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‘always attracts a constant quantity of another.' These constant quantities are the 'affinivalencies' of the elements : one affinivalency of element a always binds to itself one affinivalency of element b. The affinivalency of carbon = 3, of oxygen = 8. In CO, we have 3 parts by weight of carbon combined with 8 of oxygen, but in CO the same amount of carbon with only 4 parts by weight of oxygen; Erlenmeyer's general law is therefore erroneous. If it be said that a constant quantity of one element attracts (not combines with) a constant quantity of another, then, as in CO, 6 parts by weight of carbon attract 16 of oxygen, we must suppose that in CO 16 parts by weight of oxygen are attracted by 6 of carbon, and that the remaining 6 of carbon have no attractive action on the oxygen.

Atoms and relative quantities of matter are compared by Erlenmeyer, but relative quantities do not attract each other. In the molecule CO there is one atom of carbon and one atom of oxygen, and these atoms attract one another; half an atom cannot attract because it has no existence. The hypothesis that an atom is nonhomogeneous, although indivisible, might be made, but is not made, by Erlenmeyer. If an equivalent is regarded as a constant quantity, this quantity attracts sometimes one, sometimes two (or more) equivalents of other elements. The molecule CH, contains one atom of carbon and four atoms of hydrogen; we may say that 3 parts by weight of carbon here attract i part by weight of hydrogen: so in CCI, it may be said that 3 parts of carbon attract 35'5 parts of chlorine. But in CH,Cl 12 parts of carbon attract 3 parts of hydrogen and 35'5 parts of chlorine; in place of 12 parts of carbon we may, if we choose, say 9+ 3 parts, just as we might say that 7+ 5 = 12, or 7144 = 12; but we cannot say that 9 parts of carbon attract 3 parts of hydrogen and the remaining 3 parts of carbon attract the 35.5 parts of chlorine. If we suppose the carbon atom to be perfectly homogeneous, then the whole atom acts on the chlorine atoms and on each of the hydrogen atoms: if we suppose that the atom of carbon is possessed of a structure, it remains to explain in what respect one part of the atom differs from other parts;

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but a part of an atom is not the same thing as a fraction of the relative weight of an atom.

Hofmann speaks of ‘an affinity' as a force proceeding from a constant mass of an element, which mass he regards as the equivalent, and defines it as 'the minimum atom-binding quantity' of the element. He nevertheless uses equivalent as a varying quantity. By an arbitrary choice of certain values for the equivalents of the elements it is possible that the number obtained by dividing the atomic weight by the equivalent weight of any element should be the same as the number expressing the maximum number of hydrogen atoms which can be bound by one atom of the given element.

L. Meyer also speaks of the action of quantities by weight of one element on atoms of another element. In one place he defines equivalent quantities of elements as those quantities which are able to bind to themselves, directly and without the intervention of a third substance, equal quantities of other substances. We should expect 16 parts by weight of oxygen to be equivalent to 12 parts by weight of carbon, and to 14 parts by weight of nitrogen, because 16 parts of oxygen directly bind 16 of oxygen in 0,, 14 of nitrogen in NO, and 12 of carbon in CO: but L. Meyer supposes two free affinities in the last named molecule, i.e. he supposes that carbon bind 16 of oxygen, although the molecule CO contains one indivisible atom of carbon and one indivisible atom of oxygen.

Those hypotheses in which ‘affinities' are regarded as constant weights of matter, or as actions proceeding from constant weights, arise, according to Lossen, from not sufficiently marking the distinction between equivalent and atom. Equivalent, or combining, weights are relative weights of divisible masses; atomic weights are relative weights of indivisible masses. If the atomic hypothesis is adopted, we must regard atomic weights as relative weights of mutually reacting bodies; but equivalent weights, in so far as they differ from atomic weights, are relative weights of imagined sums, or fractions, of these bodies. Bodies, whose relative weights are equal to these equivalent weights, do not mutually react within molecules. To find equivalents, parts by weight

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should be compared with parts by weight, or atoms with atoms.

II. Besides the hypothesis of ‘affinivalencies' already referred to, Erlenmeyer also speaks of mutual actions between atoms as occurring at certain points of these atoms. This may mean either that contact (not of course absolute contact) between the reacting atoms is made at these points, or that mutual atomic action occurs only when these attracting points coincide. The attracting points must be considered as qualitatively different from the rest of the atoms. The form of polyvalent atoms must be such that several points of one can touch the same number of points of another: the positions of the points must be such that when some of these points are in contact it is not necessary that all should be in contact. To fulfil these conditions without supposing the form of the atoms, or at any rate the positions of the points, changeable, is exceedingly difficult. This hypothesis of Erlenmeyer tends to foster the notion of an attractive force proceeding from different points of elementary atoms; Kekulé's graphic formulæ do not, probably, imply this conception, but these formulæ may be, and have been, used as if this conception were true.

A qualitative difference between parts of an atom, can only mean that some parts are chemically active while others are chemically inactive. If the inactive parts are composed of imponderable matter then each n-valent atom must be made up of n atoms; we thus arrive at atomic weights different from those on which the science of chemistry at present rests. If the inactive parts consist of ponderable matter, then in the case of action between different atoms we have action through the ether, but in the case of action between parts of the same atom we have action through ponderable chemically inactive matter. In either case it appears that the notion of atom must be very different from that at present adopted, and, it would seem, necessarily adopted, if facts are to be explained.

But it may be supposed that the active parts of the atom are in a different electrical condition from the inactive parts. If electricity be a form of motion, then some parts of an indivisible atom must be supposed in motion while others are not; if electricity be a fluid, then we have a material difference, arising from the partial fixation of this Auid, between the active and inactive parts of the atom. Both of these hypotheses are opposed to the fundamental conception of atom.

Michaelis has supposed that the attractive force of an atom is exerted in certain fixed directions only. On this hypothesis a straight line joining two atoms which are directly bound together may be regarded as expressing the direction of the mutually exerted force; an n-valent atom has n such directions. If this atom is directly bound to fewer than n atoms, say to n- x atoms, then the mutual action is exerted in n-x directions. Lossen expresses his general agreement with this interpretation of the hypothesis of Michaelis. But if that chemist supposes that to every atom, regarded as a point, there are always attached a fixed number of such ‘lines of force,' then it is asked on what does the atom act when it is bound to less than its maximum number of other atoms?'

The objection urged to van't Hoff's form of the hypothesis now being discussed, is, that by this chemist the 'affinities' of an atom are imagined as arranged in a definite form in space; but as we cannot define an 'affinity,' much less can we assign geometrical figures to the arrangement of these affinities.'

III. L. Meyer supposes that there is one position at which a monovalent atom during its vibration can combine with another atom to form a stable compound, that there are two positions at which a divalent can combine with another atom, and so on. In the molecule NH, we have one trivalent and three monovalent atoms; the nitrogen atom swings through three positions, at each of which it can take up one hydrogen atom. In the molecule OH, the divalent oxygen

1 This criticism is rather weak: we know too little as to what electricity is to hazard such criticism as this; besides, Helmholtz has shewn that there is probably a close and definite connection between the valency of an atom and the electrical charges on that atom; see book is.

atom swings through two such positions. In the molecule NO it appears as if the three positions of possible combination passed through by the triad nitrogen atom must be also touched by the path of the diad oxygen atom, but if so the oxygen atom may, in some circumstances, be trivalent.

The results of 0. E. Meyer's physical and dynamical investigation of the forms of molecules are not in harmony with this view of L. Meyer. The form of a molecule would appear to be dependent more on the number of the constituent atoms than on the valencies of these atoms. But on L. Meyer's hypothesis the nature of the path of the atoms swinging in the molecule must condition the form of the molecule, and the nature of this path is itself conditioned by the valencies of the atoms.

Kekulé has advanced hypotheses as to the motion of atoms within molecules, but these hypotheses are not sufficiently definite to admit of detailed criticism. Lossen however objects to applying to the motion of atoms within molecules the conceptions which arise from a study of the motion of molecules in a confining vessel. If the atoms composing a mass of hydrogen molecules undergo mutual collisions, why, when they have separated a certain distance from one another, is the direction of their motion changed until a second collision occurs ? There is no confining molecular wall answering to the sides of a containing vessel. If it be supposed that the atoms in molecule a enter into collision with the atoms in molecule b or <, then this is equivalent to asserting that a mass of hydrogen is composed not of diatomic, but of monatomic molecules'.

98. Among the various developments of the bond-theory of valency not mentioned in the text, is that which concerns itself with the question whether all the bonds of a polyvalent atom are of equal value, or whether one may be stronger' than another. If the criticism applied to the subject of

1 Here again, I think Lossen carries his criticism too far. The methods of molecular enquiry are necessarily statistical ; a mass of hydrogen may contain many free atoms (or monatomic molecules), and yet for all practical purposes behave as if composed entirely of diatomic molecules.

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