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 103; 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 157. 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 Fe✪ and ferric oxide Fe0.

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

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 Na,H) 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 3503.Fе20 ̧. Is it not evident that he was less consistent than Gay-Lussac, and that these formula 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.

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,

NO, expressed two volumes; those of hydrochloric acid, HCl, of ammonia, NH,, of phosphoretted hydrogen, PH,, &c., represented four.

Gerhardt was the first to draw attention to these errors, and to the necessity of considering as equivalents quantities of water, ammonia, hydrochloric acid, &c., corresponding to equal volumes. Regarding water, H2O, as formed of two atoms or volumes of hydrogen and as occupying 2 volumes, if one atom of hydrogen occupies one volume, he compares it to hydrochloric acid, HCI, formed of one atom or volume of hydrogen and of one atom or volume of chlorine, and occupying 2 volumes; to ammonia, NH,, formed of one atom (volume) of nitrogen and of 3 atoms (volumes) of hydrogen, and occupying 2 volumes. In the same manner the formulæ N2O, NO, CO, CO2, CH, C2H,, which correspond to 2 volumes, represent molecules (Gerhardt still used the term equivalents) of protoxide of nitrogen, dioxide of nitrogen, carbonic oxide, carbonic acid, and of marsh gas and olefiant gas. The atomic weights on which the preceding formulæ are founded are the same as those of Berzelius, i.e. 0=100, H=6.25, N=88, C=75. But the formula of hydrochloric acid, H2Cl2, of ammonia, NH, of marsh gas, C,H,, of olefiant gas, CH, which Berzelius had employed were halved and made to represent 2 volumes. Here lies the true progress.

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It will be interesting to recall the considerations which led Gerhardt to propose this reform in the notation of Berzelius.

Regarding a molecule of water as formed of 2 atoms of hydrogen and 1 atom of oxygen, and carbonic acid as

containing 1 atom of carbon and 2 atoms of oxygen, he was struck, in the attentive study of the reactions of organic chemistry, by the fact that in none of these reactions, represented by the formulæ and equations of Berzelius then in use, were quantities of water and carbonic acid corresponding to H2O and CO2 set free, but that the quantities formed were never less than those corresponding to the formulæ H402 and C2O1.

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We may therefore conclude, he says, that an error has been cominitted in the construction of organic formulæ, for it would be strange if no reaction should give rise to the formation of a single molecule of water or a single molecule of carbonic acid. This is the error: organic formulæ are twice as great as they should be, and must be halved, as well as the atomic weights of metals. These two facts are correlative, and it was precisely those high atomic weights attributed by Berzelius to the metals which gave to organic compounds. formulæ double what they should be. Thus amongst the organic combinations with which we are most fully acquainted we must reckon the acids; their molecular magnitude is determined by their capacity of saturation, and we admit that a molecule of acid saturates a molecule of basic oxide--that is to say, a quantity of base containing one atom of metal. Thus, for example, the formula of acetic acid is constructed by combining it with oxide of silver and analysing the acetate of silver. The composition of this salt, containing one atom of silver, is represented by the formula CHAgО, derived from the atomic weights C=75, H=625,0=100, Ag=1351·6, which are those of Berze

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