5 o6 THE POPULAR SCIENCE MONTHLY. 



as reflection easily assures us, than when the hall is filled with a bus- 

 tling multitude. So, though the stars give us their whole light in the 

 daytime, our eye, with the stimulus of an illuminated atmosphere, fails 

 to discover them. This law, first stated by Fechner, is, in mathemati- 

 cal language, the excitement of a nerve varies in arithmetical progres- 

 sion as the exciting cause varies in geometrical progression, or degrees 

 of sensation correspond to logarithms of the quantities perceived. 

 Since, as just shown, the scale of magnitudes is that of equal differ- 

 ences in sensation, it must be at the same time that of equal ratios of 

 light. We must thus have a constant light-ratio between each mag- 

 nitude and the one next it, and these magnitudes must be logarithms 

 of the quantities of light given, this ratio being taken as the base of 

 our system. In fact, one of the first discoveries in photometry was 

 that such a ratio actually exists ; that, for example, if each star rated 

 as third magnitude by good observers gives as much light as 2^- stars 

 of the fourth magnitude, a star of the fourth equals 2 of the fifth, and 

 so on. Here was a practical confirmation of the character ascribed to 

 ancient estimates of magnitude, and, at the same time, of Fechner's 

 law. 



This relation affords us the means of substituting exact measure- 

 ment for estimates on an ill-defined scale by different observers, among 

 whom a perfect agreement as to standard is out of the question. The 

 idea that each observer has of the meaning of second or fifth magnitude 

 is derived entirely from tradition and confirmed by habit, very much as 

 are his notions of the significance of ordinary adjectives of degree 

 the only precaution observed being to alter the estimates of antiquity 

 as little as possible, a vague limitation at best. Measures with the 

 photometer depend no less on estimates with the eye, but the deter- 

 mination in them, as to the exact agreement of two lights, is subject 

 to far less uncertainty. 



Photometers agree in this particular, whatever their differences in 

 mechanical construction. Seidel, of Munich, who was twelve years in 

 comparing the light of but 208 fixed stars, used an apparatus where 

 two stars seen through a telescope with divided object-glass, each out 

 of focus, were made of the same brightness to the eye by diffusing or 

 concentrating the light of one of them, its half of the object-glass 

 being drawn out or in. The stars thus appeared as two disks, of 

 different sizes but equally bright, and the amount of light given by 

 each was taken as proportionate to the area covered by its disk. The 

 same Dr. Zollner who has lately become so conspicuous in " spiritualist " 

 investigations, invented a much more convenient style of photometer, 

 with which he made some interesting researches into the comparative 

 light of the planets. Other astronomers, European and American, 

 have also used it. With one of these instruments, belonging to the 

 observatory of Harvard University, Mr. Peirce finished, a few years 

 ago, perhaps the most extensive and methodical photometric work that 



