220 Proceedings of Philosophical Societies. [Sept. 



These results of calculation and experiment appear as though 

 they ought to be considered as part of the small number of truths 

 which geology affords us. 



The two following memoirs of M. Poisson relate also to two 

 fundamental points in the system of the world, which could only 

 be explained by the most subtle analysis. One is concerning 

 the precession of the equinoxes, the other treats of the libralion of 

 the moon. 



" The theory of the variation of arbitrary constant quantities, 

 in questions relating to mechanics, has the remarkable advan- 

 tage of making the solution of the two principal problems of 

 physical astronomy to depend on the same analysis, and to be 

 comprehended in the same formulee ; namely, the determination 

 of the motion of a planet round its centre of gravity, and also that 

 ot the motion of this centre round the sun. In a former memoir 

 upon this theory, and in applying it to the rotatory motion of the 

 earth, I found, to express the differentials of the two elements 

 which determine the position of the equator, some formula?, 

 exactly similar to those relating to the longitude of the nodes, 

 and the inclinations of the planetary orbits. The use of these 

 formulae in determining the secular displacing of the equator 

 may be much simplified by observing, that if the earth was 

 covered with a fluid in equilibrio upon its surface, the function 

 dependent on the perturbating forces which these formulas con- 

 tain is immediately reduced to a converging series by the known 

 theory of the attraction of spheroids. Now on combining this 

 series with the expressions deduced from the variation of con- 

 stant qualities, there will result from thence . . . .the simplest 

 and the most direct solution of the problem of the precession." 



This singular phenomenon, discovered by Hipparchus, deter- 

 mined more exactly by the Arabs, and since that confirmed by 

 the observations of all the modern astronomers, remained unex- 

 plained until the time of Newton. The mechanism of it had 

 been shown by Copernicus ; and this was the newest and most 

 ingenious part of his famous work, on the Celestial Revolutions. 

 He rendered his explanation complex by unnecessarily mixing 

 with it considerations which were totally foreign and useless. 

 From these it was freed by Kepler. The physical cause 

 remained unknown. Kepler's hardy imagination was stopped by 

 a difficulty which was really unsurmountable at that time. New- 

 ton showed that according to the law of gravity, the earth ought 

 to be flattened at the poles, and that the explanation of the 

 precession which had been so long desired resulted from this 

 flattening. All the great geometricians of the last century 

 endeavoured to bring the calculation of Newton to perfection. 

 M. Poisson has now reduced it to its least terms ; but notwith- 

 standing all these simplifications, the demonstration is far from 

 being elementary ; it will always depend upon deep calculations. 

 The phenomenon has been rendered sensible to the eye by a 



