OBLIQUITY OF THE ECLIPTIC. 369 



are perpetually varying in position. It becomes therefore 

 desirable to ascertain some fixed plane to which the move- 

 ments of the planets in all ages may be referred, so that the 

 observations of one epoch might be rendered readily compar- 

 able 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 in- 

 stant be easily referred. This plane passes through the cen- 

 tre of gravity of the solar system, and its position is such, that 

 if the movements of the planets be projected upon it, and it 

 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 35' 31", and that the longitude of the ascending node is 

 [02 57/ 30". The position of the plane when calculated for 

 year 1950, with respect to the ecliptic of 1750, gives 



35' 31" for the inclination, and 102 57' 15" for the longi- 

 tude of the ascending node. It will be seen that a very sat- 

 isfactory accordance exists between the elements of the posi- 

 tion 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 deter- 

 mined 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 



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