THE FIXED STARS. 505 



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 mag- 

 nitude as from a third, and there must be as little doubt in distinguish- 

 ing between the fifth and sixth magnitudes as between the third and 

 second. The numbers expressing magnitudes, then, must actually rep- 

 resent 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 mag- 

 nitudes, whether faint or bright. HerschePs 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 fol- 

 lowed 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 dis- 

 criminating power of the eye, it should be stated. In deciding a ques- 

 tion 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 quan- 

 titative 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 guess- 

 work. 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, 



