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physical evidence on which, in its more recent development, the theory so largely rests, that I must endeavour very briefly to give a sketch of that evidence, remembering always that it is as chemists, not as physicists, that we are interested in this subject.

There are two general theories of the structure of material substances: one assumes that apparently homogeneous bodies are really homogeneous throughout-a theory which is incapable of explaining the observed properties of matterand the other, that apparently homogeneous bodies are possessed of a grained structure.

Viewed from a distance, a brick wall, or a body of soldiers, appears to be one reddish-coloured homogeneous mass, but a nearer observer sees that the wall is made up of distinct parts, that the company is composed of individual men.

The molecular theory supposes that were our senses sufficiently acute, we should see the grains or particles of which an apparently homogeneous mass of matter is composed.

The theory begins by assuming that any material body ' is made up of parts (each of which is capable of motion)

and that these parts act on each other in a manner consistent 'with the principle of the conservation of energy? These parts are called molecules; the dynamical definition of a gaseous molecule is That minute portion of a substance 'which moves about as a whole, so that its parts, if it has any, 'do not part company during the motion of agitation of the 'gas'

This definition is entirely independent of chemical facts.

All the molecules of one element are of the same mass, else differences would be observed in the properties of an elementary gas, e.g. hydrogen, such differences arising from the separation of the gas into portions each more or less unlike the others.

The relations between the motions and the space occupied by these little parts, assuming their existence and mutual independence, may be dynamically deduced by the aid of a theorem of Clausius, and, with a justifiable assumption as to the dynamical meaning of temperature, the equation thus arrived at expresses with considerable accuracy the relations actually existing between temperature and pressure, and volume, in the case of rarefied gases; the equation that is to say expresses the laws of Charles and of Boyle. When the gas is more condensed the equation ceases to express the relations existing between temperature and pressure, and volume; hence the theory asserts the existence in such a gas of mutual attractions or repulsions between the little parts, or molecules, it asserts that these parts are no longer mutually independent.

1 Clerk Maxwell, Article . Atom' in Encycl. Britannica. (9th Ed.)

2 Ibid.

•The hypothesis that a gas consists of molecules in motion, which act on each other only when they come together 'during an encounter, but which during the intervals between their encounters—which constitute the greater part of their 'existence—are describing free paths, and are not acted on by ‘any molecular forces", having been justified by dynamical reasoning, the next step is made by investigating mathematically the properties of such a system of molecules. And one deduction thus made is If equal volumes of two gases are 'at equal temperatures and pressures, the number of molecules 'in each is the same, and therefore the masses of the two

kinds of molecules are in the same ratio as the densities of the 'gases to which they belong? '.

This statement is of paramount importance to the chemist, inasmuch as on it is based his system of molecular weights. It is very necessary to bear in mind that this proposition is deduced by dynamical reasoning from a simple hypothesis as to the structure of matter, itself justified by many facts.

By analogous reasoning, various deductions are made from the theory, which express generalisations of experimentally determined facts concerning gaseous phenomena'.

Passing to more complex occurrences, the molecular theory gives a simple explanation of the diffusion of matter, diffusion of motion, and diffusion of heat in gases; these phenomena being regarded by the theory as dependent on the frequency of the molecular encounters, and on the nature of the actions between the encountering molecules.

1 Clerk Maxwell, Article ' Atom' in Encycl. Brit.

3 Ibid.

3 For some of the most important of these see Clerk Maxwell's Theory of Heat, pp. 307–322 (6th edition).

The molecular theory has also been successfully applied to explain, broadly, many of the phenomena of evaporation, condensation, electrolysis, and spectroscopy.

To explain spectroscopic phenomena it is apparently necessary to assume molecules to be elastic substances, but elasticity is just the property of matter to explain which the molecular hypothesis was first assumed. The theory of 'vortex atoms,' developed by Sir William Thomson from the original conception of Helmholtz, explains spectroscopic facts—and generally those facts which must be explained by a successful molecular theory—better than any other which has yet been suggested. A short account of this theory will be found in the article 'Atom' in the last edition of the Encyclopædia Britannica, where we read “The success of this 'theory in explaining phenomena does not depend on the ‘ingenuity with which its contrivers “save appearances" by 'introducing first one hypothetical force and then another. 'When the vortex atom is once set in motion all its properties ‘are absolutely fixed, and determined by the laws of motion of 'the primitive fluid which are fully expressed in the funda'mental equation.'

Attempts have been made to determine the absolute size of molecules', and although the results must be regarded as but rough estimates, nevertheless they shew that to measure molecules is a legitimate object of scientific investigation. The smallest portion of matter visible by the help of a good microscope may be taken to be a cube each side of which measures tooth of a millimetre in length; such a cube will contain-according to the rough measurements hitherto made_from 60 to 100 millions of molecules?

1 See especially Sir W. Thomson, Nature 1. p. 551, and also 28. pp. 203, 250, 274

? Clerk Maxwell, loc. cit.

The foundations of a truly mathematical theory have been laid by Helmholtz and Thomson in their theory of vortex atoms; but, apart from this, the fact that the proposition commonly known as Avogadro's law may be deduced by dynamical reasoning from a simple hypothesis which admits, although as yet only to a limited extent, of the application of mathematical methods, and which is justified by a large number of physical facts, suffices to make that law of extreme importance.

Mathematical theories of physical phenomena in which the forces at work are thoroughly known, are complete, and are capable of making predictions which may afterwards be verified by experiment, or even of predicting phenomena which are altogether beyond the reach of experimental verification. When however the forces are but partly known, the theory may predict results but cannot give a complete account of the phenomena to which it is applied'. Now, we know very little of the forces at work in the phenomena called chemical, hence a mathematical theory of chemical action cannot as yet be formed. A beginning has been made in the knowledge of molecular forces, but until our knowledge is much extended, until we can generalise the conditions of molecular actions and reactions, and also of molecular decompositions and recompositions, we cannot expect to gain a complete mathematical theory of chemical action. At present we can use the molecular theory of matter only in a most general form, trying to make our deductions therefrom as accurate as possible, and always testing these deductions by experiment.

Attempts have recently been made to apply a more strictly dynamical method of reasoning than is presented by the molecular theory, to certain chemical phenomena ; these will be referred to under the second main division of this book.

An atomic theory has been elaborated by the chemist; a molecular theory of matter has been propounded by the physicist, and has been advanced so far as to allow of wide conclusions being deduced therefrom by strictly dynamical

1 See Thomson and Tait, Treatise on Natural Philosophy, 1. p. 445.

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reasoning; no theory asserting the continuity of matter has been found capable of explaining the observed phenomena of matter; hence to accept the molecular theory, as, at present, the only feasible working hypothesis, is simply to obey the dictates of the scientific method. 14. Equal volumes of gases contain equal numbers of

molecules. Let us now consider one or two chemical reactions between gaseous substances.

Hydrogen combines with chlorine to form hydrochloric acid.
2 vols.

2 vols.

4 vols. But since equal volumes contain equal numbers of molecules, and since each molecule of hydrochloric acid contains both hydrogen and chlorine, it is evident that each molecule of hydrogen by combination with one molecule of chlorine produces not one but two molecules of hydrochloric acid. So again,

Nitrogen combines with hydrogen to form ammonia.
2 vols.

6 vols.

4 vols. Here again each nitrogen molecule has given rise to two molecules of ammonia. Hence it is evident that although the parts of a molecule of hydrogen, nitrogen, or chlorine 'do not 'part company during the motion of agitation of the gas' to which the molecule belongs, these parts nevertheless do part company in those chemical reactions which are stated above. When various reactions between gaseous substances are studied this conclusion is found to hold good throughout a large range of chemical phenomena. Hence the chemist is obliged to recognise a portion of matter smaller than the molecule; this smaller portion of matter is the atom'

In the above and in other reactions it is shewn that the molecules of hydrogen, nitrogen, and chlorine split into two parts when these molecules act chemically on each other or on other molecules; hence the molecules of these elements may be

* It is well to note that the molecular theory of matter as applied to chemical phenomena does not assert or deny the finite divisibility of matter. In C. S. Journal [2], 13. 501, there is a most interesting paper by Clerk Maxwell on. The dynamical evidence of the molecular constitution of bodies.'

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