108 HISTORY OF MECHANICS. 



8. Mecanique Celeste, &p. Laplace also resumed 

 the consideration of the secular changes ; and, 

 finally, undertook his vast work, the Mecanique 

 Celeste, which he intended to contain a complete 

 view of the existing state of this splendid depart- 

 ment of science. We may see, in the exultation 

 which the author obviously feels at the thought of 

 erecting this monument of his age, the enthusiasm 

 which had been excited by the splendid course of 

 mathematical successes of which I have given a 

 sketch. The two first volumes of this great work 

 appeared in 1799. The third and fourth volumes 

 were published in 1802 and 1805 respectively. 

 Since its publication, little has been added to the 

 solution of the great problems of which it treats. 

 In 1808, Laplace presented to the French Bureau 

 des Longitudes, a Supplement to the Mecanique 

 Celeste ; the object of which was to improve still 

 further the mode of obtaining the secular variations 

 of the elements. Poisson and Lagrange proved 

 the invariability of the major axes of the orbits, as 

 far as the second order of the perturbing forces. 

 Various other authors have since laboured at this 

 subject. Burckhardt, in 1808, extended the per- 

 turbing function as far as the sixth order of the 

 eccentricities. Gauss, Hansen, and Bessel, Ivory, 

 Lubbock, Plana, Pontecoulant, and Airy, have, at 

 different periods up to the present time, either 

 extended or illustrated some particular part of the 

 theory, or applied it to special cases; as in the 



