PRIMARY CONCEPTS OF MODERN SCIENCE. 357 



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," be- 

 gins by assuming the atomic or molecular constitution of the attract- 

 ing 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 summa- 

 tion 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 com- 

 bine, as atoms of definite weight and figure, and the resulting com- 

 pounds 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 sym- 

 bols 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 re- 

 flection." 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 phe- 

 nomenon of interference was observed. In 1824 Sady Carnot de- 

 duced 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 mat- 

 ter), 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 phenom- 

 enon 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 pre- 

 diction has since been verified by experiment, just as Hamilton's pre- 

 diction of conical refraction was verified by the experiments of Lloyd ; 

 but, of course, neither Clausius's and Rankine's formulae, 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 



