251. Helmholtz thus presents us with a theory of chemical affinity in many respects resembling that held by Berzelius, We are taught to look on each atom as carrying with it a definite quantity of positive or negative electricity; but in place of the varying 'intensity of polarity,' which Berzelius, regarded as closely associated, if not identical, with chemical affinity, we have the varying attractive force with which the equivalents of electricity are held by different atoms1.

252. The theory of chemical equilibrium propounded by Pfaundler, on the lines of that of Williamson, is quite in keeping with the electrical theory developed by Helmholtz, inasmuch as no work need be done in a chemically homogeneous system in which mutual exchange of similar atoms with similar electrical charges is occurring between the molecules which constitute the system 2.

253. I have attempted, in the preceding paragraphs of this section to sketch the present state of knowledge regarding affinity, and at the same time to indicate the methods, and the steps, by which this knowledge has been gained.

In the theory of Guldberg and Waage, we are presented with a general statement of the influence exerted by the relative masses of the substances forming a chemically active system on the equilibrium attained by the system, when all the constituents are free mutually to act and react. The total chemical change, in such a case, is the sum of many changes, each of which may be regarded as determined by the resultant of the actions of various forces, both chemical and physical, Eliminating, as far as possible, the physical actions, Guldberg and Waage call the resultant of the actions of the chemical forces, concerned in each part of the total change, the coefficient of affinity for that reaction. The equilibrium of the entire system is determined by the various coefficients of affinity, and by the active masses of all the constituents. If chemical operations are chosen for study which consist, as far as possible, of one primary and one reverse change, values may be found for various coefficients of affinity in terms of some one chosen as unity.

1 Compare book 1. chap. II. par. 47.

2 See Arrhenius, Ber. 17. 49.

459 But these coefficients of affinity may be further analysed. Ostwald has shewn us how to set about this, in the case of the reactions between acids and bases. When two acids and a single base react, the coefficient of affinity for the reaction may, according to Ostwald, be divided into two parts, one depending only on the nature of the base and the other only on the nature of each acid. In other words, each acid, and each base, exerts a specific influence on the course of the reaction and on the final equilibrium attained by the system. By pursuing this method of enquiry, Ostwald arrives at certain numbers which represent the relative affinities of the acids in terms of that of hydrocloric acid taken as 100. The subsequent researches of this naturalist, we found, on the whole confirmed the values he had assigned to the relative affinities of the acids.

But, as we saw in par. 202, measurements of the changes of energy which accompany changes in the distribution of the chemically different kinds of matter of a system, must throw light on the actions of the forces which come into play in these changes. Such measurements of changes of energy are best accomplished by means of the calorimeter. We found that the thermochemical researches of Thomsen on the phenomena which occur when two acids and one base mutually react, lead, practically, to the same conclusions regarding the relative affinities of acids, as those gained by Ostwald by different methods of investigation.

But the energy-changes which accompany chemical reactions are regarded by the molecular theory as essentially connected with changes in the arrangements of the atoms of the elements which form the reacting systems. Hence, what is desired, is, if possible, to measure the energy-changes which occur along with definite actions and reactions between atoms. Now, we found that thermochemical measurements really represent the sums of many operations, some of which involve evolution of heat, and some, absorption of heat; some of which again are physical and some chemical.

If the term affinity is to be applied only to the transactions between atoms, when viewed from the side of one kind

of the reacting atoms, then thermal methods of investigation cannot at present help us much to a knowledge of affinity. I think it must have been noticed that the term affinity appeared to be continually changing its meaning in the paragraphs wherein the bearings of thermochemical data on this subject were considered. Sometimes affinity appeared to be only another term for chemical change, sometimes it was the force exerted by one atom on another, sometimes it was the energy-change accompanying a change in the arrangement of various chemical substances. When we came to glance at the electrical aspects of the subject, then affinity appeared as nearly if not quite identical with electrical forces. The investigations of Helmholtz seemed to shew us the atoms of every element carrying with them, in their movements, definite charges of electricity, but holding these charges with a force which varies for the atom of each element. Chemical changes appeared to be very largely conditioned by the magnitudes of these electrical charges, and by the forces wherewith the charges are held to the different atoms.

If, in the light of these investigations, the term affinity is still to be employed, it must, at present, have a meaning somewhat vague, or at least wide. When we say that, under given conditions, this compound is produced rather than that, or more of this is produced than of that, because of the differences between the affinities of the reacting elements, we mean, that the final arrangement of the reacting elements is conditioned by the mutual actions of their atoms, and that these actions are largely determined by the electrical charges, and electrical conditions, of those atoms.

Whether the term affinity should be employed at all, with such a meaning as this, is open to doubt.

As long as we deal with certain numbers representing the relative affinities of definite substances, we are on firm ground; these numbers summarise a great deal of information about the substances themselves. But when we attempt to frame a general theory of affinity, we are practically endeavouring to construct a general theory of chemical action, and it is very questionable whether the former, apparently

narrower and more definite term, should not be abandoned in favour of the latter, or some other similar expression. The study of affinity would then be advanced by all the methods which are available for studying the general conditions of chemical equilibrium. These methods, as we found in pars. 185 et seq., are broadly divisible into two groups, thermodynamical and molecular.

Researches such as those of Horstmann, and Gibbs, must largely advance our knowledge of affinity, considered from the thermodynamical point of view, while such investigations as those of Wright, and Helmholtz, must do much to elucidate this subject when regarded from the molecular stand-point.

The theory of Guldberg and Waage, and its development and application by Ostwald, will remain, as the great advance made in recent times in what may be called the practical aspects of the subject of affinity.

CHAPTER IV.

OTHER APPLICATIONS OF KINETICAL METHODS.

254. I HAVE frequently referred to the need of keeping distinct the consideration of molecular phenomena occurring in gases, from that of analogous phenomena occurring in solid or liquid substances. Even in the former cases, many occurrences are more probably to be regarded as connected with the actions and reactions of groups, or aggregates, of molecules, than with mutual actions between the individual molecules themselves.

A full consideration of this subject would lead us into the domain of pure physics; there are however some points which suggest important chemical questions.

In examining the phenomena of isomerism, we found that the formula chosen to represent this or that compound, is sometimes selected from among several possible formulæ, by considering certain physical constants of the compound when in the liquid (or even solid) state. In such a case the assumption is made, that some of the physical properties of the compound in question are connected with the relative arrangement of the atoms in the molecule of this compound. The fact that the compound can be gasified and again condensed without any change of properties renders this assumption very probable. In any case, however, the term molecule, as here employed, means, 'that small part of the gas', obtained by heating the liquid compound, 'the parts of which do not part company during the motion of agitation of that gas.' But there are other physical properties which are more usually regarded as depending on the nature of those