
to the height of the tide at any instant. The
argument x will therefore be the time reckoned
from any convenient commencement.
Again, the motion of vibration of a violin
string is submitted to a similar harmonic
analysis, and so are the vibrations of the
ether and the air, corresponding respectively
to waves of light and waves of sound. We
are here in the presence of one of the fundamental processes of mathematical physicsnamely, nothing less than its general method
of dealing with the great natural fact of
Periodicity.