PHOTOMETRIC SCALE. 99 



PHOTOMETRIC ARRANGEMENT OF THE FIXED STARS. 



I close this section with a table taken from Sir John Herschel's Out 

 lines of Astronomy, p. 645 and 646. I am indebted for the mode of its 

 arrangement, and for the following lucid exposition, to my learned 

 friend Dr. Galle, from whose communication, addressed to me in March, 

 1850, I extract the subjoined observations: 



" The numbers of the photometric scale in the Outlines of Astron- 

 omy have been obtained by adding throughout 041 to the results calcu- 

 lated from the vulgar scale. Sir John Herschel arrived at these more 

 exact determinations by observing their " sequences" of brightness, and 

 by combining these observations with the average ordinary data of mag- 

 nitudes, especially on those given in the catalogue of the Astronomical 

 Society for the year 1827. See Observ. at the Cape, p. 304-352. The 

 actual photometric measurements of several stars as obtained by the 

 Astrometer {op. cit., p. 353), have not been directly employed in this 

 catalogue, but have only served generally to show the relation existing 

 between the ordinary scale (of 1st, 2d, 3d, &c, magnitudes) to the act- 

 ual photometric quantities of individual stars. This comparison has 

 given the singular result that our ordinary stellar magnitudes (1,2, 3 . . .) 

 decrease in about the same ratio as a star of the first magnitude when 

 removed to the distances of 1, 2, 3 ... by which its brightness, accord- 

 ing to photometric law, would attain the values 1, Jth, ^th, y^th . . . 

 {Observ. al the Cape, p. 371, 372 ; Outlines, p. 521, 522) ; in order, how- 

 ever, to make this accordance still greater, it is only necessary to raise 

 our previously adopted stellar magnitudes about half a magnitude (or, 

 more accurately considered, 0'41), so that a star of the 2 - 00 magnitude 

 would in future be called 2-41, and star of 2-50 would become 2-91, 

 and so forth. Sir John Herschel therefore proposes that this " photo- 

 metric" (raised) scale shall in future be adopted {Observ. at the Cape, 

 p. 372, and Outlines, p. 522) a proposition in which we can not fail to 

 concur ; for while, on the one hand, the difference from the vulgar scale 

 would hardly be felt {Observ- at the Cape, p. 372), the table in the Out- 

 lines (p. 645) may, on the other hand, serve as a basis for stars down 

 to the fourth magnitude. The determinations of the magnitudes of the 

 stars according to the rule, that the brightness of the stars of the first, 

 second, third, fourth magnitude is exactly as 1, |th, ^th, -pjfh ... as is 

 now shown approximatively, is therefore already practicable. Sir John 

 Herschel employs a Centauri as the standard star of the first magnitude 

 for his photometric scale, and as the unit for the quantity of light {Out- 

 lines, p. 523; Observ. at the Cape, p. 372). If, therefore, we take the 

 square of a star's photometric magnitude, we obtain the inverse ratio 

 of the quantity of its light to that of a Ceutauri. Thus, for instance, if 

 k Orionis have a photometric magnitude of 3, it consequently has ^th 

 of the light of a Centauri. The number 3 would at the same time in- 

 dicate that k Orionis is 3 times more distant from us than a Centauri, 

 provided both stars be bodies of equal magnitude and brightness, if 

 another star, as, for instance, Sirius, which is four times as bright, were 

 chosen as the unit of the photometric magnitudes indicating distances, 

 the above conformity to law would not be so simple and easy of recog- 

 nition. It is also worthy of notice, that the distance of a Centauri has 

 been ascertained with some probability, and that this distance is the 

 smallest of any yet determined. Sir John Henchel demonstrates {Out- 

 lines, p. 521) the inferiority of other scales to the photometric, which 



