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measured in investigations of thermal changes accompanying chemical processes; but the work done by the free energies of the system, the free work (freie Arbeit), which determines the direction of the chemical change, is different from this, and cannot be measured by merely finding the total quantity of heat evolved.

244. But it may be admitted that chemical affinity, considered as some form of atomic energy, cannot as yet be satisfactorily measured by thermal methods, and at the same time it may be held that thermal measurements do throw light on the differences between the affinities of substances in various analogous reactions, using the term affinity in a sense similar to that wherein it is employed by Guldberg and Waage.

Thus, let us compare the thermal values of the reactions which occur in the formation of gaseous hydrochloric, hydrobromic, and hydriodic acids from gaseous hydrogen, and gaseous chlorine, gaseous bromine, and gaseous iodine respectively?. The change is expressed in thermal notation as [H, X]; the following are the numbers to be compared,

[H, X] gaseous.
X=Cl=22,000 gram-units +.
X=Br=12,000

t.
X=1 = 1,530

Are the affinities of Cl, Br, and I for H in the proportion of the numbers 22:12:- 1'5?

When the reaction is written, as our former study of chemical changes has taught it ought to be written, in the form [H, Xo] =2[H, X]-[H, H]-[X, X], we see that the numbers given do not measure the affinities of the atoms of chlorine, bromine, and iodine for that of hydrogen. We have at present no means for measuring the absorptions and evolutions of heat the sums of which are represented by the numbers 22,000, 12,000, and – 1530. We are not even justified in concluding that the value – [X, X] is the same whether X = CI, Br, or I ; indeed experiments on the densities

i Compare Jahn, Die Grundsätze der Thermochemie, 35–43.

of these gases at high temperatures rather tend to shew that this assumption is untenable. But if the term affinity is used as meaning the resultant of the actions of the various forces which come into play in any chemical change, eliminating as far as possible actions which are manifestly physical, then I think we may say that the differences between the affinities concerned in the three strictly comparable reactions, viz. formation of gaseous hydrochloric, hydrobromic, and hydriodic acids, from their gaseous elements, are expressed by the differences between the numbers 22, 12, and — 195.

245. If this conclusion is sound, then the differences between the thermal values of analogous chemical changes in which the same elements take part should be capable of being represented as multiples of a common number.

Here are some data suited for our purpose.

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(1)[H, X,Aq]; X=Cl=39,315:X=Br=28,370: X=I=13,170grm.-units +.

.:[H, CI, Aq]-[H, Br, Aq]=10,945,

and [H, CI, Aq]-[H, I, Aq] =26,145. (2)[K,X, Aq];X=Cl=101,170:X=Br=90,230: X=I=75,020 grm.-units +.

:: [K, CI, Aq]-[K, Br, Aq]=10,940, and [K, CI, Aq]-[K, I, Aq) = 26,150. Also [Na, Cl, Aq]-[Na, Br, Aq]=10,930, and [Na, Cl, Aq]-[Na, I, Aq] =26,150.

The difference between the heat of formation, in solution, of a chloride and an analogous bromide, is 10,940 units; and that between a chloride and an analogous iodide is 26,150 units.

Now these differences reappear in the following data.

[M, Cl,, Aq] - [M, Brg, Aq]=2 x 10,940 } when M=Ca, Sr, or Cu. and [M, Cl2, Aq]-[M, 12, Aq] = 2 26,150

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Here we notice a constant thermal value attending the substitution of one halogen by another, the metallic radicle being unchanged; now, if the halogen remain the same, is there a constant thermal value for the substitution of one metal by another, chemically analogous, metal ? M. C.

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The following data shew that there is such a constant thermal value.

4,660 when X=C1, [K, X, Aq] - [Na, X, Aq] 4,650 when X=Br,

4,620 when X=I; and [Sr, X?, Aq]-[Ca, X, Aq]=2 X 4,020 when X=CI, Br, or İ.

The thermal values of another series of analogous reactions are given in the following table.

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The data presented in this paragraph justify the conclusion that a study of the thermal values of analogous chemical changes occurring between similar elements is fitted to throw light on the differences between the affinities of the substances taking part in these reactions.

246. The theory of vortex atoms promises to help towards a solution of the problem of affinity.

The theory has been applied to chemical combinations by J. J. Thomson.

A compound molecule of a gas is regarded by this theory as consisting of two, or more, vortex rings. This united vortex ring will separate into its parts when subjected to a disturbing influence, such as the action due to other vortex rings in the neighbourhood. The theory thus leads to a conception of chemical combination closely resembling that enunciated by Williamson, and afterwards altered and developed by Pfaundler (chap. II. pars. 186, 187). But for a compound gas to be more than a mere mixture of elementary gases it is necessary that 'the mean time during which an atom is paired with another of a different kind, which we shall call the paired time,

1 On the motion of vortex rings. The Adams Prize Essay for 1882. See especially p. 114 et seq.

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should be large, compared with the time during which it is alone and free from other atoms, which we shall call the free time' (loc. cit. p. 115).

The ratio of paired to free time will be diminished by any disturbance to which the gas is subjected; when the diminution is carried past a certain amount, the gas is decomposed. Now the pairing of two atoms......is attended by a large 'increase in the translatory energy;' but as these atoms are only paired for a time, the whole increase in the translatory 'energy of a large number of molecules will depend......on 'the ratio of the paired to the free times' of the vortex atoms which form the molecules of the substance (loc. cit. p. 116). The value of this ratio in the case of an elementary gas will to a great extent condition the chemical properties of that gas; it will also determine whether chemical combination shall or shall not occur between two gases, and if it occurs, it will fix the proportions between the amounts of the various compounds produced. An elementary gas will readily enter into chemical combination, only when the ratio of free to paired time is larger for the molecule of the element, than for that of the compound produced. The value of the ratio in question may therefore afford a measure of the relative affinities for each other of the atoms of various compound molecules'.

247. In the general remarks made on the subject of affinity in par. 202 it was said that attempts might be made to obtain measurements of affinities by electrical methods. I wish now to draw the student's attention to some of the more important of these attempts.

The views of Davy.and of Berzelius regarding the connections between electrical and chemical actions have already been referred to (book 1. chap. II. pars. 46 to 48).

Faraday discovered that when an electric current passes through an electrolytic cell, the amount of decomposition is definite for each element of the electrolyte, and is dependent on the quantity of electricity which is transmitted. Let e be the mass of an element separated from any of its salts by the 1 For more details see J. J. Thomson, loc. cit.

passage of one unit of electricity. Then e is called the electrochemical equivalent of that element. Since unit quantity of electricity is transmitted by unit current in unit time, we may say that one electrochemical equivalent of an element is separated from any of its combinations by unit current in unit time.

The minute verification of this law is still being worked out experimentally.

In the course of his applications of the conception of the conservation of energy, Joule undertook a series of researches on the energetics' of the electric current'. The case of the passage of a current through a wire was considered, and the quantity of heat evolved was found to be expressed by the equation

H=CE, where H is the quantity of heat developed per second, and C and E are the current and the electromotive force respectively.

Since Joule had himself shewn that heat is changeable into work, the equation took the form

W=JH=CE, where j = the mechanical equivalent of heat.

The phenomena attending the evolution of heat during the passage of a current through an electrolyte were then examined by Joule, and it was shewn that the total quantity of heat could be separated into two parts. One part was expressible as the result of overcoming ordinary resistance in accordance with his previous law, and the other part was due to chemical changes in the cell. He then determined the quantity of heat evolved, during a given time, in a process of electrolysis by a current of given strength; then, by applying Ohm's law, and the law stated connecting heat with resistance and current, he found the heat which would have been evolved, had a wire with resistance equal to that of the electrolyte been substituted for the electrolyte. The difference between these two quantities of heat is, Joule said,

1 Phil. Mag. 20. 98; 22. 204; and do. (2) 3. 481. See also the article Electricity'in Encycl. Brit. Vol. 8. (9th Ed.) pp. 88-92.

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