60 COSMOS. 



ascended before sunrise by scientific travelers provided with 

 instruments, I would hope that this reiterated invitation on 

 my part to the observation of the undulation of the stars 

 may not be wholly disregarded. 



I have already called attention to the fact that the basis 

 of a very important part of the astronomy of our planetary 

 system was already laid before the memorable years 1608 

 and 1610, and therefore before the great epoch of the in- 

 vention of telescopic vision, and its application to astronom- 

 ical purposes. The treasure transmitted by the learning of 

 the Greeks and Arabs was augmented by the careful and 

 persevering labors of George Purbach, Regiomontanus (i. e., 

 Johann Miiller), and Bernhard Walther of Nurnberg. To 

 their efforts succeeded a bold and glorious development of 

 thought the Copernican system ; this, again, was followed 

 by the rich treasures derived from the exact observations of 

 Tycho Brahe, and the combined acumen and persevering 

 spirit of calculation of Kepler. Two great men, Kepler and 

 Galileo, occupy the most important turning-point in the his- 

 tory of measuring astronomy ; both indicating the epoch that 

 separates observation by the naked eye, though aided by 

 greatly improved instruments of measurement, from tele- 

 scopic vision. Galileo was at that period forty-four, and 

 Kepler thirty-seven years of age ; Tycho Brahe, the most 

 exact of the measuring astronomers of that great age, had 

 been dead seven years. I have already mentioned, in a pre- 

 ceding volume of this work (see vol. ii., p. 328), that none of 

 Kepler's cotemporaries, Galileo not excepted, bestowed any 

 adequate praise on the discovery of the three laws which 

 have immortalized his name. Discovered by purely emph> 

 ical methods, although more rich in results to the whole do- 

 main of science than the isolated discovery of unseen cos- 

 mical bodies, these laws belong entirely to the period of nat- 

 ural vision, to the epoch of Tycho Brahe and his observa- 

 tions, although the printing of the work entitled Astronomia 

 nova seu Physica cozlestis de motibus Stellce Martis was 

 not completed until 1609, and the third law, that the squares 

 of the periodic times of revolution of two planets are as the 

 cubes of their mean distances, was first fully developed in 

 1619, in the Harmonice Mundi. 



The transition from natural to telesoopic vision which 

 characterizes the first ten years of the seventeenth century 

 was more important to astronomy (the knowledge of the re- 

 gions of space) than the year 1492 (that of* the discoveries 



