'equivalent to the heat which is due to the reverse chemical 'combination by combustion or other means' (loc. cit. (2) 3. 494).

248. The problem was further considered by Sir W. Thomson'. His reasoning was somewhat as follows.

Let unit quantity of electricity pass through a cell of infinitely small resistance; then, by Joule's law, the work done by the current is equal to E, the electromotive force. But 'e' gram of one of the elements of the electrolyte has been electrolysed, in accordance with Faraday's law. Let 0 be the quantity of heat developed by the combination of one gram of this element to reproduce the electrolyte, then, according to Thomson, since no work is expended in any other part of the circuit,

To realise this equation in practice a great many corrections have to be applied.

This formula presents us with an electrical method for determining the heats of combination of various elements, or, we may say, the energy-changes attending the formation of various compounds. In Joule's papers, the values of the quantity represented by were regarded as affording measures Ө of the intensities of affinity' of different substances (loc. cit. 20. 99); but we have seen that this cannot now be held, except the term 'affinity' is used in a very wide sense.

249. Wright has applied Joule and Thomson's method of research, and has endeavoured to determine 'chemical affinity ' in terms of electromotive force".'

In Wright's use of the term, the 'affinity' between the constituents of a compound is measured by the work done in separating the compound into these constituents. This work can be measured by electrical methods; thus, Wright says, the affinity between the final products of an electrolyte, i.e. 'the work done in resolving it into these final products...... 1 Phil. Mag. for December, 1851: see Mathematical and Physical Papers 1. 472.

2 Phil. Mag. (5) 9. 237, 331: 11. 169, 261, 348: 13. 265: 14. 188: 16. 25. See also a general account of his work to the end of 1880 in Chem. News, 42. 249.

'is readily determinable, by determining the difference of 'potential subsisting between the electrodes, and the heat ' evolved as such, during the electrolysis of a gram-equivalent ' (Chem. News, loc. cit.).

But in a process of electrolysis, the electrolyte is first separated into primary, or nascent products, which are such that their change into the secondary, or final products is attended with evolution of heat. The E.M.F. required to separate the electrolyte into the nascent products would therefore be numerically greater than the E.M.F. required to separate it into the final products. Moreover, the E.M.F. required to break up a given electrolyte, under given conditions, into the nascent products of electrolysis, varies, because of the occurrence of secondary physical and chemical actions between the electrodes and the dissolved gases, &c. Heat is generated in these secondary changes, and the energy thus produced diminishes the work that would otherwise be done by the current in effecting electrolysis. Hence the E.M.F. which corresponds to the total electrolytic work actually done by the current, is less than the constant amount which would be required were the process not complicated by secondary reactions'. Wright attempts to find the value of that part of the E.M.F. which corresponds to the secondary changes, (1) when none of the products of electrolysis are developed in the nascent state, and (2) when the products are entirely developed in this state. The determination becomes very difficult in the latter case: if it can be successfully made, we shall have data for finding the E.M.F. produced by the combination of the constituents of certain compounds, starting with these constituents in the nascent

state.

But as the nascent state of a substance most probably represents its condition when the great majority of the molecules are separated into atoms, it follows that Wright's determinations of the two parts of the E.M.F. concerned in

1 Wright, Phil. Mag. (5) 13. 265. For a short and clear statement of the whole of this subject, see Clerk Maxwell's Elementary Treatise on Electricity, pars. 182-192.

2 See Chem. News, loc. cit. p. 253.

electrolytic decompositions, if successfully conducted, must throw considerable light on the actions of the forces which condition the combinations of atoms, and therefore, on the most profound parts of the problem of chemical affinity.

250, The subject of the connection between the forces which come into play in chemical and electrical phenomena, has been considered by Helmholtz in the Faraday Lecture for 18811.

Faraday's statement that 'the equivalent weights of 'bodies are simply those quantities of them which contain 'equal quantities of electricity,......or, if we adopt the atomic 'theory or phraseology, then the atoms of bodies which are 'equivalent to each other in their ordinary chemical action, 'have equal quantities of electricity naturally associated with 'them,' is developed by Helmholtz in the light of modern conceptions of molecular structure.

Helmholtz regards each monovalent atom, or group of atoms, forming an ion, as moving about with an equivalent of electricity, each divalent atom (or ion) with two equivalents of electricity, and so on. An ion may be attracted to the surface of an electrode, and if the electromotive force is sufficient, the electric charge of the ion may be attracted, and so the ion may itself become electrically neutral. A gas, e.g. hydrogen, evolved during electrolysis is electrically neutral; this may be because each atom is electrically neutralised, or more probably, because neutrality is obtained by the union of one atom, with its positive charge, with another atom, carrying a negative charge of electricity. Helmholtz then shews by experiment that 'electrolytic conduction is not......necessarily connected with 'a small resistance to the current;' and that 'the connection 'of electric and chemical force is not at all limited to the 'acid and saline solutions usually employed' (loc. cit. p. 293). But why is the electric attraction at the poles of a battery of, say, two Daniell's cells, so small, when this combination is nevertheless able to decompose water, a liquid in the forma

1 C. S. Journal, Trans. for 1881. 277.

2 Experimental Researches in Electricity, Series VII. par. 869.

tion of 1 gram of which from its elements an amount of heat equal to 1,600,000 gram-metres of work is developed? Helmholtz finds the answer to this question in the enormous electrical charges of the elementary atoms. He calculates that 'the electricity of 1 milligram of water, separated and 'communicated to two balls, I kilometre distant, would pro'duce an attraction between them equal to the weight of '26,800 kilograms;' or comparing 'the gravitation acting 'between two quantities of hydrogen and oxygen with the 'attraction of their electric charges,' the electrical force is 71,000 billion times greater than the gravitation force (loc. cit. pp. 293-294). A very small battery can decompose water, because the attracting force exerted by the poles on the enormous charges of the atoms of hydrogen and oxygen is very great.

Helmholtz shews by various experiments that an electromotive force as small as Daniell is able to attract the ions to the electrodes of a small cell, and to charge these electrodes as condensers. Indeed no phenomenon has been discovered which indicates any limit to the smallness of the electromotive force which is able to do this, and 'we must, 'therefore, conclude that no other force resists the motions of 'the ions through the interior of the liquid than the mutual 'attractions of their electric charges' (loc. cit. p. 297). The electric attraction produces an equal distribution of the opposite constituent atoms throughout the liquid, which is thus electrically as well as chemically neutralised.

But let the liquid be decomposed, there must be electrical attraction between the ions with their charges of electricity and the electrodes of the battery. If this attraction is not sufficient to deprive the ions of their charges, the cation is attracted to, and retained by the cathode, and the anion by the anode, with a force so great that no diminution of pressure over either electrode suffices to remove the ion. But 'increase the electric potential of the electrodes so that the electric 'force becomes powerful enough to draw the electric charge ' of the ions over to the electrode,' and the ions are liberated as gases, or diffuse into the liquid. If the ponderable matter

of the ions were attracted by the electrodes, this attraction would remain after discharge, but it does not, therefore 'we 'must conclude that the ions are drawn to the electrodes only 'because they are charged electrically' (loc. cit. p. 299).

The mechanism is then described whereby the electrical force is concentrated at the surface of electrodes, until, acting at molecular distances, it becomes able to compete with the 'powerful chemical forces which combine every atom with its 'electric charge, and hold the atoms bound to the liquid' (p. 300).

Helmholtz then develops the view that equivalents of positive and negative electricity (using the language of the dualistic hypothesis) are attracted by different atoms with different forces; e.g. the atom of zinc has probably a greater attraction for positive electricity than the atom of copper has for negative electricity. These attractive forces act only through molecular distances. This hypothesis of 'different 'degrees of affinity between the metals and the two elec'tricities' explains the facts of contact electricity; e.g. the greater attraction of zinc for positive electricity than of copper for negative produces chemical decomposition of the electrolyte present, and electrical equilibrium is not possible until this decomposition is completed (loc. cit. pp. 300—302)1.

Each atom is thus regarded as charged with a definite 'equivalent of electricity.' A divalent atom has two equivalents, a trivalent atom three equivalents, and so on, but these equivalents are held to the atoms by varying attractive forces. A compound which is electrically neutral will have each equivalent of positive electricity neutralised by an equivalent of negative electricity on another atom.

'I think' says Helmholtz 'the facts leave no doubt that the 'very mightiest among the chemical forces are of electric 'origin. The atoms cling to their electric charges, and op'posite electric charges cling to each other, but I do not 'suppose that other molecular forces are excluded, working directly from atom to atom' (loc. cit. pp. 302—303).

1 Compare also Davy's view, as quoted in book 1. chap. 11. par. 46.