It seemed impossible to determine the equivalent weight of carbon, just as in Dalton's system it was impossible to determine the atomic weight of carbon'.

If the unit of equivalency is 8 parts by weight of oxygen, what is the equivalent of copper? An electric current is passed through a voltameter and also through molten cuprous chloride; for every 8 parts by weight of oxygen set free in the voltameter 635 parts by weight of copper appear in the second vessel: cupric chloride is substituted for cuprous chloride, and now 3175 parts of copper are eliminated for every 8 parts of oxygen. So in the compounds of copper and oxygen, we have in one case 63.5 of copper combined with 8 of oxygen, in the other 3175 of copper with 8 of oxygen.

So long as the term equivalent was applied to acids and bases, or to oxides, it had a definite meaning. The amount of oxide which neutralised unit weight of standard acid was the equivalent of that oxide, because it was equal, so far as neutralising power went, to some other weight of another oxide. 'When we speak of the equivalent of a body,' said Gerhardt, 'we should always indicate to what other body, to what func'tions, to what properties, that equivalent corresponds". Richter shewed that there is a constant relation between the amount of oxygen in an oxide and that in the acid which neutralises this oxide: e.g., in sulphuric acid, he said, the oxygen is three times, and in nitric acid five times that in the oxide neutralised, &c. This rule was made general. Now the equivalent of aluminium was said to be 137: the formula of sodium sulphate, in accordance with Richter's rule, was written NaO. SO,; hence the formula of aluminium sulphate should have been written AlO. SO,, (137 x = amount of aluminium uniting with 8 parts by weight of oxygen); but the formula was almost invariably written Al,O,. 3SO,, which is a departure from a strictly equivalent notation.

1 Thus for iron we have the equivalents 28 and 186: for carbon, the equivalents 3, 4, 8, and 12: for nitrogen, 4'6 and 23: for oxygen, 8 and 16: for silicon, 7 and 3'5, &c. &c. Williamson, C. S. Journal, 22. 328.

2 Quoted by J. J. Griffin in the The Radical Theory in Chemistry, p. 32.

Mohr (Mechanische Theorie der Chemischen Affinität) who strongly upheld an equivalent notation, admits (loc. cit. pp. 143 -144) that no equivalency exists between the oxides RO and R,O,; he also despairs of determining the equivalent of phosphoric acid. Those quantities of two substances are, he says, equivalent, which, by combination with other bodies, produce similar compounds; but he fails to define 'similar 'compounds,' or rather he admits the impossibility of such a definition.

That the weights of elements which mutually combine do not always represent equivalent quantities of these elements was gradually discovered; but the so-called equivalent notation assumed that these weights do represent equivalent quantities of the combining elements.

8. The systems of chemical notation founded respectively on the atomic weights of Dalton, and on the equivalents of Wollaston continued to hold divided sway over the minds of chemists1. A man of preeminent powers of classification was required.

The system of chemical classification and notation elaborated by JACOB BERZELIUS (1779-1848) was essentially electrical. The dualism of the Berzelian school was the logical development of the views of Lavoisier concerning salts, and of the hypothesis of Davy upon the relations between electrical and chemical actions. At present, however, this part of the work of the great Swedish chemist does not specially concern us.

Berzelius recognised the necessity of extending the generalisations already made concerning the combinations of atoms. To say that when two elements, by combining together, form only one compound, that compound contains one atom of each

The student who wishes to pursue this subject in greater detail may consult any of the older text-books, on the laws of combination and atomic weights, e.g. Turner's Chemistry, pp. 212—235; he will thus become persuaded how impossible it was to determine the values of atomic weights with certainty. Some interesting points especially regarding the proposal to give two equivalents, or atomic weights, to some of the elements will be found in Griffin's Radical Theory, pp. 30-43.

2 For a brief notice of the system of Berzelius regarding the constitution of compounds see chap. II. pp. 108-111.

element, was, according to Berzelius, not fully warranted by facts.

To discover the laws which govern atomic combinations was the task that Berzelius proposed to himself. He argued that inasmuch as the number of compounds formed by the mutual actions of any two or three elements is evidently very limited, there must be certain laws expressing the conditions under which alone atoms combine.

Berzelius regarded Gay Lussac's law of gaseous combination-'equal volumes contain equal numbers of atoms'as the most important of the generalisations made concerning atomic combinations, but he restricted the application of this law to elementary gases. He admitted that a compound gas might contain half, or even less than half as many atoms as were present in an equal volume of an elementary gas, he did not compare the atomic composition of elementary and compound gases; he thus evaded the objections urged by Dalton against the law of Gay Lussac, and at the same time he declined to accept the statement of Avogadro, ' equal volumes contain equal numbers of molecules.'

The ratios of the weights of the combining volumes of elementary gases were regarded by Berzelius as representing the ratios of the weights of the atoms of those elements; therefore to water, nitric oxide, and ammonia he gave the formulæ, H2O, NO, and NH, because two volumes of hydrogen unite with one volume of oxygen to form water, one volume of nitrogen unites with one volume of oxygen to form nitric oxide, and ammonia is produced by the union of one volume of nitrogen with three volumes of hydrogen.

But the volumetric method was of limited application to the problems of chemical synthesis. Berzelius attempted to state general rules with regard to the combinations of atoms in solid and liquid compounds. These rules referred chiefly to oxygen compounds which play so important a part in mineral chemistry wherewith Berzelius largely concerned himself. The most important of the Berzelian rules were three.

I. If an element form two oxides with twice as much oxygen by weight in one as in the other, that with the

M. C.

2

smaller amount of oxygen is to be represented as a compound of one atom of element united with one atom of oxygen, and that with the larger quantity of oxygen as one atom of element combined with two atoms of oxygen.

II. If an element form two oxides, one of which contains one and a half times as much oxygen as the other, that with the less oxygen is to be represented as composed of one atom of element and one atom of oxygen, and the other compound as formed by the union of two atoms of element with three atoms of oxygen.

III. The amount of oxygen in an acid is a simple multiple of the amount of oxygen in any base with which the acid combines', and this multiple generally also expresses the number of atoms of oxygen in the acid: thus in the case of sulphuric acid and potash, an amount of acid containing 24 parts by weight of oxygen combines with that amount of potash which contains 8 parts of oxygen, therefore, by the Berzelian rule, there are three atoms of oxygen in one atom of sulphuric acid. When nitric acid neutralises potash there are 40 parts of oxygen in the acid for every 8 parts in the base; therefore an atom of nitric acid contains five atoms of oxygen.

By the use of these rules Berzelius determined the formulæ of many metallic oxides and salts. While he was thus engaged, Dulong and Petit" announced their 'law of atomic 'heats'; and shortly afterwards Mitscherlich, his 'law of 'isomorphism.'

Berzelius adopted both laws, and by their helpʻ, along with his own rules, he drew up a table of atomic weights which in very many cases were almost identical with those now in general use.

1 This had been stated by Richter many years before Berzelius: see ante p. 15. 2 See p. 46. 3 See pp. 65-71.

4 Berzelius formulated the law of isomorphism in its bearing on the problem of determining atomic weights, thus (Lehrbuch 3rd ed., p. 98)—when one body is isomorphous with another, the number of atoms in which is known, then the number of atoms in the other is known also, because isomorphism is a mechanical consequence of identity of atomic structure.

Berzelius himself admits that the atomic weights determined by his rules are in many cases open to doubt (Lehrbuch Ist edition, vol. III. part i. pp. 87-102). Berzelius had a remarkable amount of tact; his rules were empirical but he balanced probabilities so well that he generally got the best possible result.

9. The separation which Berzelius made between formulæ of elementary and compound bodies, and his refusal to accept Avogadro's hypothesis while admitting Gay Lussac's generalisation, led him to a very curious result.

Two volumes of hydrogen, weighing 2, combine with one volume of oxygen, weighing 16, to form two volumes of water-gas. Therefore said Berzelius, two atoms of hydrogen combine with one atom of oxygen to form one atom of water-gas. But water contains less oxygen, relatively to hydrogen, than any other known oxide of hydrogen, therefore it is better to regard it as a compound of one atom of oxygen with one double atom, or with one atom itself composed of two equivalents, of hydrogen. Again in the formation of the lowest oxide of nitrogen two volumes of nitrogen combine with one of oxygen; but it is better to regard the nitrogen as composed of double atoms each occupying twice the volume of the atom of oxygen. Once more; hydrogen and chlorine combine in equal volumes, and the volume of the product-hydrochloric acid-is equal to the sum of the volumes of its constituents; but as the hydrogen atom was regarded by Berzelius as double, he wrote the atomic synthesis of hydrochloric acid as