atomic hypothesis rests, therefore, upon the sure founaation of experiment. The same may be said of the considerations upon atomicity. They are founded upon the fact that the forms of combinations are various, as we have learnt, in the first place, from the discovery of multiple proportions by Dalton, and, in the second place, from the discovery by Gay-Lussac of the relations by volume according to which gaseous bodies combine— relations which are simple, but not identical for different gases. The considerations, therefore, upon the valency or the combining value of elements would survive the hypothesis of atoms if the latter were one day replaced by a more general hypothesis. But this day has not arrived; it is useless to attempt to discredit the former as long as it proves itself productive. Its fertility and its power are clearly manifested in the incessant progress of the science. It has thrown light upon the most recent discoveries, as well as been, since the time of Dalton, its immortal author, the most perfect instrument in the most profound theoretical conceptions and the safest guide in experimental researches.

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APPENDIX.

NOTE I.

WATER OF CRYSTALLISATION.

THE combination with water of crystallisation is a phenomenon both of a chemical and of a physical order: of a chemical order, since the chemical force, elective affinity, plays a part in the phenomenon, and of a physical order, since it is connected with external form and change of state. Let us consider salts, properly so called. Their hydration or their degree of hydration is determined by the nature of the base, rather than by the nature of the acid; for we know that all the sulphates, for example, do not crystallise with the same quantity of water, and that two` very similar sulphates-those of potassium and of sodium, for instance-can exist one in the anhydrous, and the other in the hydrated condition. If, therefore, it is the nature of the base which determines the degree of hydration, at least in certain salts, it seems that it is the base also, or rather the metal, which attracts the molecules of water. This attraction may be due to the development of supplementary atomicities in the metal of the salts and in the oxygen of the water. are now upon a ground riddled with hypotheses. brevity's sake, therefore, I will take a single example.

We

For

Copper sulphate crystallises with five molecules of water. The copper becoming quadrivalent can attract these molecules, supposing the oxygen of the water itself to have

become quadrivalent, and we may conceive that the five molecules can be joined together so as to leave at the end of the chain two free atomicities by which the system is attached to the copper. This idea is expressed in the following formula :

The molecules of water were free; they are now riveted to one another and to the sulphate of copper: they have lost something, and changed their state by becoming solid, and this double condition has given rise to a disengagement of heat. And let us notice that this chain of molecules of water can be increased, so to speak, at will. In ferrous sulphate, for instance, it is increased by two links. Lastly, the molecules, especially when they are numerous, can fix themselves upon several polyatomic elements in the same compound. This might easily be developed, but I stop: I am satisfied with having stated the idea and given an example.

NOTE II.

THE CONSTITUTION OF DOUBLE SALTS.

Let us take as an example the double sulphates of the magnesium series. In order to explain the attraction which sulphate of magnesium exercises upon sulphate of potassium, several hypotheses may be brought forward. The magnesium becomes quadrivalent, and exchanges two valencies either

with two atoms of oxygen, or with the atom of hexatomic sulphur of the molecule of sulphate of potassium.

The two molecules are united by the sulphur of one to the oxygen of the other, or, which appears less probable, by the sulphur of one to the sulphur of the other, or by the oxygen of one to the oxygen of the other, the atoms of oxygen becoming quadrivalent. It is not necessary to develope this at length by formula which are moreover easy of construction. I here give two of these formulæ, and only add that such combinations between molecules rich in oxygen appear to me to be caused rather by the union, that is to say, by the affinity of heterogeneous atoms, than by the union of atoms of the same nature, as sulphur with sulphur and oxygen with oxygen.

Here two atoms of oxygen of the potassium sulphate have become quadrivalent, as well as the magnesium of the molecule of magnesium sulphate.

Here magnesium, becoming quadrivalent, is attached to the hexatomic sulphur of the molecule of potassium sulphate. I will not dwell at greater length upon this view, since it is entirely hypothetical.

NOTE III.

THE ISOMERISM OF THE AMYL ALCOHOLS.

In order to give an idea of the facility with which the theory of atomicity interprets and foretells cases of isomerism, we will here discuss at greater length the isomerism of the amyl alcohols. We were unwilling to introduce it into the text, in order to avoid complicating our explanation.

Primary, secondary, and tertiary alcohols are known (see p. 296). The normal amyl alcohol, discovered by Lieben, and the amyl alcohol of fermentation are both primary. The fermentation alcohol rotates a ray of polarised light to the left. A. Le Bel has recently discovered the amyl alcohol which possesses a dextro-rotatory power. Pasteur made known the inactive variety, which is a mixture of the dextro-rotatory alcohol with the levo-rotatory alcohol.

The following formulæ express the constitution of these alcohols :

Comparing the constitution of these alcohols with that of ordinary alcohol, we may regard the two first as ethyl hydrate in which one atom of hydrogen of the group CH, is