Allow me, in the first place, to correct the opinions concerning the teaching of chemistry in France, which I find expressed in your article, and which have been propagated, perhaps intentionally, in foreign countries. There is no regulation which makes it obligatory on professors of the Faculties to adopt any particular notation, and, as a matter of fact, both notations, by equivalents and by atoms, are about equally represented in our lectures. At the Sorbonne, MM. Würtz and Friedel have adopted the system of atoms; the College of France presented last year a professor who uses the atomic notation; I was commissioned to make the report to the Minister, who gave his approval and made the nomination. In examinations both notations are equally accepted, and, if any pressure exists on the candidates, it is exerted by the partisans of atoms rather than by the others. Officially, therefore, perfect freedom exists on this question. If the atomic notation has not been generally accepted in France, it is because it has not succeeded, so far, in obtaining the good opinion of the majority of scientists; but, notwithstanding, imputations have not been spared that the partisans of equivalents are animated with a retrograde spirit.
Allow me, in the next place, to point out some observations on the fundamental part of the question under discussion. It presented itself before the Paris Academy of Sciences under two heads: the system of atoms, and the language or notation of atomic weights. You were right in separating these two things. I had tried to do the same thing, but with less distinctness, in my last work, On Chemical Synthesis, in which I explained the system very fully, but without adopting it, and I said that the notation by atoms possesses certain advantages, but also some disadvantages. The discussion recently raised could not, in the nature of things, assume this methodical form; but I believe that I kept the same ground, as I always said that the two languages expressed the same ideas in the same way, in most cases, except that special advantages belonged to each system of notation. Your conclusions seem to be about the same as mine.
The definition of equivalents, which you accuse me of not giving, was nevertheless presented during the discussion, and I will take the liberty of reproducing it: "Equivalents express, in my opinion, the ratios of weight according to which bodies combine or substitute themselves for one another." These ratios may be determined by the balance with infinitely greater precision than can be ascribed to most physical laws. As, however, experience proves that bodies combine according to several proportions, which are multiples of one another, it follows that equivalents themselves are only determined within an approximation of a multiple of a certain unity, precisely as axes are determined in crystallography. The choice of the unity belonging to each body is therefore somewhat arbitrary. It may be determined from purely chemical considerations, which are never wanting, by taking the weight which agrees the best with the general reactions of the body, which affords the simplest form, and that which conforms the best with analogies.
These analogies are generally expressed by precise rules which are founded on the reciprocal substitution of metals and metalloids, the formation of oxides and acids, and their reciprocal combinations, and the multiple proportions according to which elements combine. In only one case, that of alumina, have we had to appeal to more delicate analogies, drawn from the existence of a remarkable class of double salts of this base with those of the sesquioxides. It is only in a subordinate way, and for the purpose of giving greater precision to chemical analogies, which are often somewhat vague, that physical properties have been introduced, such as the gaseous density, the specific heat, the crystalline form, the molecular volume in the solid state, etc.
The part which physical properties are to play in the determination of equivalents, and the relative importance of these properties seem to me to constitute the only difference between your views and mine. If it was possible to make equivalents agree exactly with gaseous densities, as the old atomic school had hoped to accomplish, the numbers obtained would probably be adopted by all chemists. This has happened in organic chemistry, in which the same equivalent weights are accepted by every body. Unfortunately, however, this concordance does not exist in mineral chemistry, whence the attempt of the new school to establish atomic weights by means of specific heats. But I persist in the opinion, although I am sorry to find that it is opposed to yours, that this base has not sufficient theoretical solidity when it is in contradiction with gaseous densities. The specific heats of simple gases, which obey the laws of Mariotte and of Gay Lussac (an obedience which is expressed by he constancy of their gaseous densities), are necessarily the same under the same volume, because the specific heat measures the work accomplished in fulfilling these laws. If the specific heats of the elements in the solid state do not observe the same ratios as in the gaseous state, it is for one of the two following reasons, either the specific heats of the solid elements change unequally with the temperature, as I believe is the case, or two gaseous molecules are united in one solid molecule, as the atomists suppose. In either case, it seems to me that the specific heats of solids must be put aside in the determination of absolute equivalents.
I insist the more on this point that the new equivalents, if we attribute to this word the extensive meaning that you rightly give to it, introduce an undeniable complication in chemical reactions. In your classical researches on the specific heats of saline solution you found yourself obliged to double the atomic weights of hydrochloric and of nitric acid and of their salts, with the object of expressing with greater clearness the analogies and parallelism of their properties. You wrote:
H2Cl2; Na2Cl2; N2O5,H2O; N2O5,K2O,and in the same manner you were led to double acetic acid and the acetates:
C4H6O5, H2O; C4H6O5, K2O.
The same necessity has been felt by all those who have had to express the equivalent ratios of acids, of water and of bases, as may be seen in the remarkable papers of Mr. Thompson on Thermo-chemistry, and even in the new edition of Gmelin, now publishing in Germany (see, among other things, iodic acid I2O5, H2O).
The agreement of the numbers adopted by the partisans of atomic weights is then more apparent than real.
But I have no wish to prolong this controversy, particularly, as, between us, the only question is as to ascribing one value or another to the unity, of which the various equivalents of the same body are multiples. If we confine the question within these limits, it certainly does not present the excessive importance which has been ascribed to it for the last twenty years. The new atomic school has not, it appears to me, justified its pretension of changing the very base of chemical doctrines, and of founding a new chemistry, essentially different from the old. The only thing it has done has been to intermix the meshes of its hypotheses with our demonstrated laws, and this to the great detriment of the teaching of positive science. I believe that it would be advisable, in the future, to set aside all these systems, and to turn the minds of young scientists towards the really new views offered by molecular mechanics, which promise such rich harvests of discoveries.
Benzeval-sur-Dives (Calvados), August 10th, 1877
I cannot accept your opinion on the absolute value of the law of Woestyn in the calculation of the specific heats of solid compounds. You know very well that M. Kopp, who went to the bottom of this question in 1864, found himself obliged, in verifying this relation, to attribute to the solid elements in their combination specific heats varying from 6.4 (silver, chlorine, nitrogen), down to 4 (oxygen), 2.3 (hydrogen), and 1.8 (carbon). [original note]