Forty years ago Kolbe showed that a strong aqueous solution of potassium acetate, when subjected to the influence of the electric current, is decomposed with formation of the following products. At the anode a gaseous mixture is evolved which consists chiefly of carbonic acid and ethan; while at the cathode hydrogen escapes, and potassium hydrate is formed in the solution. When dilute solutions of the same substance are electrolysed under similar conditions, the decomposition products at the cathode are the same as in the previous case, but at the anode the gas evolved is now oxygen, and free acetic acid makes its appearance in the solution. The difference between the two cases must, on modern views of electrolysis, be attributed to the occurrence of secondary reactions. The primary process is in all cases the transference of the electrically-charged submolecules or ions to the corresponding poles, where they lose their charges, and thereby become capable of reacting with one another or with neighbouring molecules. As a general rule they are, when discharged, themselves incapable of independent existence.

Since reading this paper, I have seen Sir Benjamin Brodie's paper on “The Calculus of Chemical Operations,” read before the Royal Society of London.

The two papers resemble one another, merely in being applications of mathematical language to chemistry. They entirely differ in method, object, and result.

I may here mention, what I have omitted to state explicitly in the paper, that I have no idea of attempting to substitute a functional notation for that in common use. I only propose to use a functional notation to express certain general and serial relations in those cases where the common atomic notation is inconvenient or obscure.

When we consider that the Phlogistic Theory formed, as it were, the central point round which the facts of chemistry first crystallized into regular scientific form, and that for more than a hundred years it was recognised by all as the foundation of the science, we might reasonably suppose that it should contain at least some germ of truth.

I think I shall be able to show in the following note that not only is this the case, but that the theory itself, as stated by its founders, Beccher and Stahl, is, if not strictly true, a very close approximation to what we now recognise as truth.

In this paper the author proposes to use for purposes of classification those radicals or parts of molecules which are common to genera of substances, and within which the changes characteristic of these genera take place.

The idea of chemical structure, as founded on that of atomicity (or the equivalence of atoms), enables us to divide any molecule, whose chemical structure is known, into radicals. The number of ways in which this may be done increases with the complexity of the molecule. Each of these modes of division corresponds to a series of conceivable reactions, some of which have been observed. Any one of these series may be made the basis of classification; but it is obviously most convenient to select for this purpose the most characteristic reactions, and those which are common to such substances as form natural groups. In studying these, we find that each series implies the presence of a particular radical, within which the reactions in question take place. We may call such series of reactions the Generic reactions, and the corresponding radicals Generic radicals. These are sometimes residues of double decomposition, but very frequently this is not the case, and this may account for the fact, that the importance of these generic radicals has been very much overlooked.

We now know a considerable number of elements which exhibit, in their compounds, two or more distinct degrees of atomicity. Thus we have N triatomic in ammonia and its analogues, in nitrous acid, the nitrites and the nitroso-substitution products; pentatomic in the ammonia salts, in nitric acid, and the nitro-substitution products. P triatomic in PH3, PCl3, phosphorous acid, and the phosphites; pentatomic in PCI5, POCI3, H3PO4, HPO3, &c.; C diatomic in CO, and tetratomic in almost all other compounds; a large number of such examples might be adduced, but these may suffice.