.; another a little before Christ; and
one, the oldest of all of which any authentic record has been preserved,
observed by the Chaldaean astronomers in Babylon in the reign of
Hezekiah.

Calculating back to this splendid old record of a solar eclipse, over
the intervening 2,400 years, the calculated and the observed times were
found to disagree by nearly two hours. Pondering over an explanation of
the discrepancy, Halley guessed that it must be because the moon's
motion was not uniform, it must be going quicker and quicker, gaining
twelve seconds each century on its previous gain--a discovery announced
by him as "the acceleration of the moon's mean motion." The month was
constantly getting shorter.

What was the physical cause of this acceleration according to the theory
of gravitation? Many attacked the question, but all failed. This was the
problem Laplace set himself to work out. A singular and beautiful result
rewarded his efforts.

You know that the earth describes an elliptic orbit round the sun: and
that an ellipse is a circle with a certain amount of flattening or
"excentricity."[26] Well, Laplace found that the excentricity of the
earth's orbit must be changing, getting slightly less; and that this
change of excentricity would have an effect upon the length of the
month. It would make the moon go quicker.

One can almost see how it comes about. A decrease in excentricity means
an increase in mean distance of the earth from the sun. This means to
the moon a less solar perturbation. Now one effect of the solar
perturbation is to keep the moon's orbit extra large: if the size of its
orbit diminishes, its velocity must increase, according to Kepler's
third law.

Laplace calculated the amount of acceleration so resulting, and found it
ten seconds a century; very nearly what observation required; for,
though I have quoted observation as demanding twelve seconds per
century, the facts were not then so distinctly and definitely
ascertained.

This calculation for a long time seemed thoroughly satisfactory, but it
is not the last word on the subject. Quite lately an error has been
found in the working, which diminishes the theoretical
gravitation-acceleration to six seconds a century instead of ten, thus
making it insufficient to agree exactly with fact. The theory of
gravitation leaves an outstanding error. (The point is now almost
thoroughly understood, and we shall return to it in Lecture XVIII).

But anoth