296 HISTORY OF FORMAL ASTRONOMY. 



often failed him during the task; 4 and subscribes to the judgment of 

 Bailly : " After this sublime effort, Kepler replunges himself in the 

 relations of music to the motions, the distance, and the eccentricities 

 of the planets. In all these harmonic ratios there is not one true rela- 

 tion ; in a crowd of ideas there is not one truth : he becomes a man 

 after being a spirit of light." Certainly these speculations are of no 

 value, but we may look on them with toleration, when we recollect 

 that Newton has sought for analogies between the spaces occupied by 

 the prismatic colors and the notes of the gamut. 5 The numerical rela- 

 tions of Concords are so peculiar that we can easily suppose them to 

 have other bearings than those which first offer themselves. 



It does not belong to my present purpose to speak at length of the 

 speculations concerning the forces producing the celestial motions by 

 which Kepler was led to this celebrated law, or of those which he de- 

 duced from it, and which are found in the Epitome Astronomice Coper- 

 nicance, published in 1622. In that work also (p. 554), he extended 

 this law, though in a loose manner, to the satellites of Jupiter. These 

 physical speculations were only a vague and distant prelude to Newton's 

 discoveries ; and the law, as a formal rule, was complete in itself. 

 We must now attend to the history of the other two laws with which 

 Kepler's name is associated. 



Sect. 3. Kepler' 's Discovery of his First and Second Laws. Elliptical 

 Theory of the Planets. 



THE propositions designated as Kepler's First and Second Laws are 

 these : That the orbits of the planets are elliptical ; and, That the 

 areas described, or swept, by lines drawn from the sun to the planet, 

 are proportional to the times employed in the motion. 



The occasion of the discovery of these laws was the attempt to 

 reconcile the theory of Mars to the theory of eccentrics and epicycles; 

 the event of it was the complete overthrow of that theory, and the 

 establishment, in its stead, of the Elliptical Theory of the planets. 

 Astronomy was now ripe for such a change. As soon as Copernicus 

 had taught men that the orbits of the planets were to be referred to 

 the sun, it obviously became a question, what was the true form ot 

 these orbits, and the rule of motion of each planet in its own orbit. 

 Copernicus represented the motions in longitude by means of eccen- 



A. M. a. 358. 5 Optics, b. ii. p. iv. Obs. 5. 



