tions of
the various bodies may at any instant be easily referred. This plane
passes through the centre of gravity of the solar system, and its
position is such, that if the movements of the planets be projected upon
it, and if the mass of each planet be multiplied by the area which it
describes in a given time, the sum of such products will be a maximum.
The position of the plane for the year 1750 has been calculated by
referring it to the ecliptic of that year. In this way it has been found
that the inclination of the plane is 1 deg. 35' 31", and that the longitude
of the ascending node is 102 deg. 57' 30". The position of the plane when
calculated for the year 1950, with respect to the ecliptic of 1750,
gives 1 deg. 35' 31" for the inclination, and 102 deg. 57' 15" for the longitude
of the ascending node. It will be seen that a very satisfactory
accordance exists between the elements of the position of the invariable
plane for the two epochs.

_Diminution of the obliquity of the ecliptic._--The astronomers of the
eighteenth century had found, by a comparison of ancient with modern
observations, that the obliquity of the ecliptic is slowly diminishing
from century to century. The researches of geometers on the theory of
gravitation had shown that an effect of this kind must be produced by
the disturbing action of the planets on the earth. Laplace determined
the secular displacement of the plane of the earth's orbit due to each
of the planets, and in this way ascertained the whole effect of
perturbation upon the obliquity of the ecliptic. A comparison which he
instituted between the results of his formula and an ancient observation
recorded in the Chinese Annals exhibited a most satisfactory accordance.
The observation in question indicated the obliquity of the ecliptic for
the year 1100 before the Christian era, to be 23 deg. 54' 2".5. According to
the principles of the theory of gravitation, the obliquity for the same
epoch would be 23 deg. 51' 30".

_Limits of the obliquity of the ecliptic modified by the action of the
sun and moon upon the terrestrial spheroid._--The ecliptic will not
continue indefinitely to approach the equator. After attaining a certain
limit it will then vary in the opposite direction, and the obliquity
will continually increase in like manner as it previously diminished.
Finally, the inclination of the equator and the ecliptic will attain a
certain maximum value, and then the obliquity will a