PHOTOMETRIC SCALE. 133 



bv which its brightness, according to photometric law, would 

 attain the values 1, , -J-, ^th. ..(Observ. at the Cape, pp. 371, 

 872: Outlines, pp. 521, 522); in order, however, to make this 

 accordance still greater, it is only necessary to liaise our pre- 

 viously adopted stellar magnitudes about half a magnitude (or 

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

 nitude would in future be called 2 -41 , and star of 2 '50 would be- 

 come 2 -9 1 , and so forth. Sir John Herschel therefore propose? 

 that this " photometric'' (raised) scale shall in future be adopted 

 ( Observ. at the Cape, p. 372, and Outlines, p. 522) a proposition 

 in which we cannot fail to concur. For while on the one hand 

 the difference from the vulgar scale would hardly be felt (Ob- 

 serv. at the Cape, p. 372) ; the table in the Outlines (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 1st, 2nd, 3rd, 4th magnitude is exactly as 1 , ^, -> -^g- . . .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 ( Outlines, p. 523 ; Observ. at the Cape, p. 372). 

 If therefore we take the square of a star's photometric mag- 

 nitude, we obtain the inverse ratio of the quantity of its light 

 to that of a Centauri. Thus for instance if K Orionis have a pho- 

 tometric magnitude of 3, it consequently has i of the light of 

 a Centauri. The number 3 would at the same time indicate 

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

 provided both stars be bodies of equal magnitude and bright- 

 ness. 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 recognition. 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 Herschel 

 demonstrates (Outlines, p. 521,) the inferiority of other scales 

 to the photometric, which progresses in order of the squares, 

 1, ^, --, -i^. He likewise treats of geometric progressions, as 

 for instance, 1, , \, \, . . . or 1, , i, -^. . . . The gradations 

 employed by yourself in your observations under the equator, 

 during your travels in America, are arranged in a kind of 



