48 ASTRONOMY 



mathematical difficulties of this problem and the im- 

 portance of its solution for Astronomy, particularly for 

 an understanding of the motion of the moon, challenged 

 the attention and abilities of the mathematicians of the 

 entire world. No great mathematician, until very 

 recent times, has escaped the charm of this problem. 

 From France, however, has come the greater part of our 

 present knowledge of a subject which has tested to 

 the utmost the strength of the human intellect since the 

 time of the immortal NEWTON. The first two analytical 

 theories of the motion of the moon were presented on the 

 same day to the Paris Academy by CLAIRAUT and by 

 D'ALEMBERT (1717-1783), and these were the first efforts 

 at an analytical solution of the problem of three bodies. 

 D'ALEMBERT introduced even the rotation of the earth 

 into his theories, and thus developed the theory of the 

 precession of the equinoxes. The first rigorous solution 

 of the problem of three bodies, due to LAGRANGE (1736- 

 1813), is contained in a paper of great elegance published 

 in 1772. Many other theorems of great importance were 

 contained in his later papers. In his epochal "Meca- 

 nique analytique" he made it his boast that he had freed 

 the subject of mechanics from geometrical intuition, and 

 brought all of its problems into the domain of pure 

 analysis. In striking contrast to the method of 

 Lagrange was that of POISSON (1781-1840), who strove 

 to develop the geometrical intuitions to the utmost in 

 the solutions of mechanical problems. 



LAPLACE (1749-1827), however, even more than 

 Lagrange, devoted himself to the mechanics of the 

 celestial bodies. The theory of the motion of the moon, 

 the mutual perturbations of the planets and their satel- 

 lites, and the determination of the orbits of comets, 

 received masterly treatment in his hands; and no prob- 

 lem in this field escaped his critical attention. His 



