this formula must necessarily be a saturated molecule'. But each polyvalent atom in a molecule does not necessarily act on the maximum number of other atoms; in many molecules

n1 < ng+2n4 +375 +46 +2:

when this holds good, some polyvalent atoms must have within their 'binding spheres' less than the maximum number of atoms, in other words, some atoms usually divalent must, in this molecule, be monovalent, or some usually trivalent must, in this molecule, be divalent &c. This is expressed in ordinary nomenclature by saying that some of the polyvalent atoms must be linked by 'double' or 'treble bonds', or that some of the bonds' (sometimes it is said, of the 'affinities') of the polyvalent atoms must be 'mutually satisfied.' But I have tried to shew that these expressions are delusive, and that Lossen's method of regarding valency is preferable to any yet proposed.

71. The number of ways in which the atoms comprising a complex molecule may be arranged is evidently very great: to determine the maximum number of possible isomerides of a given formula is a purely mathematical problem. At present we seem justified in concluding that many atomic configurations which are mathematically possible, are physically impossible; this is equivalent to saying that the stability of molecules does not depend solely on the valencies of their constituent atoms. To determine which of the possible configurations of a given number of atoms are stable; to generalise the connections undoubtedly existing between molecular structure and stability, and also between this structure and the functions of the molecule or of parts thereof; this is the task that chemists are now elaborating.

1 See definition on p. 130.

2 Thus, Prof. Cayley, Brit. Ass. Reports for 1875, p. 257, gives the following statement, exhibiting the relations between the number of carbon atoms in the molecules of paraffins and the number of isomeric modifications of each molecule allowed by the theory of valency.

Number of carbon atoms in molecule of paraffin, 1. 4. 7. 10.
Number of possible isomerides

12. 13.

I. 2. 9. 75. 357. 799.

72. The molecular formula of a compound alone sometimes gives us a considerable amount of information regarding the structure of the molecule of that compound. Thus we appear justified, at present, in making the following assertions; (1) molecules containing only monovalent atoms cannot exhibit isomerism; (2) molecules containing a single polyvalent atom united with monovalent atoms only cannot exhibit isomerism; (3) isomerism cannot be exhibited by molecules containing two polyvalent atoms united with monovalent atoms, provided the latter are all atoms of the same element, or all but one atoms of the same element, when the two polyvalent atoms are themselves atoms of the same element.

73. Any molecule containing more than two atoms and not belonging to one of the classes above defined, may exhibit isomerism. The possible variations of structure even in molecules containing a small number of atoms may be large. Thus N2O may have the structure

(1) N-N, or the structure (2) N-N-0,

(neither the nitrogen nor the oxygen atoms can act on more than two atoms, i.e. neither can be more than divalent1). NO can be regarded only as N-O. NO, may be

(1) O— N—O, or (2) O—N-O, or (3) N—O— 0.

or (5) N—0—0—0—0—N, or (6) N-N-0-0-0-0, &c.

In the case of N.O, the first of the possible structures

1 Lossen's nomenclature and notation are used here and generally throughout the rest of this book.

better represents the arrangement of atoms in this molecule than the other, inasmuch as the reactions of this compound shew that there is no difference in the functions of the two nitrogen atoms in the molecule; for a similar reason the third formula for NO, and the sixth for NO are inadmissible; the fifth formula for NO, is improbable because, among other reasons, it would lead to N-O-O as the formula for NO; the fourth formula for N,O, would lead us to expect that this compound when heated would decompose into NO and O, but we know that it gives 2NO. Formulæ (1) and (2) very simply express the formation of NO, by cooling 2NO, and the formation of 2NO, by heating NO, and therefore the structure of the molecule N,O, is more probably expressed by one or other of these formulæ than by any other of the six given above.

The compounds of carbon present the best field for the study of isomerism.

It has been already stated that a molecule containing two carbon (tetravalent) atoms united with five monovalent atoms of one element and one monovalent atom of another element, (i.e. a molecule of the form C,X,X') cannot exhibit isomerism. If however there are four monad atoms of one kind, and two of another in the molecule (if the form of the molecule is represented by the symbol C2X,X') isomerism becomes possible; thus C,H,Cl, may have the structure

atoms combine with monovalent atoms, the existence in the molecule thus produced of a single monad atom of an element different from that forming the other monad atoms renders isomerism possible; thus C,H,Cl (which belongs to the general form C,X,X') may have the structure

So also four molecules C,H,Cl2, five molecules CH¿Cl, six CHCI,', five C,H,Cl,, &c. may exist. Molecules containing four, or more than four atoms of carbon combined with monovalent atoms may exhibit isomerism even when all the monad atoms are of one kind, (i.e. molecules of the general form CX): thus C.H10 may have the structure

Molecules containing five carbon atoms may have these atoms arranged in three ways, as represented by the formulæ

C

C-C-C-C-c, c-c-C-C, and C-C-C.

When six carbon atoms are present in the molecule these atoms may be arranged in five ways, viz.

When eight carbon atoms are present, they may be arranged

in 18 different ways, &c. The maximum number of monovalent atoms which can be combined with any of these arrangements of carbon atoms is found by the formula n1 =2n+2 where n = number of carbon atoms1. But all the carbon atoms in a molecule are not necessarily tetravalent in that molecule (in the ordinary nomenclature some of the carbon atoms may be doubly or trebly linked to one another, or there may exist 'free affinities'). Now the general formula given on p. 139, viz.

shews that the maximum number of monad atoms in such a molecule is dependent only on the number of trivalent and tetravalent, and is independent of the number of divalent, carbon atoms in the molecule. But in applying this formula it is assumed that the number of carbon atoms which are actually trivalent, and of those which are actually tetravalent in any given molecule, can be determined. It is better to represent the molecule of a carbon compound, if possible, as containing only tetravalent carbon atoms: in many cases however this cannot be done; in any case the reactions of the compound must be studied before a formula is given to it.

Let us suppose we are required to assign formulæ to compound molecules containing carbon, hydrogen, and oxygen atoms. When the equation n1 = 2n, +2 is satisfied, the structural formula assigned to the molecule must evidently contain only tetravalent carbon atoms; several such formulæ may however be possible,-thus for the molecule C,HO, two structural formulæ