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of knowledge, confine itself to gaseous bodies. We do not know how to determine the relative weights of the molecules of solid or liquid substances. We have reason to believe that the molecular structure of a mass of solid or liquid is much more complex than that of a mass of a gaseous substance; no generalisations have yet been made regarding molecular phenomena of solids or liquids comparable with those which under the names of the laws of Boyle, Charles, and Avogadro—have been made regarding molecular phenomena of gases. We must recognise the limits within which a theory of atomic structure can assist advance; if it be pushed too far it will become, with some a dogma, with others a thing to be scorned.

Considering these molecular formulæ HCI, H,O, H,N, H.Si, it is seen that one atom of chlorine is combined with one atom of hydrogen in the molecule HCl, that one atom of oxygen is combined with two atoms of hydrogen in the molecule H,O, that one atom of nitrogen is combined with three atoms of hydrogen in the molecule H N, and that one atom of silicon is combined with four atoms of hydrogen in the molecule H.Si. Considering the molecular formulæ CIH, Cl, Hg, Cl,Bi, and CI,Sn, it is seen that one atom of hydrogen is combined with one atom of chlorine, one atom of mercury with two atoms of chlorine, one atom of bismuth with three atoms of chlorine, and one atom of tin with four atoms of chlorine, in various compound molecules.

These facts may be expressed by saying that the atoms of oxygen and mercury are divalent, the atoms of nitrogen and bismuth are trivalent, and the atoms of silicon and tin tetravalent, i.e. so far as the data at present before us are concerned, the atom of oxygen or of mercury can combine with two atoms of hydrogen or of chlorine, the atoms of nitrogen and bismuth can combine with three atoms of hydrogen or chlorine, &c., to form compound molecules.

56. But these terms monovalent, divalent, &c., must be more strictly defined.

If the table on pp. 37–40 is examined, it will be found that all molecules of gases containing only atoms of hydrogen,

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[fluorine]', chlorine, bromine, iodine?, and thallium, contain two atoms; the molecules in question are,

H,, Cly, Brg, I., (HF]', HCI, HBr, HI, ICI, TICI. These then--H,[F]', CI, Br, I, Tl-are monovalent atoms, i, e. atoms which combine each with one other atom to form molecules.

Now if we tabulate the formulæ of molecules composed of two elements, one of which is H, F, CI, Br, I, or Tl, we have this result,

HgCl : OH, OCI, SH, SeH, TeH, Cd Bro, ZnCl, HgCl, HgBrg,
Hgln, SnCly, PbCl2: BF3, BC, BBrz, NH, PH3, PCI, AsH ,
AsCl3, Asiz, SbClz, BiCl3, InClz : CH4, CC14, SiF4, SiCl4, Sily, TiClų,
ZrCl., VC1,, SnCl,, SnBr, U Bry, UCI: PF:, NbCl, TaCig, MoCl.,
WClz : WCI. [A1,Clo, Al,Bre, Al.16, Fe,Cle, Cu,Cl2, Ga,Cla, Sn,C1..]

Omitting the formulæ in brackets,-inasmuch as these molecules contain more than a single atom of the element other than H, F, CI, Br, I, or T1,--the following arrangement expresses the results of this tabulation.

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Monovalent atoms H, F, Cl, Br, I, TI.
I. Atoms which combine with one monovalent atom to form a

compound molecule Hg.
II. Do. two do. O, S, Se, Te, Cd, Zn, Hg, Sn, Pb.
III. Do. three do. B, N, P, As, Sb, Bi, In.
IV. Do. four do. C, Si, Ti, Zr, V, Sn, U.

V. Do. five do. P, Nb, Ta, Mo, W.
VI. Do. six

do. W.

When it is said that one atom is combined with another, direct action and reaction between these atoms in the molecule is assumed. In saying, therefore, that one bismuth atom

1 Mallet (Amer. Chem. Journal 3. 189] has shewn that at low temperatures the molecule of hydrofluoric acid must be represented by the formula H,F2; at higher temperatures however the formula HF represents the molecule of this gas. It is possible that hydrofluoric acid is a ‘molecular compound' at low temperatures (see Section 5 of the present chapter); determinations of the density of this gas for a considerable range of temperature would throw light on this question.

2 The iodine molecule is probably monatomic at very high temperatures, and so forms an exception to this statement. (See ante, p. 42, par. 20.)

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is combined with three chlorine atoms in the molecule BiCly, it is assumed that the bismuth atom acts directly upon (and is acted on by) each chlorine atom. This is not proved by the formula BiCl,: it might be assumed that the bismuth atom acts indirectly on one chlorine atom through another chlorine atom; but, considering that all molecules which contain a single atom of chlorine contain only one other atom, the simplest hypothesis is that the bismuth atom is trivalent in the molecule BiCl,.

57. A monovalent atom has been defined to be an atom which combines with one other atom to form a molecule. The best definition of a di-, tri-, &c.-valent atom would probably be,—an atom which combines with two, three, &c. other atoms to form a molecule'; but the definition generally adopted is,-an atom which combines with two, three, &c. monovalent atoms to form a molecule.

According to this definition the valency (or equivalency, or quantivalence) of an elementary atom is a number which tells the number of monovalent atoms (i.e. atoms of H, F, CI, Br, I, or Tl) with which the given atom combines to form a molecule. Of the 26 elements (not including, that is, the typical monovalent atoms) in the foregoing six series, four, viz. P, Sn, W and Hg, are found each in two series. Recalling the fact that an element has frequently more than one equivalent number, and remembering that we are now endeavouring to arrange the elementary atoms in groups, the members of each of which are to be equivalent among themselves, this variation in the valency of the atoms of these four elements is not surprising.

The fact that the number of monovalent atoms combining with some of the other elementary atoms is variable, necessitates an addition to the definition of valency, which may now run thus. The valency of an elementary atom is a number which tells the maximum number of monovalent atoms (i.e.

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1 In Frankland's paper already referred to [Phil. Trans. 142. 417.) this definition is apparently adopte:1, ‘no matter what the character of the uniting atoms may be, the combining power of the attracting element...... is always satisfied by the same number of these atoms' (p. 440).

atoms of H, F, CI, Br, I, or Tl) with which the given atom combines to form a molecule. Of the four atoms in the arrangement on p. 121 whose valency is expressed by more than one number, two,-mercury and tungsten,-combine with an odd or an even number of monovalent atoms, one,tin,-combines with an even number only, and one,-phosphorus,-combines with an odd number only, of monovalent atoms, to form compound molecules.

If those molecules which contain only H, F, CI, Br, I, or Tl atoms and the group of atoms methyl (CH) or ethyl (CH) are tabulated', it is found that such molecules contain two atoms, that is if it be permitted to apply the term 'atom' to the group (CH) or (C,H). These groups may therefore be regarded as monovalent. By tabulating the formulæ of molecules composed of two 'elements,' one of which is methyl or ethyl, we find that lead is to be added to the list of those elements the valency of whose atoms varies but is always expressed by an even number”.

Molecules which do not contain monovalent atoms cannot be employed for decisively fixing the valencies of atoms, although arguments for or against a certain valency may be drawn from consideration of such molecules.

58. From the data already given, the oxygen atom is said to be divalent: now it might be argued that if a molecule is found containing one atom of oxygen and one atom of another element, the second atom is divalent; if a molecule is found containing two atoms of oxygen and one atom of another element, the second atom is tetravalent, &c. The molecules CO and Co, are cases in point. The latter (CO2) has been often used-e.g. by Kekulé in his paper of 1858to prove the tetravalency of the carbon atom. Let the valency of an atom be represented by one, two or more straight lines proceeding from the atomic symbol, thus H -, -O-, - Bi -, &c., then the formula O=C= expresses

1 These molecules are (CH3)H, (CH3)F, (CH)CI, (CH2)Br, (CH3)I, (CH3)H, (C,H,)CI, (C,H,)Br, (C,Hg)I.

• The molecules in question are Hg(CH3)2, Hg(C,H5),, Zn(CH3)2, B(CH3)2, Sb(C2H3)2, Si(C2H3),, Sn(C2H5)s, Pb(CH3),.

the supposed fact that the carbon atom is tetravalent in the molecule CO,. But this formula assumes that there is direct action between the carbon and each oxygen atom, but not between the oxygen atoms themselves; this cannot be accepted as proved. Further, the formula appears to assume a double action of some kind between the carbon and oxygen atoms, such double action being represented by the double

lines =.

59. Let us consider the meaning of these lines (-).

The carbon atom is tetravalent, i.e. the carbon atom combines with not more than four monovalent atoms: but the carbon atom has four equivalencies, or four valencies, or four bonds, or four units of affinity-each of these expressions is in common use—what does this mean??

(1) It cannot mean that the force of affinity of a carbon atom is divided into four parts within that atom, for 'force' has no meaning apart from two or more reacting bodies: force is a name given by one of the parties to a transaction, but a transaction involves at least two transacting parties. The force between a carbon atom and another atom must vary with external conditions, probably with the distance, the mass, and the chemical nature (a vague term, but perhaps as good as can be given at present) of both atoms.

(2) The carbon atom has four equivalencies, or four units of affinity. This cannot mean that four parts of the carbon atom are chemically active, and the other parts inactive: such a hypothesis leads at present to contradictions (see appendix to Section 4); moreover in the present state of knowledge it is inadvisable to hazard hypotheses as to the inner structure of atoms in order to explain chemical phenomena. Atoms may not be homogeneous, but at present they are the ultimate particles to be considered in chemical changes.

(3) The expression under consideration cannot mean that the chemical energy of a carbon atom is divided, or is

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1 A paper of the greatest importance entitled Ueber die Vertheilung der Atome in der Molekel,' by W. Lossen, appeared in Annalen, 204. 265. I have made free use of this paper in the present chapter. (See also Claus, Ber. 14. 432 ; and Lossen, ibid. 760.)

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