90 A Short History of Astronomy [Cn. ill 



abstractions, which enabled the planetary motions to be 

 represented with tolerable accuracy. Each planet moved 

 freely in space, its motion being represented or described 

 (not controlled} by a particular geometrical arrangement 

 of circles. Purbach suggested a compromise by hollowing 

 out Aristotle's crystal spheres till there was room for 

 Ptolemy's epicycles inside ! 



From the new Niirnberg press were issued also a suc- 

 cession of almanacks which, like those of to-day, gave the 

 public useful information about moveable feasts, the phases 

 of the moon, eclipses, etc.; and, in addition, -a volume of 

 less popular Ephemerides^ with astronomical information 

 of a fuller and more exact character for a period of about 

 30 years. This contained, among other things, astronomical 

 data for finding latitude and longitude at sea, for which 

 Regiomontanus had invented a new method.* 



The superiority of these tables over any others available 

 was such that they were used on several of the great voyages 

 of discovery of this period, probably by Columbus himself 

 on his first voyage to America. 



In 1475 Regiomontanus was invited to Rome by the 

 Pope to assist in a reform of the calendar, but died there 

 the next year at the early age of forty. 



Walther carried on his friend's work and took a number 

 of good observations ; he was the first to make any 

 successful attempt to allow for the atmospheric refraction 

 of which Ptolemy had probably had some knowledge (chap- 

 ter ii., 46) ; to him is due also the practice of obtaining 

 the position of the sun by comparison with Venus instead of 

 with the moon (chapter n., 39), the much slower motion 

 of the planet rendering greater accuracy possible. 



After Walther's death other observers of less merit carried 

 on the work, and a Niirnberg astronomical school of some 

 kind lasted into the lyth century. 



69. A few minor discoveries in astronomy belong to this 

 or to a slightly later period and may conveniently be dealt 

 with here. 



Lionardo da Vinci (1452-1519), who was not only a 

 great painter and sculptor, but also an anatomist, engineer, 

 mechanician, physicist, and mathematician, was the first 



* That of " lunar distances." 



