MAGNITUDES OF STARS. 91 



640 stars of .the sixth magnitude. The nebulous stars (ve- 

 deXoeLdds') of Ptolemy and of the Pseudo-Eratosthenian Ca- 

 iasterisms are mostly small stellar swarms,* appearing like 

 nebulae in the clearer atmosphere of the southern hemisphere. 

 I more particularly base this conjecture on the mention of a 

 nebula in the right hand of Perseus. Galileo, who, like the 

 Greek and Arabian astronomers, was unacquainted with the 

 nebula in Andromeda which is visible to the naked eye, says 

 in his Nuntius sidereus that stellce nebulosts are nothing 

 more than stellar masses scattered in shining groups through 

 the ether (areolce, sparsim per cethera fulgent).^ The ex- 

 pression (r&v fj,eydA.d)v raft^), the order of magnitudes, al- 

 though referring only to luster, led, as early as the ninth cen- 

 tury, to hypotheses on the diameters of stars of different bright- 

 ness ;J as if the intensity of light did not depend on the dis- 

 tance, volume, and mass, as also on the peculiar character 

 of the surface of a cosmical body in more or less favoring the 

 process of light. 



At the period of the Mongolian supremacy, when, in the 

 fifteenth century, astronomy nourished at Samarcand, under 

 Timur Ulugh Beg, photometric determinations were facili- 

 tated by the subdivision of each of the six classes of Hippar- 

 chus and Ptolemy into three subordinate groups ; distinctions, 

 for example, being drawn between the small, intermediate, 

 and large stars of the second magnitude an attempt which 

 reminds us of the decimal gradations of Struve and Argelan- 

 der. This advance in photometry, by a more exact determ- 

 ination of degrees of intensity, is ascribed in Ulugh Beg's 

 tables to Abdurrahman Sufi, who wrote a work " on the 

 knowledge of the fixed stars," and was the first who men- 

 tions one of the Magellanic clouds under the name of the 

 White Ox. Since the discovery and gradual improvement 

 of telescopic vision, these estimates of the gradations of light 

 have been extended far below the sixth class. The desire 

 of comparing the increase and decrease of light in the newly- 



* Plot. Almas., ed Halma, torn, ii., p. 40, and in Eratosth. Catast., 

 cap. 22, p. 18: rj de KtQa/.Tj Kai ij apnr) uvaifTOf dparai, 6ia de ve0e?.u<5otf 

 avarpo<j>jjc do/ccl TLGIV opuadai. Thus, too, Geminus, Pheen. (ed. Hilder, 

 1590), p. 46. t Cosmos, vol. ii., p. 330, 331. 



t Muhamedis Alfragani Chronologica et Ast. Elementa, 1590, cap. 

 xxiv., p. 118. 



$ Some MSS. of the Almagest refer to such subdivisions or interme- 

 diate classes, as they add the words pei&v or ehdaauv to the determ- 

 ination of magnitudes. (Cod. Paris, No. 2389.) Tycho expressed thia 

 increase or diminution by points. 



