These numbers were not given as truly measuring affinities; but, it was said that the sum of the affinities of the products of a reaction is always greater than the sum of the affinities of the original substances. Thus, barium acetate is decomposed by potassium sulphate with the production of barium sulphate and potassium acetate. Now the affinity of baryta for acetic acid is represented in the table by the number 29, and that of potash for sulphuric acid by 62: but the numbers representing the affinities of barium for sulphuric acid and potash for acetic acid are 66 and 26 respectively; hence 29+62=91, but 66 +26=92.

Bergmann regarded the relative quantities of acids needed to neutralise a given quantity of base (or vice versa) as measures of the affinities of the acids for that base. Thus he said that 100 parts by weight of potash are neutralised by 78 parts of sulphuric acid, and by 64 parts of nitric acid; he therefore concluded that the affinity for potash of sulphuric acid is greater than that of nitric acid.

The phenomena of affinity were regarded by Boyle as connected with the mutual attractions between the small particles of bodies. Newton had adopted a similar view and had more especially insisted on the two-sidedness of this attraction1.

201. The subject of affinity was regarded by Berthollet (in the Essai de Statique Chimique) also from this point of view. The mutual attractions between the small particles of bodies which give rise to chemical phenomena Berthollet regarded as probably of the same kind as the mutual attractions which occur between the masses of bodies. The immediate effect of the affinity exerted by one substance on another is the combination of these substances. 'Every substance,' said Berthollet, 'which tends to enter into combination reacts by reason of its affinity and its mass'2.

But chemical action does not depend solely on affinity and mass. The physical states of the bodies, the degree of condensation or dilatation, &c. condition the chemical change;

1 For a full historical account of affinity see Kopp's Geschichte der Chemie 2. 285-324.

2 Essai 1. 2.

'these are the conditions which, in modifying the properties 'of the elementary parts of a substance, form what I call its 'constitution".

Berthollet thus distinguishes between chemical properties which do, and physical properties which do not, depend immediately on affinity. But at the same time he recognises the close connection between these properties; he even speaks of different kinds of affinity of which chemical affinity is one. As we saw in chapter II. (par. 173), Berthollet insists on the reciprocity of all chemical actions; even in the case of a liquid he regards the small particles as exerting mutual attraction, or, as he says, mutual affinity.

The object of Berthollet's Essai is to consider the causes which produce variations in the results of chemical action, i.e. the product of affinity and mass.

It should, I think, be especially noted that Berthollet recognised the possibility of reversing a chemical change by varying the conditions, more especially the masses of the reacting substances, under which the change proceeds. A substance with a small affinity for another, if present in large quantity, might decompose a compound of the second substance with another for which the affinity of the second substance was comparatively large. 'The measure of the affinity 'proper to every substance is', according to Berthollet's view, 'the saturation which it is able to produce with those sub'stances that can combine with it'. It follows therefore that, that acid the smallest quantity of which is needed to saturate a given weight of a base has the greatest affinity for that base. We must remember that Berthollet' regarded chemical compounds as of no definitely fixed composition, and that he therefore had not gained the conception of equivalent, or combining, weights. We shall then see that his statement, that chemical action is proportional to the products of the masses and the affinities of the acting substances, really supplies a means for determining the equivalents of the reacting substances. Until Berthollet's theory of affinity was 1 Essai 1. 3. See also ante, chapter II. par. 173. 2 Essai 1. 535.

supplemented by the knowledge of the equivalent weights of acids, bases, and other compounds, it was of necessity unproductive.

The theories of affinity which prevailed before Berthollet were all founded on the assumption, that, if a substance, A, decomposes another, BC, with production of AC and B, then the affinity of A for C is greater than the affinity of B for C. Berthollet declared this conclusion to be erroneous. Whether A shall or shall not decompose BC, depends, according to Berthollet, not only on the affinities of A and B for C, but also on the quantities of A and BC which take part in the reaction.

202. When we come to more recent times, it is very difficult to gain a clear conception of the meaning of the term affinity'.

I think we shall do well to regard the subject, in the first place, from the dynamical point of view, as far as possible apart from any theory of the structure of matter.

The compounds, AB and CD, react to produce two new compounds, AC and BD; there is mutual action and reaction. Looking at the transaction from one side only, we may say that AB exerts force on CD, or CD on AB. Now this force may be measured; (1) by finding the acceleration imparted to the acting masses of AB or CD, i.e. practically, by measuring the velocity of the chemical change; or (2) by arranging the conditions so that the new compounds, AC and BD, are free to act and react, in which case AC will exert force on BD, and BD on AC, the final result being the establishment of equilibrium in the whole system. By determining the masses of AB, CD, AC, and BD, present when this equilibrium is established we shall have the data for finding the ratio of the force tending to change AB and CD into AC and BD, to the force tending to change AC and BD back into AB and CD2.

1 See, for instance, the article 'Affinity' in Watts's Dictionary, vol. I.

2 The dynamical expressions force, velocity, &c., are used here and throughout the paragraphs dealing with affinity in senses not strictly accurate, and which vary somewhat from time to time. This is especially marked in some of the quotations

But the question of affinity may be approached from another point. When actions and reactions between the parts of a material system are attended with changes in the configuration of the system, these actions and reactions are also attended with changes in the form and the distribution of the energy of the system. Hence, measurements of the losses or gains of energy of a chemical system under defined conditions may furnish data from which comparative estimates may be deduced of the mutual actions between members of that system. Measurements of the quantities of heat evolved or absorbed during definite chemical changes appear to afford the easiest means of measuring gains or losses of energy, and in this way of the comparative magnitudes of the affinities of different substances.

But before we can hope to gain exact measurements of affinity, we must have a clear conception of what it is we want to measure. Affinity, I think, is usually regarded as an action, or sometimes as the cause of an action, of some kind, which occurs between the atoms of chemical elements, such action resulting in a loss, or gain, of energy to the system of which these atoms are the constituents. Now it is possible that chemical affinity may be analogous to electrical potential; that as the existence of a difference of electrical potential between two particles implies the possibility of electrical work being done, so the existence of what might perhaps be called chemical potential between two atoms means the possibility of chemical work being done. If this supposition were adopted, we should look to electrical methods for the means of investigating chemical affinity.

To sum up. We may regard affinity as essentially connected with interatomic, and perhaps intermolecular, actions; and we may attempt to obtain measurements of different affinities by electrical methods: or we may be content to connect the term affinity with the actions and reactions which

from the memoirs of Guldberg and Waage. But it is almost impossible to do otherwise, unless one were to invent a series of new terms. To do this would, I think, be less advisable than to employ the terms in common use even if the meanings attached to them are less precise than could be wished.

occur when two, or more, chemically distinct substances combine to form new substances; and we may seek to deduce measurements of these actions, either from the velocities of the chemical changes, or from the conditions of equilibrium of the changing systems, or from observations of the changes of the energies of the reacting bodies.

The more important attempts which have been made to solve the problems of affinity may all, I think, be classed under these headings. Most important work has been done by Guldberg and Waage, and by Ostwald, in framing and applying a theory of affinity founded on measurements of the velocities of chemical changes, and of the conditions under which equilibrium is attained by given systems.

Berthelot and Thomsen have devoted themselves chiefly to the thermal aspects of the subject. Helmholtz, following on the older work of Berzelius, Faraday, Joule, and Thomson, has recently made some advances in applying electrical methods to these questions.

SECTION I. The Theory of Guldberg and Waage.

203. We have seen how much Berthollet insisted on the importance of considering the relative masses of the reacting substances which take part in every chemical change. It is to this special part of the general question of affinity that Guldberg and Waage have chiefly devoted themselves'.

Berthollet's statement "Toute substance qui tend à en'trer en combinaison agit en raison de son affinité et de sa 'quantité" (Essai 1. 2), has been extended and rendered more exact by the researches of these naturalists. They thus express themselves: "Suppose that two bodies, A and B, can 'be converted, by double decomposition, into A' and B', 'and that A' and B' can be reconverted, under similar con'ditions, into A and B; neither of these changes will be com'plete. At the close of the reaction there will always be 'present four bodies, A, B, A' and B'; and the force which

1 Études sur les Affinités Chimiques (Christiania, 1867), and Journal für prakt. Chemie (2) 19. 69.