The Scientific American Supplement of May 14,1881, contains, under this head, Mr. Wm. H. Greene's objections to my demonstration (in No. 270 of the same paper) of the error of Avogadro's hypothesis. The most important part of my argument is based on the evidence afforded by the compound cyanogen; and Mr. Greene, directing his attention to this subject in the first place, states that because cyanogen combines with hydrogen or with chlorine, without diminution of volumes, I have concluded that the hypothesis falls to the ground. This statement has impressed me with the conviction that Mr. Greene has failed to perceive the difficulty which is at the bottom of the question, and I will, therefore, present the subject more fully and comprehensively.

The molecule of any elementary body is, on the ground of the hypothesis, assumed to be a compound of two atoms, and the molecule of carbon consequently C=24; that of nitrogen N=28. Combination of the two, according to the same hypothesis, takes place by substitution; the atoms are supposed to be set free and to exchange places, forming a new compound different from the original only in this: that each new particle contains an atom of each of the two different substances, while each original particle consists of two identical atoms. The product is, therefore, assumed to be, and can, under the circumstances, be no other than particles of the composition CN and weight 26. These particles are molecules, according to the definition laid down, just as C and N; but there is this essential difference, that the specific gravity of cyanogen gas, 26, coincides with the molecular weight, while the assumed molecular weight, N=28, is twice as great as the specific gravity of the gas, N=14.

In using the term molecular weight, it is to be remembered that it does not express the weight of single molecules, but only their relative weight, millions of millions molecules being contained in the unit of volume. But on the hypothesis that there is the same number of molecules in the same volume of any gas, the specific gravities of gases can be, and are, identified with their molecular weights, and, on the ground of the hypothesis again, the unit of the numbers which enter into every chemical reaction and constitute the molecular weight, is stipulated to be that contained in two volumes.

The impossibility of the correctness of the hypothesis is now revealed by the fact just demonstrated, that in the case of nitrogen the specific gravity does not coincide with the molecular weight. If equal volumes contain the same number of molecules, the specific gravities and the molecular weights must be the same; and if the specific gravities and molecular weights are not the same, equal volumes cannot contain the same number of molecules. The assumed molecular weight of nitrogen is twice as great as the specific gravity, but the molecular weight and the specific gravity of cyanogen are identical; the number of molecules contained in one volume of cyanogen must, therefore, necessarily be twice as great as the number contained in one of nitrogen, and this is fully and completely borne out by the chemical facts.

In saying that when cyanogen combines with chlorine there is naturally no condensation, Mr. Greene has no idea that this natural law is fatal to his artificial law of Avogadro and Ampere; "for," continues he, "the theory is fulfilled by the actual reaction." It is not. The theory requires two vols. of cyanogen and two vols. of chlorine, that is, the unit of numbers, to enter into reaction and to produce two vols. of the compound. But they produce four vols., and the non-condensation is therefore in opposition to the theory. It is true beyond doubt that the molecular weight of cyanogen chloride is contained in two volumes, in spite of the hypothesis, not on the ground of it; two vols. + two vols., producing four vols.; two vols. could, theoretically, contain only half the unit of numbers, and there seems to be no escape from the following general conclusions:

1. Two vols. of CNCl, representing the unit of numbers, the constituent weights, C=12, N=14, Cl=35.5, must each, likewise, represent the same number; the molecular weight is, therefore, contained in one vol. of N or Cl, but in two of CNCl and equal numbers are not contained in equal volumes.

2. The weights N=14, Cl=35.5 occupy in the free state one volume, but in the combination, CNCl, two volumes; their specific gravity is, therefore, by chemical action reduced to one half. The fact thus elicited of the variability and variation of the specific gravity is of fundamental importance and involves the irrelevancy of the mathematical demonstration of the hypothesis. In this demonstration the specific gravity is assumed to be constant, and this assumption not holding good, and the number of molecules in unit of volume being reduced to one half when the specific gravity is reduced to the same extent by chemical action, it is obvious that the mathematical proof must fail. Mr. Greene states that I have proceeded to demolish C. Clerk Maxwell's conclusion from mathematical reasoning. This is incorrect; I have found no fault with the conclusion of the celebrated mathematician, and consider his reasoning unimpeachable. I am also of opinion that he is entitled to great credit and respect for the prominent part he has taken in the development of the kinetic theory, and further think that it was for the chemists to produce the fact of the variability of the specific gravities, which they would probably not have failed to do but for the prevalence of Avogadro's hypothesis, which is virtually the assertion of the constancy of the specific gravities.

3. The unit of numbers being represented by Cl=35.5, it is likewise represented by H=1, and as the product of the union of the two elements is HCl, 36.5 = two vols., combination takes place by addition and not by substitution; consequently are

4. The elementary molecules not compounds of atoms? And the distinction between atoms and molecules is an artificial one, not justified by the natural facts.