as reflection easily assures us, than when the hall is filled with a bustling 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 mathematical language, the excitement of a nerve varies in arithmetical progression 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 differences 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 magnitude 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 212 stars of the fourth magnitude, a star of the fourth equals 212 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 measurement 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 determination 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. Zöllner 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
