166 LAPLACE. 



Aciulemy of Sciences an analytical method for determining the elements 

 of a comet's orbit. This method has been extensively employed in 

 France. Indeed, previously to the appearance of Olbers's method, about 

 the close of the last century, it furnished the easiest -md most expedi- 

 tions process hitherto devised for calculating the parabolic elements of 

 a comet's orbit. 



Invariable plane of the solar system. — In consequence of the mutual 

 perturbations of the different bodies of the planetary system, the planes 

 of the orbits in which they revolve are perpetually varying in position. 

 It becomes, therefore, desirable to ascertain some fixed plane to which 

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

 observations of one epoch might be rendered readily comparable with 

 those of another. This object was accomplished by Laplace, who dis- 

 covered 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 center of gravity of the solar system, and its position is snch 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° 35' 31", and that the longitude of the ascending node is 102^ 

 57' 30". The position of the plane when calculated for the year 1950, 

 with respect to the ecliptic of 1750, gives 1° 35' 31" for the inclination, 

 and 102^ 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 ohliqnity of the ecliptic. — The astronomers of the 

 eigliteentli 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 tbeory of gravi- 

 tation had shown that an effect of this kind must be produced by the 

 disturbing action of the planets on the earth. Laplace determined the 

 sccalar 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 tiie 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 obser- 

 vation in question indicated the obliquity of the ecliptic for the year 1100 

 before the Christian era to be 23° 54' 2"-5. According to the principles 

 of the theory of gravitation, the obliquity for the same epoch would be 

 230 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 



