ime agrees very
closely with the actual, but not exactly. Why not exactly?

Partly because of the acceleration of the moon's mean motion, as
explained in the lecture on Laplace (p. 262). The orbit of the earth was
at that time getting rounder, and so, as a secondary result, the speed
of the moon was slightly increasing. It is of the nature of a
perturbation, and is therefore a periodic not a progressive or
continuous change, and in a sufficiently long time it will be reversed.
Still, for the last few thousand years the moon's motion has been, on
the whole, accelerated (though there seems to be a very slight retarding
force in action too).

Laplace thought that this fact accounted for the whole of the
discrepancy; but recently, in 1853, Professor Adams re-examined the
matter, and made a correction in the details of the theory which
diminishes its effect by about one-half, leaving the other half to be
accounted for in some other way. His calculations have been confirmed by
Professor Cayley. This residual discrepancy, when every known cause has
been allowed for, amounts to about one hour.

The eclipse occurred later than calculation warrants. Now this
would have happened from either of two causes, either an
acceleration of the moon in her orbit, or a retardation of the
earth in her diurnal rotation--a shortening of the month or a
lengthening of the day, or both. The total discrepancy being, say,
two hours, an acceleration of six seconds-per-century per century
will in thirty-six centuries amount to one hour; and this,
according to the corrected Laplacian theory, is what has occurred.
But to account for the other hour some other cause must be sought,
and at present it is considered most probably due to a steady
retardation of the earth's rotation--a slow, very slow, lengthening
of the day.

The statement that a solar eclipse thirty-six centuries ago was an
hour late, means that a place on the earth's surface came into the
shadow one hour behind time--that is, had lagged one twenty-fourth
part of a revolution. The earth, therefore, had lost this amount in
the course of 3600 x 365-1/4 revolutions. The loss per revolution
is exceedingly small, but it accumulates, and at any era the total
loss is the sum of all the losses preceding it. It may be worth
while just to explain this point further.

Suppose the earth loses a