out ever dreaming that thereby he is in the least affecting the nature of the curve whose properties are under discussion. The astronomer, in calculating the attraction of a sphere upon a "material point," begins by assuming the atomic or molecular constitution of the attracting sphere, establishing a series of finite differences as one of the terms of his equation; but thereupon he takes the series to be infinite and the differences to be infinitely small, and very effectually dismantles the molecular scaffolding by integrating instead of effecting a summation of a series of finite differences. Observe: the astronomer begins with two fictions—the fiction of the "material point" (which is, in truth, a contradiction in terms), so as to insulate the attractive force and treat it as proceeding from the sphere alone, and the fiction of the finite differences representing the molecular constitution of the sphere; but the validity of his result depends upon the eventual rescission of these fictions and the rehabilitation of the fact. In like manner, the chemist represents the proportions of weight in which substances combine, as atoms of definite weight and figure, and the resulting compounds as definite groups of such atoms; and this mythical coinage has, no doubt, been serviceable in some ways. But, apart from the circumstance, avowed by thoughtful chemists themselves, that the symbols have become wholly inadequate to the proper representation of the facts, and that new representative fictions will have to be resorted to, it is important to bear in mind always that the symbol is not the fact, and that the fiction is very different from the reality. Newton derived many of the leading optical laws from his corpuscular theory of light and from the hypothesis of "fits of easy transmission and reflection." His theory for a time served a good purpose; but it proved, after all, to be but a convenient mode of symbolizing the phenomena with which he was familiar, and had to be discarded when the phenomenon of interference was observed. In 1824 Sady Carnot deduced the law of thermic action, which still bears his name, from an hypothesis respecting the nature of heat (supposed by him, as by nearly all the physicists of his time, to be imponderable matter), which is now known, or universally believed to be, erroneous. Since his time, Clausius, Rankine, Thomson, and Clerk Maxwell, have shown that thermic phenomena find a very convenient representation in the hypothesis that gaseous molecules are in a state of incessant motion; and Maxwell has even succeeded in predicting the phenomenon of the gradual cessation of the oscillatory movement of a disk, suspended between two other disks, in consequence of the friction of a gaseous medium, whatever be the degree of its tenuity, and this prediction has since been verified by experiment, just as Hamilton's prediction of conical refraction was verified by the experiments of Lloyd; but, of course, neither Clausius's and Rankine's formulæ, nor Maxwell's experiments, are conclusive as to the real nature of a gas. In all such cases science erects a scaffolding which is invariably kicked down as
