120 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1936 



Ptolemy. The Arab astronomers, Albategnius, Abul Wafa, Ibn 

 Yunus, Arzabel, Nassir Eddin, and the Tartar, Ulegh Begh, made 

 some observations of value, computed tables of planetary and other 

 positions, and kept alive the knowledge of the works of the Greeks. 

 But they added very little of original discovery to the body of 

 astronomical knowledge. Indirectly, however, by their introduction 

 from India of our present system of writing numbers, which we 

 still call the Arabic notation, they conferred an immense boon upon 

 astronomy. 



Regiomontanus, with his master Purbach and his pupil Walther, 

 in the latter half of the fifteenth century, published in Nurnberg a 

 treatise on planetary theory, invented the method of lunar distances 

 for determining longitude at sea, and published for many years 

 almanacs giving astronomical information. He was invited to Rome 

 to reform the calendar, but died there at the age of 40. 



Here then we come to the end of the astronomical knowledge of 

 Shakespeare's time. The Greeks and earlier observers had proved the 

 earth and moon to be spheres, and had inferred that the other heav- 

 enly bodies were spheres also. They had devised means of determin- 

 ing latitude, the length of the year, the times of the equinoxes and 

 solstices, and had discovered the periodicity of eclipses. The planets 

 from Mercury to Saturn were known, and their curious motions in 

 advance and in retrograde among the stars had been observed for 

 many centuries. The motions of the sun and moon with respect to the 

 stars were also long observed. By the theorems of geometry, ampli- 

 fied by some of the powers of trigonometry, ingenious, yet fatally 

 complex theories of the celestial motions had been worked out. Such 

 obscure phenomena as the precession of the equinoxes and the various 

 inequalities of the apparent motions of the sun and moon had been 

 discovered. 



All of this was done without the telescope or the exact clock. No 

 sufficient accuracy was possible without them to build a true edifice of 

 astronomical theory. Neither was the cloud of ignorance so far lifted 

 as to reveal to most men the improbability of the claims of astrology. 

 Shakespeare showed his superiority of mind by declining to believe 

 that twinkling stars could order human destiny. He made use of 

 other men's beliefs in astrology, nevertheless, to impart mystery and 

 awe to dramatic situations. By the happiest references he often used 

 bits of true or fanciful astronomical lore to make facets of gemlike 

 brilliancy shine from out his verse. What added beauties he would 

 have created had he possessed the knowledge of the Universe that awes 

 us now, it is difficult to imagine. 



I have a mind to end this paper gallantly by quoting some lines 

 from the plays to present Shakespeare's heavenly outlook vividly. 



