CONCLUSION. 229 



a common center of gravity. In our solar system, which is 

 constituted of very heterogeneous elements, dark cosmical 

 bodies revolve round a self-luminous one, or much rather 

 again round a common center of gravity, which at different 

 times is situated within and without the central body The 

 individual members of the solar system are of dissimilar na- 

 ture — more dissimilar than for many centuries astronomers 

 were justified in supposing. They arc principal and sec- 

 ondary planets ; among the principal planets a group whose 

 orbits intersect each other ; an innumerable host of comets ; 

 the ring of the zodiacal light ; and, with much probability, 

 the periodic meteor-asteroids. 



It still remains to state here fully, as actual relations, the 

 three great laws of planetary motion, discovered by Kepler. 

 First laiv : each orbit of a planetary body is an ellipse, in 

 one of whose foci the Sun is situated. Second law : each 

 planetary body describes in equal times equal sectors round 

 the Sun. Third law : the squares of the times of revolu- 

 tion 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, seu Physica 

 Cozlestis, tradita Commentariis de Motibus stellce tylartis, 

 ex observ. Tychonis Br alii 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 after- 

 ward, fixes the motions of two planets to one law. (The 

 manuscript of the Harmonice Miindi, 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 Kep- 

 ler's laws were to be considered as necessary consequences ; 

 so the end of the eighteenth century has had the merit of de- 

 monstrating the stability of the 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 y^T of the mass of the all-governing central 

 body ; finally, the arrangement that, according to the eternal 



