tions. This fact becomes evident if we allow ourselves to be guided in determining atomic weights and in constructing formulæ, not only by chemical considerations, but also by the great physical laws which have been described—namely, the law of volumes, of specific heats, and of isomorphism. Purely chemical considerations might lead us into error. Thus it is not correct to say that the strong bases ought always to contain one atom of metal and one atom of oxygen. Lime, baryta, strontia, cupric oxide, mercuric oxide, &c., contain, it is true, 1 atom of metal and 1 atom of oxygen; but oxide of silver, which is a strong base, contains 2 atoms of metal for 1 of oxygen, the atomic weight of silver being determined by the law of specific heats. As far as concerns oxide of silver, therefore, we make a mistake if we invoke analogy in order to connect it with the preceding oxides in respect to its atomic constitution.

4. The principle of equivalence made use of by Dalton, Wollaston, Gay-Lussac, and Gmelin for the determination of equivalents (which Dalton and Gmelin called atomic weights) would be admirable if it could be applied rigorously either to elements or to compounds.

But we now know that all atoms are not equivalent, and that the case is the same with molecules and with the reactions to which they give rise.

Atoms differ in their combining or substituting value -in their valency, as it is called-molecules in their state of condensation and their degree of saturation, and reactions in the greater or less extent of their com

plexity.

As we have remarked above concerning oxides, it is impossible to cast all this in the same mould.

To return to the exact point of the discussion, it is impossible to consider a molecule of nitric acid and of phosphoric acid as equivalent; and if, in conformity with the rule laid down by Gmelin, 14 is the equivalent of nitrogen because nitrate of silver contains 14 parts of nitrogen for 108 of silver, 10-5 should be the equivalent of phosphorus, for it is the weight of phosphorus contained in a quantity of phosphate of silver containing 108 parts of silver. Now, all chemists admit that the equivalent of phosphorus is 31·4; but then we must no longer consider a molecule of nitric acid as equivalent to a molecule of phosphoric acid, for if the former saturates a quantity of oxide of silver containing 1 atom of silver, the latter saturates a quantity of oxide of silver containing 3 atoms. In fact, the discovery of polybasic acids proved a serious difficulty to the theory of equivalence; it showed that chemical molecules are not equivalent, as was shown for atoms by the law of volumes. Moreover, Gmelin felt that he had met with a difficulty, for he mentions polybasic acids as forming an exception to the theory of equivalence. It is sometimes said-I do not know for what reason- --that exceptions prove the rule; in the present case they have become so numerous and so striking that they have overthrown it. The discovery of polybasic acids has, in fact, been supplemented by other discoveries, and they have completely modified the old ideas upon the equivalence of molecules and of reactions. But

this is not the proper place to develope this point, and we will merely add a remark which seems important.

Dalton and Gay-Lussac alone applied true principles to the determination of equivalents. Dalton attributed to phosphorus the atomic weight 10-3; it represents the quantity of phosphorus which combines with 1 part of hydrogen: to carbon the atomic weight 4.3 (instead of 6); it represents the quantity of carbon which unites with 1 of hydrogen to form bicarburetted hydrogen. Gay-Lussac started from another point of view. Considering ordinary phosphate of soda as neutral, he admitted in this salt the presence of one equivalent of base and consequently one equivalent of sodium. He therefore expressed its composition by the formula PO2.NaO + Aq,' and attributed to phosphorus the proportional number 15.7. The quantity of neutral phosphate of soda which is proportional or equivalent to a molecule of nitrate of soda, NO,.NaO, or of silver, NO..AgO, ought, in fact, only to contain 1 atom of metal, like the latter.

Applying the same principles in other cases, he wrote ferrous oxide FeO and ferric oxide Fe0.

Ferrous sulphate, SO..FeO, was strictly equivalent to ferric sulphate, SO3.FeŝO.

Berzelius, on the contrary, who had at last decided

1 P=15·7; 0=8. At this time no account was taken of basic water. Gay-Lussac therefore involuntarily committed an error in the determination of the equivalent of phosphoric acid. In fact, the quantities of phosphate of soda and of nitrate of silver which enter into reaction, and which are strictly equivalent, are (PO,Na2H) and NO,Ag, and the quantity of phosphorus in (PO,Na,H) is 10.5. This is the number of Dalton.

to admit the existence of sesquioxides, proved that they unite with 3 atoms (molecules) of acid. He consequently represented ferrous and ferric sulphates by the formulæ SO,.FeO and 3SO,.FeО. Is it not evident that he was less consistent than Gay-Lussac, and that these formulæ do not represent equivalent quantities? It is only a strange abuse of language, not to say a logical error, to consider as equivalent a molecule of ferric oxide, which saturates 3 molecules of sulphuric acid, and a molecule of ferrous oxide, which only saturates 1 molecule. Formulæ analogous to those of the sulphates of the sesquioxides, such as those of the phosphates and of several other compounds, which are now distinguished by the name polyatomic, reveal, therefore, serious inconsistencies in the equivalent notation, and we must choose between such inconsistencies and the graver inconvenience of misrepresenting reactions by referring them to strictly equivalent proportions. This point will be developed in the following chapter.

The preceding discussion renders it sufficiently evident that the system of chemical equivalents, and of the notation derived from them, introduced by Dalton, Wollaston, Davy, Gay-Lussac, and Gmelin, were based upon too narrow a foundation for the enlarged edifice of chemistry. Our present system of atomic weights and our notation rest upon a wider foundation. Their establishment has required the numerous efforts which have been perseveringly maintained for a period of thirty years.

79

CHAPTER V.

PRESENT SYSTEM OF ATOMIC WEIGHTS.

GERHARDT AND LAURENT-CANNIZZARO.

I.

THE equivalent notation of the English chemists and of Gay-Lussac, which was adopted by Liebig and defended by Gmelin in 1843, had, at the period of which we are speaking, gained the almost unanimous approval of chemists; they were struck with the exceptions presented by the law of volumes as it was then interpreted, by the useless complication which the conception of the double atoms of Berzelius had introduced into a large number of formulæ, and they were satisfied with the more simple expressions which the notion of equivalents offered for chemical reactions and combinations. The law of volumes was entirely sacrificed. The equivalents of hydrogen, nitrogen, chlorine, &c., corresponded to two volumes, whilst that of oxygen only constituted one. The formulæ of water, HO, of sulphuretted hydrogen, HS, of protoxide of nitrogen,