ed by the help of our clocks
and of the graduated circles on the instruments. These observations are
no doubt wonderfully accurate; but they do not, they cannot, possess
absolute accuracy in the mathematical sense of the word. We can, for
instance, determine the place of a planet with such precision that it
is certainly not one second of arc wrong; and one second is an extremely
small quantity. A foot-rule placed at a distance of about forty miles
subtends an angle of a second, and it is surely a delicate achievement
to measure the place of a planet, and feel confident that no error
greater than this can have intruded into our result.

When we compare the results of observation with the calculations
conducted on the assumption of the truth of Kepler's laws, and when we
pronounce on the agreement of the observations with the calculations,
there is always a reference, more or less explicit, to the inevitable
errors of the observations. If the calculations and observations agree
so closely that the differences between the two are minute enough to
have arisen in the errors inseparable from the observations, then we are
satisfied with the accordance; for, in fact, no closer agreement is
attainable, or even conceivable. The influence which the want of
rigidity exercises on the fulfilment of the laws of Kepler can be
estimated by calculation; it is found, as might be expected, to be
extremely small--so small, in fact, as to be contained within that
slender margin of error by which observations are liable to be affected.
We are thus not able to discriminate by actual measurement the effects
due to the absence of rigidity; they are inextricably hid among the
small errors of observation.

The argument on which we are to base our researches is really founded on
a very familiar phenomenon. There is no one who has ever visited the
sea-side who is not familiar with that rise and fall of the sea which we
call the tide. Twice every twenty-four hours the sea advances on the
beach to produce high tide; twice every day the sea again retreats to
produce low tide. These tides are not merely confined to the coasts;
they penetrate for miles up the courses of rivers; they periodically
inundate great estuaries. In a maritime country the tides are of the
most profound practical importance; they also possess a significance of
a far less obvious character, which it is our object now to investigate.

These daily pulses of the ocean have long ceas