NOTES. x 



down as the 4th magnitude. The determination of magnitudes of stars 



according to this rule viz. that the brightnesses of stars of the 1, 2, 3, 4 



magnitudes should be to each other in the ratio of 1, %, i, T T g- exactly, as 



they already are approximately, is thus already in part practicable'. Sir 

 John Herschel (Outlines, p. 523 ; Cape Obs. p. 372) takes a Centauri as a 

 normal star for the 1st magnitude of the Photometric Scale, and as the unit 

 for the quantity of light. If, therefore, we square the photometric magnitude 

 of a star, we have the inverse ratio of its quantity of light to that of a Cen- 

 tauri. So, for example, if K. Orionis is of photometric magnitude 3, it has 

 i of the light of a Centauri. At the same time, the number 3 would show 

 K Orionis to be 3 times as far from us as a Centauri, if we assume the two 

 stars to be bodies equal in real magnitude and brightness. If another star 

 ex. gr. Sirius, which is four times as bright had been chosen as the unit 

 of the photometric magnitudes indicating distances, the regular conformity to 

 law would not have been seen with so much simplicity. Nor is it without 

 interest that the distance of a Centauri is known with some probability, and 

 that among the distances of fixed stars which have yet been investigated it is 

 the least. The author treats in the Outlines, p. 521, of the inferiority, in 

 point of suitability, of other scales as compared with the photometric one, 



which advances according to the squares 1, \, , -Jg- He also notices 



geometrical progressions as, for example, 1, i, \, ^ or 1, ^, -g, ^ 



The gradations which you selected in the Observations at the Equator in your 

 American Expedition follow an arithmetical progression (Recueil d'Observ. 

 astrou. Vol. 1, p. Ixxi. ; and Schumacher, Astron. Nachr. No. 3?4). All these 

 scales adapt themselves less well to the vulgar scale than to the photometric 

 (quadratic) progression." In the following table, the 190 stars of the " Out- 

 lines of Astronomy" are arranged solely according to their magnitudes, 

 without regard to South or North Declination. 



