600 COSMOS. 



planetary body describes in equal times equal sectors round 

 the Sun. Third law: the squares of the times of revolution 

 of two planets, are as the cubes of their mean distances. 

 The second law is sometimes called the first, because it was 

 discovered earlier. (Kepler, Astronomia nova, sen PJiysica 

 coelestiSj tradita commentariis de motibus stcllae Martis, ex 

 observ. Tychonis Brahi^elaborata, 1602; compare cap. xl. 

 with cap. lix.) The first two laws would be applicable, if 

 there were only a single planetary body ; the third and most 

 important which was discovered nineteen years afterwards, 

 fixes the motions of two planets to one law. (The manu- 

 script of the Harmonice Mundi, which appeared in 1619, was 

 already completed on the 27th of May, 1618.) 



While the laws of planetary motions were empirically dis- 

 covered at the commencement of the seventeenth century ; 

 while Newton first discovered the force, of whose action Kepler's 

 laws were to be considered as necessary consequences ; so the 

 end of the eighteenth century has had the merit of demonstrat- 

 ing the stability of tlie planetary system by the new path 

 which the perfected calculation of infinitesimals opened to the 

 investigation of astronomical truths. The principal elements 

 of this stability are: the invariability of the major axes of the 

 planetary orbits, proved by Laplace (1773 and 1784). Lagrange, 

 and Poisson; the long periodic change (comprised within 

 narrow limits) of the eccentricity of two larger planets more 

 distant from the sun, Jupiter and Saturn, themselves only 

 TTTT f the mass of the all-governing central body ; finally, 

 the arrangement that, according to the eternal plan of 

 creation, and the nature of the formation of the planets, 

 they have all a translatory and rotatory motion in one direc- 

 tion; that this motion takes place in orbits of slight and 

 but little varying ellipticity, in planes of moderate differences 

 of inclination ; and that the periods of the planetary revolutions 

 iiave among each other no common measure. Such elements 



