is previously suggested, and to some extent,
elaborated, by Kant.

A list of some of the principal astronomical researches of Lagrange and
Laplace:--Libration of the moon. Long inequality of Jupiter and Saturn.
Perturbations of Jupiter's satellites. Perturbations of comets.
Acceleration of the moon's mean motion. Improved lunar theory.
Improvements in the theory of the tides. Periodic changes in the form
and obliquity of the earth's orbit. Stability of the solar system
considered as an assemblage of rigid bodies subject to gravity.

The two equations which establish the stability of the solar system
are:--

_Sum (me^2[square root]d) = constant,_

and

_Sum (m tan^2[theta][square root]d) = constant;_

where _m_ is the mass of each planet, _d_ its mean distance from the
sun, _e_ the excentricity of its orbit, and [theta] the inclination
of its plane. However the expressions above formulated may change for
individual planets, the sum of them for all the planets remains
invariable.

The period of the variations in excentricity of the earth's orbit is
86,000 years; the period of conical revolution of the earth's axis is
25,800 years. About 18,000 years ago the excentricity was at a maximum.

LECTURE XI

LAGRANGE AND LAPLACE--THE STABILITY OF THE SOLAR SYSTEM, AND THE NEBULAR
HYPOTHESIS

Laplace was the son of a small farmer or peasant of Normandy. His
extraordinary ability was noticed by some wealthy neighbours, and by
them he was sent to a good school. From that time his career was one
brilliant success, until in the later years of his life his prominence
brought him tangibly into contact with the deteriorating influence of
politics. Perhaps one ought rather to say trying than deteriorating; for
they seem trying to a strong character, deteriorating to a weak one--and
unfortunately, Laplace must be classed in this latter category.

It has always been the custom in France for its high scientific men to
be conspicuous also in politics. It seems to be now becoming the fashion
in this country also, I regret to say.

The _life_ of Laplace is not specially interesting, and I shall not go
into it. His brilliant mathematical genius is unquestionable, and almost
unrivalled. He is, in fact, generally considered to come in this respect
next after Newton. His talents were of a more popular order than those
of Lagrange, and accordingly he acquired fame and rank, and rose to the
highest dignities. Nevertheles