90 SPECIAL RESULTS IN THE URANOLOGICAL PORTION 



small. ( 171 ) If we take the mean semi-diameter of the 

 moon at 15' 3 3 ".5., 195291 surfaces of the full moon 

 would cover the whole heavens. Assuming an equable dis- 

 tribution, and taking the entire number of stars of all classes 

 from the 1st to the 9th in round numbers at 200000,, we 

 should have about one such star for every full-moon surface. 

 This result explains to us why in any given latitude stars 

 visible to the naked eye are not oftener occulted by the 

 moon. If the calculation of occultations was extended to 

 stars of the 9th magnitude, there would be, according to 

 Galle, on the average an occultation every 44J minutes ; 

 as in this time the moon passes over a fresh piece of the 

 heavens equal to its own area. Pliny (who was certainly ac- 

 quainted with Hipparchus' s list of stars, and who calls it a 

 bold undertaking in Hipparchus to seek to " bequeath to 

 posterity the starry heavens as an inheritance") reckoned in 

 the fine sky of Italy 1600 stars, ( 172 ) having descended in 

 this estimation to stars of the 5th magnitude ; half a cen- 

 tury later, Ptolemy recorded only 1025 stars, down to the 

 6th magnitude. 



Since the fixed stars ceased to be distinguished merely in 

 respect to the constellations to which they belonged, but have 

 been tabulated according to their relations to the great circles 

 of the Equator or the Ecliptic, and therefore according to 

 determinations of their places, the number as well as the 

 exactness of such entries have constantly increased with the 

 progress of science and the increased perfection of instruments. 

 No catalogue has come down to us from Timocharis and 

 Aristyllus (283 B. c.) ; but even though their observations, 

 as Hipparchus says in his fragments " upon the length of 

 the year/' quoted in the 7th book of the Almagest (cap. 3, 



