1881.] in the Constellation Ursa Major. 95 



the various stars of the constellation have been gradually increas- 

 ing their distance from the true or virtual Pole ; which, vice versa, 

 it may be observed has been gradually approaching the star we 

 call the Pole-Star : the Declination of which must have been about 

 78° 20' in Ptolemy's time, and 74° 20' seven centuries earlier, its 

 R.A. having during the same period advanced from 22 h. 53 m. at 

 the earliest of these two eras, and 23 h. 15 m. at the next, to 

 1 h. 15 m. its present approximate amount. 



It will be understood that only comparative accuracy is claimed 

 for the results given in this paper. The latitudes of the stars dis- 

 cussed which result from the computations are on an average about 

 40' greater than those given in the catalogue ascribed to Ptolemy : 

 and it is a somewhat imperious solution of the difficulty to say 

 that Ptolemy was wrong. There are also two statements of 

 Ptolemy's, cited by Delambre, which seem to imply the possibility 

 of secular changes in other points which cannot be directly in- 

 ferred from existing phenomena. The present rate of change in 

 the obliquity of the ecliptic is given by the best authorities as about 

 48" a century: which would make the actual obliquity 23° 42' in 

 Ptolemy's time: whereas the value given by him is 23° 51'. In his 

 Geography again we find the latitude of Alexandria and Syene 

 both given about 15' too small. It is true that the latitudes of the 

 various places given by him in this work, and scattered all over 

 Europe, are so erroneous that no general inference can be safely 

 drawn from them ; but the latitude of Alexandria was one of the 

 points fixed even by Eratosthenes much before Ptolemy's time ; so 

 was that of Syene in Upper Egypt; and if we add Rome as a 

 place the latitude of which was likely to have been accurately 

 ascertained we have thus three places of note, the errors about 

 which are almost identical. We have in fact 



Latitude 

 according to True latitude. Error. 



Ptolemy. 



Alexandria 30°-58' 31°12' 14''(-) 



Syene (Assouan^. 23°-50' 24°- 5' 15' • (-) 



Rome 41°'40' 41°54' 14' • (-) 



a table which certainly shews a very nearly equal error in each 

 case. 



It is true the line of argument I am following is not very 

 strict, but those who consider the immense pains bestowed on 

 practical astronomy in the Alexandrian era will not I think be 

 satisfied without some effort to see how far the results then 

 thought to be ascertained harmonize with those of modern 

 science. 



