THE FIXED STARS. 507 



has yet been done. His measures included the visible stars, about five 

 hundred in all, of the zone between 40 and 50 of north declination 

 those passing overhead in the Northern United States and Canada. 

 The light of a kerosene lamp, in Zollner's photometer, shines through a 

 small round hole in a thin metallic plate, so as to form an imitation of 

 a star, slightly brighter than the real stars with which it is compared. 

 The light of this artificial star, having been polarized by passing 

 through one Nicol prism, is partially cut off by turning another. The 

 proportion of light so cut off depends on the angle of the second prism 

 from parallelism with the first. Having thus found the amounts of 

 light given by two or more stars, as compared with a fixed light, their 

 differences of magnitude are calculated by applying the rule involving 

 logarithms, alluded to above. 



Owing to the labor involved in making any large number of photo- 

 metric comparisons, the less accurate but more convenient method of 

 eye-estimates has not yet been entirely superseded. It becomes neces- 

 sary, then, to find some way of reducing different observers to one uni- 

 form scale, in order to have their work available for determination of 

 variability and questions of distribution. Mr. Peirce, in his "Photo- 

 metric Researches," recently published by the Harvard College Ob- 

 servatory, has shown that this may be done by the simple process of 

 counting. When we find in any catalogue a star recorded as of mag- 

 nitude 4, say, though we can not tell exactly what degree of bright- 

 ness this figure denotes, we yet know something definite, namely, that 

 this observer classes the star in question as fainter than those he calls 

 4 and brighter than those he calls 4f. And we know something more: 

 if in the northern hemisphere a limited part of the heavens must be 

 taken for the purpose, few catalogues being complete in southern stars 

 he classes 200 stars in all as brighter than 4^, while he calls 25 stars 

 4 exactly, he means to tell us that his 4^ magnitude stars would all 

 fall between 200 and 225 on a list of northern stars arranged in order 

 of brightness. It is by considering the order which stars would follow 

 when so arranged, leaving entirely out of view the numbers by which 

 their magnitudes are expressed, that Mr. Peirce brings all observers to 

 a single standard of reference; for he is justified in assuming that each 

 of them attaches the same idea of brightness to the 50th or 150th 

 star in his order, as an assumption of some such nature must be made 

 to have their estimates of any service at all. To reduce to mag- 

 nitudes these numbers expressing order of arrangement, we have to 

 notice that equal ratios among them correspond to equal differences 

 in magnitude. If we take a good catalogue and find the number of 

 stars in it brighter than 2*0, and add to this number successively 

 the number between 2*0 and 30, 3*0 and 4-0, and so on, we shall 

 find that our series of numbers increases geometrically, the common 

 ratio being nearly 3f. This is a remarkable fact, but it is not difficult 

 to account for, on the supposition that the stars are uniformly scat- 



