Dr. E. J. Mills on the Atomic Theory. 119 



10 grammes of sodium were originally present, they now con- 

 sist of two lots of, say, 5 grammes each. This makes it quite 

 conceivable that, without the addition of any more of the solvent, 

 the division may continue of its own accord, say, into ten lots of 

 1 gramme each, a thousand lots of a decigramme each, and so 

 on, without limit. The same is true of the chlorine. On en- 

 deavouring to prepare a compound from the solution, only one 

 is obtained with an invariable ratio between the sodium and the 

 chlorine. The reason of this phenomenon is presumed to be 

 unknown and to be now sought. I can only say that the fact, 

 from the above point of view, is as conceivable on the supposi- 

 tion of continuous as it is upon that of limited division. Two 

 phenomena continuously proceeding without obvious end (ma- 

 thematical " infinites ") are well known to be capable of a finite 

 ratio. . Through one point an infinite number of curves may be 

 drawn. The neutralization of aqueous hydric chloride is some- 

 thing like the process of differentiation, and its result^ a con- 

 stant finite ratio, like a differential coefficient. Or take as an 

 illustration the properties of the machine known as the " geo- 

 metric chuck." By a suitable combination of circular move- 

 ments, this beautiful instrument is capable of describing an end- 

 less variety of curves, one of which is roughly represented in the 

 margin : such a figure is drawn by a motion which is visibly 

 continuous, even at the three points, throughout the entire 

 period of delineation ; when it has been described, the machine 

 proceeds to draw an exactly similar triangle, which it accurately 

 superimposes on the first, and so on, to any num- 

 ber of triangles. The number of points in the 

 figure is regulated by previous adjustment of the 

 constants of the machine ; but the mass of the 

 instrument, its rate of motion, and the number 

 of times it is resolved (beyond the construction- 

 minimum) have nothing to do with the resulting figure. The 

 definite proportions of chemistry, in like manner, precede or 

 accompany each of our experiments ; they are independent of 

 mass, rate of action, repetition of action ; and doubtless they 

 are produced, like these points, by compound uninterrupted 

 motion. They certainly suggest nothing that is by nature 

 atomic. These mathematical conceptions, however, involve no 

 breach of continuity, which is rather their essential condition; 

 and the chemical phenomenon is at least as conceivable as they 

 are without introducing the supposition of a limit. 



I may adduce the process of diffusion as one that, in accord- 

 ance with the large number of experiments already made, is pro- 

 bably capable of continuance without any clear reason for a limit. 

 Yet if matter consisted of indivisibles, some sign, at any rate, of 



