SEQUEL TO THE EPOCH OF KEPLER. 305 



allows that he is much embarrassed by the deviations. His arguments 

 show a singularly clear and strong apprehension of the features of the 

 case, and their real import. He says, 4 " these errors of the tables are 

 alternately in excess and defect ; how could this constant compensa- 

 tion happen if they were casual ? Moreover, the alternation from ex- 

 cess to defect is most rapid in the Moon, most slow in Jupiter and 

 Saturn, in which planets the error continues sometimes for years. If 

 the errors were casual, why should they not last as long in the Moon 

 as in Saturn ? But if we suppose the tables to be right in the mean 

 motions, but wrong in the equations, these facts are just what must 

 happen ; since Saturn's inequalities are of long period, while those of 

 the Moon are numerous, and rapidly changing." It would be impos- 

 sible, at the present moment, to reason better on this subject; and 

 the doctrine, that all the apparent irregularities of the celestial motions 

 are really regular, was one of great consequence to establish at this 

 period of the science. 



Sect. 3. — Causes of the further Progress of Astronomy. 



We are now arrived at the time when theory and observation sprang 

 forwards with emulous energy. " The physical theories of Kepler, and 

 the reasonings of other defenders of the Copernican theory, led inev- 

 itably, after some vagueness and perplexity, to a sound science of 

 Mechanics ; and this science in time gave a new face to Astronomy. 

 But in the mean time, while mechanical mathematicians were general- 

 izing from the astronomy already established, astronomers were ac- 

 cumulating new facts, which pointed the way to new theories and new 

 generalizations. Copernicus, while he had established the permanent 

 length of the year, had confirmed the motion of the sun's apogee, and 

 had shown that the eccentricity of the earth's orbit, and the obliquity 

 of the ecliptic, were gradually, though slowly, diminishing. Tycho 

 had accumulated a store of excellent observations. These, as well as 

 the laws of the motions of the moon and planets already explained, 

 were materials on which the Mechanics of the Universe was afterwards 

 to employ its most matured powers. In the mean time, the telescope 

 had opened other new subjects of notice and speculation ; not only 

 confirming the Copernican doctrine by the phases of Venus, and the 

 analogical examples of Jupiter and Saturn, which with their Satellites 



4 Astron. Kepler. Proleg. p. 17. 

 Vol. I.— 20 



