are adjusted, we would expect to find one principle underlying such a classification, making it that of greatest convenience. It must be just as easy to tell a fourth magnitude star, for instance, from a fifth magnitude as from a third, and there must be as little doubt in distinguishing between the fifth and sixth magnitudes as between the third and second. The numbers expressing magnitudes, then, must actually represent a scale of equal differences as measured by the sensibility of the eye. When an astronomer pays attention to differences of luster, measured also by the sensibility of the eye, but closer than the founders of the science cared to notice, he naturally finds that he can distinguish the same number of intermediate grades between two adjoining magnitudes, whether faint or bright. Herschels estimates, having been of this character, are, as we have seen, subject to the same condition.
The system of comparisons introduced by Herschel was not followed by later astronomers. Determinations of brightness in which accuracy is sought are now made by means of instruments constructed expressly for the purpose. These instruments, called photometers—measurers of light, that is, their office being to show the amount of light that one star gives as compared with others—add nothing to the discriminating power of the eye, it should be stated. In deciding a question as to which is the brighter of two stars, situated sufficiently near together, no appliance yet invented can assist. But they have these three advantages: they facilitate comparison between faint stars, they furnish a means of comparing distant stars as though side by side, and they give results in a numerical form. That is to say, we get by means of them a definite difference, which may be expressed as a fraction of a magnitude. The magnitude, we see, is no longer regarded as a class, but as a fixed point on a continuous scale; a striking example of that progress of science in all its branches from a qualitative to a quantitative stage, on which philosophers delight so to insist.
But how are measures of light to give us fractions of a magnitude? How can the vague, qualitative relation, the brighter the light the higher the magnitude, become an exact and quantitative one? The discussion of this question may be of use by showing that, even with matters of so uncertain a nature, science does not proceed by guesswork. It is a general law, that the human senses measure ratios and not differences. If I am carrying a small weight, for example, and the addition of an ounce is required to make the burden perceptibly heavier to me, two ounces will have to be added in order that I may notice a difference when I carry twice the weight, and a whole pound when I carry sixteen times the weight. Similarly with the other senses, and, in no slight degree, with the emotions as well. Sensibility to grief and joy, as the experience of every one will attest, becomes feebler with an increase of the amount sustained. So, a faint sound can be heard only in comparative silence, and our footsteps surprise us by their resounding din on the floor of an empty hall, though no louder,
