comparable with those of another.  This object was accomplished by Laplace, who discovered that notwithstanding the perpetual fluctuations of the planetary orbits, there exists a fixed plane, to which the positions 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 again diminish.  Thus the angle contained between the two planes will perpetually oscillate within certain limits.  The extent of variation is inconsiderable.  Laplace found that, in consequence of the spheroidal figure of the earth, it is even less than it would otherwise have been.  This will