64 EQUIVALENCY OF ELEMENTS. it seem probable that any class containing a larger proportion of hydrogen can exist. (1066) Mode of determining the Equivalency of an Element.It is not surprising that in the application of a new theory of such generality, some difficulties have been experienced. Chemists, indeed, are not yet agreed in all cases, as has been already stated, as to the class in which some even of the most important elements are to be placed, because they are not yet agreed as to the mode in which the equivalency of an element is to be determined, and because that equivalency in some cases seems, at first sight, to be variable. The method of determining the equivalency of an element theoretically, least open to objection, appears to be that followed by Naquet. It consists in ascertaining the greatest number of atoms of any monad with which a single atom of the element in question is capable of combining. Chlorine combines with but a single atom of hydrogen, and these two elements have been uniformly regarded as the types of the monad group. The maximum number of atoms of chlorine or of hydrogen with which a single atom of any element is capable of uniting, may therefore be employed to determine its equivalency. Yet there are difficulties when we carry out the principle rigidly. Iodine and thallium are both usually recognised as monads, but if this rule be applied, inasmuch as the compounds ICl, and TICI, are known, each ought to be regarded as a triad. Each atom of oxygen and sulphur may unite with two atoms of hydrogen or with two of chlorine, but never with a larger proportion of either of these elements. They are therefore regarded as dyads; but selenium and tellurium, which are often included in the same class, must according to this rule be reckoned as tetrads, for they form compounds with four atoms of chlorine, SeCl, and FeCl. Sometimes the rule fails in the opposite direction. No compound of lead with hydrogen has hitherto been formed, and the combination PbCl is unknown. Yet it can scarcely be doubted that lead, from its power of forming plumbic tetrethyl, Pb(Є,H.),, should be referred to the group of tetrads. 4 2 It has already been stated that Frankland regards phosphorus and antimony as pentads, since each forms a compound with five atoms of chlorine; and nitrogen and arsenicum are by him also referred to the same group, from their close analogy with phosphorus and antimony, as well as from the composition of several of their compounds, such as the haloid salts of ammonium and the ethyl compounds of arsenicum. THEORY OF POLYAD OR POLYBASIC ELEMENTS. 65 Excepting in the case of lead, there are, however, difficulties in the way of admitting these alterations; inasmuch as the groups of the closely allied elements at present exhibited in the classification shown at p. 24 of vol. I, would be disturbed. Iodine would be severed from the other halogens: selenium and tellurium would be separated from sulphur; and the nitrogen group, at present regarded by most chemists as triads, owing to the well marked character of its hydrogen and chlorine compounds, would be displaced. In the group last named, it is, moreover, a significant fact that the vapour volume of many of their pentad combinations is anomalous, for it has been found that in most cases the atom of the compound yields four volumes of vapour instead of two. This it has been attempted to account for on the principle of dissociation (note § 67), but the explanation is not applicable in every case. Again, chromium forms with fluorine a hexad compound, Er F, of which the vapour density has not hitherto been determined. Chromium, by Naquet's rule, must be a hexad, and if this be so, iron, aluminum, manganese, as well as cobalt and nickel, would require to be transferred to this group, from their close chemical analogies with chromium, and to this there are serious objections. It is, however, not improbable that all these metals should be regarded, not as dyads but as tetrads, for reasons which we shall proceed now to consider, as it will help us towards a solution of some of the difficulties which the fact of combination in multiple proportion seems to present to the theory as above stated. (1067) Bearing of the Law of Multiple Proportion on the Theory of Equivalency-It has been observed that the elementary bodies may be subdivided into two principal groups: one of these comprising the monads, triads, and pentads, combines with the monads, according to the progression of the uneven numbers 1, 3, 5; the other group comprising the dyads, tetrads, and hexads, combines with the monads in the progression of even numbers, 2, 4, 6. In a few remarkable instances the elements appear to form compounds belonging to both the odd and the even series, as in the case of iron, chromium, manganese, and iridium. There are two ways in which this tendency of an element always to combine either with 1, 3, 5, or an odd number of atoms of a monad, or else as regularly with 2, 4, or some even number of atoms, has been attempted to be explained. First, taking Naquet's rule, it is supposed that the highest known compound 66 THEORY OF POLYAD OR POLYBASIC ELEMENTS. determines the equivalency of an element, and that in each of the lower compounds two of the centres of attraction neutralize each other (Frankland). In thallious chloride (TICI), for instance, two of the three points of thallium neutralize each other, whilst in the rarer instances, as when thallic chloride TICI, is formed, each of the three centres is saturated by chlorine. In such cases (TL) of atoms of a Every element cr of partial saturation of the atom as TICI, the centres of attraction in each atom neutralize each other in pairs; and hence the tendency of all the elements to preserve their mode of combination, either always with an odd number monad, or else always with an even number. tends to form one particular class of compounds, which are more stable than any other series into the formation of which it enters. For example, the stable thallium compounds are generally those in which the metal appears to act the part of a monad, not of a triad; corresponding, that is, to TICI, not to TIC. With gold, on the contrary, though compounds like aurous chloride (AuCl) may be obtained, the most stable series is that in which the triad character of the metal is distinctly shown, as in the trichloride (AuCl2). (Pt (Pt Again, in the group of tetrads, though platinum generally which it may be supposed that the two unsaturated centres are neutralized by reacting one against the other. Such a mode of representing the formation of the inferior compounds seems to be suited especially to gaseous compounds like carbonic oxide, as compared with carbonic anhydride O ; where the specific 0 gravity of the gas defines distinctly the molecule of each. There is, however, a second explanation of the method of combination in multiple proportion, which is admissible in certain cases; upon this view it is supposed that in the lower compounds, such as the aurous and platinous groups, two atoms of the element have partially neutralized each other; for instance, aurous chloride, (Au,C) may be represented Cl (Au) (Au (cl THEORY OF POLYAD OR POLYBASIC ELEMENTS. 67 and platinous chloride (Pt,Cl) as (Pt (Pt case, however, it becomes necessary to double the formula ordinarily employed to represent the molecule. Upon either hypothesis a reasonable explanation may be given of the remarkable cases presented where the same element, like iron, seems to combine with the monads in proportions represented by both odd and even numbers. It is, however, necessary to suppose that in such cases as those of iron and the other metals allied to it, viz., cobalt, nickel, manganese, chromium, uranium, and aluminum, instead of being regarded as dyads, they should be viewed as tetrads. If this be granted, the ferrous compounds, such as ferrous chloride, may be represented either as FeCl2, where two of the centres neutralize each other; or as (Fe,Cl)— (CL) Fe (Fe (CL) where the two atoms of iron are represented as united by two points of attraction. In ferric compounds like ferric chloride, of which we know from the density of its vapour that the molecule cannot be less than that indicated by the formula, Fe,"Cl, each atom of iron in the molecule must be united to its fellow by a single point only, as may be represented in the diagram. (Fe) Fe K (Fe K A similar plan would be supposed to prevail in the constitution of the c molecule of aluminic chloride, the density of which corresponds with the formula Al, Cl, and in the case of the analogous body, chromic chloride. The existence of the ferrates, such as potassic ferrate, K.Fee, would be equally easily accounted for, as may be seen in the diagram. Indeed it may be shown that even in so complex a multiple scries as that exhibited by the oxides of manganese, there is no difficulty in representing the mode of combination upon this principle; for example: Even if the systematic carrying out of this view should occasionally necessitate the doubling of a formula hitherto regarded as adequate to represent the molecular constitution of a body, this can scarcely be regarded as an objection, as at present our knowledge of the molecule of any substance not reducible to the condition of vapour is extremely uncertain, and consequently liable to modification if reasonable grounds be shown. It is manifest that whatever theory of chemical combination be adopted we must admit of an additional species of combination by apposition. Such, for example, are the cases when water of crystallization enters into the formation of a salt; and such probably is also the cause of the formation of double salts, like the platinic double chlorides, the alums, and the numerous cases where the union between the two salts is less stable. (1068) Causes of the Polyad Character of Radicles.-The |