268 Proceedings of the Royal Irish Academy. 



these two notations sliould not be sufficiently clear to be clistiaguisbed 

 from each other, yet I am inclined to believe that the former may be 

 precise enough to poiat out a difference from 2 m. and the latter from 

 2" 3 m. With the next order of stars the difference is much less 

 striking ; but yet 2 m. will convey an idea which may be pretty well 

 distinguished from 3 m. 2"3 m. however, cannot be sufficiently kept 

 apart from 3'2 m., or either of these expressions from 3 m. or from 2 m. 

 Perhaps the former may be distiaguished from 3 •4 m., and the latter 

 from 4 m. The followiag step from 3 m. to 4 m., or indeed from 3*4 to 

 4"5, is less decisive than from 2 m. to 3 m. Agahi, if a star had changed 

 from 4 m. to 5 m., or from 4'5 to 5"6 since Plamsteed's time, we could 

 hardly entertain more than a very slight suspicion of the alteration. 

 From 4 to 5*6 m., or from 4' 5 to 6 m., would be a pretty considerable 

 step, and might serve as a foundation for an argument. A change 

 from 5 m. to 6 m. is such as no stress could be laid upon ; and such are 

 the changes from 5 '6 m. to 6'7 m., and from 6 m. to 7 m. In all these 

 inferior orders less than an alteration of a magnitude and a half could 

 hardly deserve attention." — {Phil. Trans., 1796, p. 166.) 



The above remarks will apply in some degree to the magnitudes as- 

 signed by Lalande, Piazzi, Bessel, and other meridional observers. In 

 the case of Plamsteed's observations, however, the discrepancies are so 

 great that I have not quoted his magnitudes. 



I have given the magnitudes of the stars, as shown in Harding's 

 Atlas (1822), which seems to have been constructed with considerable 

 care. 



The magnitudes given by Sufi, Argelander, Heis, Behrmann, and 

 Gould (especially the last named), are more reliable, as they are the 

 results of actual comparisons of the stars, inter se. 



I have also given the results of Sir "W". Herschel's observation? 

 {Phil. Trans., 1796, and 1799), the value of which has only very lately 

 been recognized. 



The following is an explanation of the symbols used by Sir W. 

 Herschel, as given by him in the Philosophical Transactions for 1796, 

 p. 189:— 



' The least perceptible difference less bright. 



Equality. 

 » The least perceptible difference more bright. 



A very small difference more bright. 



- - A considerable difference more bright. 



- - - Any great difference, more bright in general. 



