ar period suggested the explanation. It is the
period in which the moon goes through all her changes--a period known to
the ancients as the lunar cycle, or Metonic cycle, and used by them to
predict eclipses. It is still used for the first rough approximation to
the prediction of eclipses, and to calculate Easter. The "Golden Number"
of the Prayer-book is the number of the year in this cycle.

The cause of the second inequality, or apparent periodic motion of the
stars, Bradley made out to be a nodding motion of the earth's axis.

The axis of the earth describes its precessional orbit or conical
motion every 26,000 years, as had long been known; but superposed upon
this great movement have now been detected minute nods, each with a
period of nineteen years.

The cause of the nodding is completely accounted for by the theory of
gravitation, just as the precession of the equinoxes was. Both
disturbances result from the attraction of the moon on the non-spherical
earth--on its protuberant equator.

"Nutation" is, in fact, a small perturbation of precession. The motion
may be observed in a non-sleeping top. The slow conical motion of the
top's slanting axis represents the course of precession. Sometimes this
path is loopy, and its little nods correspond to nutation.

The probable existence of some such perturbation had not escaped the
sagacity of Newton, and he mentions something about it in the
_Principia_, but thinks it too small to be detected by observation. He
was thinking, however, of a solar disturbance rather than a lunar one,
and this is certainly very small, though it, too, has now been observed.

Newton was dead before Bradley made these great discoveries, else he
would have been greatly pleased to hear of them.

These discoveries of aberration and nutation, says Delambre, the great
French historian of science, secure to their author a distinguished
place after Hipparchus and Kepler among the astronomers of all ages and
all countries.

NOTES TO LECTURE XI

_Lagrange_ and _Laplace_, both tremendous mathematicians, worked very
much in alliance, and completed Newton's work. The _Mecanique Celeste_
contains the higher intricacies of astronomy mathematically worked out
according to the theory of gravitation. They proved the solar system to
be stable; all its inequalities being periodic, not cumulative. And
Laplace suggested the "nebular hypothesis" concerning the origin of sun
and planets: a hypothes