PORTION OF THE COSMOS. CONCLUSION. 451 



observ. Tychonis Bralii elaborate, 1609 : compare cap.xl. with 

 cap. lix.) The two first laws would be applicable if there were 

 only one single planetary body in existence ; the third and 

 most important of the three, which was discovered nineteen 

 years later than the other two, determines the law of the 

 motions of two planets. (The manuscript of the Harrnonice 

 Mundi, which was published in 1619, was completed on the 

 27th of May, 1618.) 



If the laws of the planetary motions were empirically dis- 

 covered in the beginning of the 17th century, and if Newton 

 first unveiled the force from whose action Kepler's laws 

 must be regarded as necessary consequences, the end of 

 the 18th century, through the new paths opened to the 

 investigation of astronomical truths by the improvement of 

 the infinitesimal calculus, has the merit of having demon- 

 strated the "stability of the planetary system." The prin- 

 cipal elements of this stability are, the invariability of the 

 major axes of the planetary orbits demonstrated by Laplace 

 (1773 and 1784), Lagrange, and Poisson; the long perio- 

 dical variation, restricted within narrow limits, of the excen- 

 tricities of two large and remote planets, Jupiter and Saturn; 

 the distribution of the masses, since the mass of Jupiter 

 itself, the greatest of all the planetary bodies, is only t ' 4 8 

 of that of the all- controlling central body; and lastly, 

 the arrangement, that by the primordial plan of creation, 

 and by the mode of their origination, all the planets of 

 the solar system move in one direction both in regard 

 to translation and to rotation, in orbits of small and little- 

 varying ellipticity, and in planes having only moderate 

 differences of inclination ; and that the periods of revolution 

 of the different planets have no common measure. 



