hydrogen atoms? Because the atomicity of carbon is even, and the valency of its atoms in combinations is expressed by the numbers 2 and 4, never by the numbers 1 and 3. This is the case with carbon, and doubtless also for other elements, though it must be confessed that there are exceptions to this rule.

Nitrogen, univalent in the protoxide NO, is bi

valent in the dioxide NO.

Chlorine, quadrivalent in the peroxide ClO2, is quinquivalent in chloric acid, ClO2(OH).

Manganese, bivalent in MnCl, and in MnO, and sexvalent in potassium manganate, MnO,(OK), is septivalent in the permanganate MnO,(OK).

Tungsten, quinquivalent in the pentachloride WCI,, is sexvalent in the hexachloride WC15.

Uranium, bivalent in the dichloride UCl2, is trivalent in uranyl chloride, UOC1, and quinquivalent in the pentachloride UCI,.

Vanadium, trivalent in the trichloride VCI,, is quadrivalent in vanadyl dichloride, VOC, and quinquivalent in vanadyl trichloride, VOCI.

The consideration with which we close this chapter —namely, the increase in atomicities-brings us back to our starting point-namely, multiple proportions. They are fundamentally considerations upon atomicity, and are the same facts which formerly guided Dalton in the statement of his law, and which at the present time lead us to attribute to elements combining values differing with the form of the compound in which they occur. Thus the notion of atomicity follows the direct interpretation

of facts. It rests upon a solid foundation. In its turn it allows us to connect, interpret, and even foresee a great number of facts. It is therefore useful, because it is productive, and we shall retain it until it is lost in a more general notion embracing a greater number of facts.

CHAPTER III.

CONSTITUTION OF BODIES DEDUCED FROM THE THEORY

OF ATOMICITY.

I.

WE have endeavoured in the preceding pages to define the notion of atomicity, or the valency of atoms. It now remains to show that this notion lies at the base of all the partial theories which have been brought forward by chemists during the last fifty years, and especially to show how it accounts for the properties of those groups of atoms which we call radicals, and which have played so important a part in doctrines relative to the constitution of chemical compounds. There was a time when chemists could confine themselves to the consideration of radicals; in the written language of formulæ they were contented to represent them by distinct expressions, which were isolated from the other elements. They have now gone beyond this. Thanks to the indications furnished by ideas upon the saturation of atoms by each other-that is to say, by the theory of atomicity-they have succeeded in resolving these radicals, in discovering their mode of generation and their structure, and in determining in a plausible

manner the connections which exist between atoms in combinations. This is the path which chemistry has recently followed, and how rapid has been the progress in this direction during the last twenty years! how many obscurities have vanished in the difficult problem of the intimate structure of chemical molecules, a problem the solution of which Gerhardt declared to be impossible! and, finally, what light has been thrown upon the question of isomerism, which has taken such an important position in chemistry! We must prove this before concluding.

Gerhardt's types expressed different forms of combination (p. 211). The hydrochloric acid type represented the combination of two univalent elements; the water type, the union of a bivalent atom with two univalent atoms; the ammonia type, the combination of a trivalent atom with three univalent atoms. These types, then, were not taken at chance; this conception was founded upon a profound idea, the form of which only has become antiquated, but which was fundamentally true, and which brought to light for the first time the differences between the combining capacities of elements. The very existence of the water type depends upon the combining capacity of oxygen, which requires for saturation two univalent elements, while chlorine only requires one. A single atom of oxygen can therefore fix not only two univalent atoms, but also groups of atoms which are one univalent atom short of saturation and the combining capacity of which is represented by that of this univalent atom. The number of these combinations, in which oxygen fixes two univa

lent atoms or residues, and acts as a kind of link between them, is very considerable; hence the richness of the water type. The same remarks apply to the ammonia type; it is therefore unnecessary to repeat them. We will merely remark that the brackets employed by Gerhardt, and which are still in general use, indicate that several elements or residues are united collectively to another element, an union or connection which is now expressed more clearly by strokes which mark the exchanges of units of saturation. The following symbols are therefore identical:

But to return to the residues or radicals which we have just mentioned. We have remarked that their substituting or combinating value is related to the state of saturation of the atoms.

Thus radicals composed of carbon and hydrogen are derived from saturated hydrocarbons by the loss of one, two, three, or four atoms of hydrogen, and we have seen how the theory of atomicity accounts for the state of saturation of the hydrocarbons of the series CH2n+2(p. 213). These remarks may be extended to all chemical compounds. Their molecules may be considered as saturated when the combining capacities of their respective atoms are exhausted. Such molecules cannot increase by direct fixation of other atoms; they can only be modified by