doubts may be raised even against Kopp's laws, although the molecular volumes of all liquids that had then been investigated with sufficient exactness could be so well calculated by them as to agree excellently with experiment. For there remains the very grave objection that by these rules one and the same volume is not always to be ascribed to one and the same atom. Thus, for instance, the volume of the oxygen atom has to be now 7:8, now 12.2; the nitrogen atom has to have a different volume in ammonia and analogous compounds from what it has in cyanogen compounds, and a third different volume in nitro-compounds. A further objection is that the molecular volumes calculated for gaseous 'Bodies cannot be represented by the atomic volumes given by Kopp for the liquid state, for this seems to contradict the assumption that the atoms are to be looked upon as invariable. But in order to obtain agreement between calculation and experiment, Lothar Meyer was obliged to assign, both to nitrogen and hydrogen, a different atomic volume in gaseous compounds than in liquid ones. The variation in the occupation of space by the atoms which we should have to assume in accordance with these investigations can only mean this, that we have not at all to do with the actual dimensions of the atoms and molecules, but with the smallest space which these particles at least require for themselves under the given circumstances. This space may really alter with circumstances. As is almost obvious, it alters with the temperature, because this determines the motion of the atoms. But the shape of the molecule and the grouping of its atoms may also have an influence on the space required by it as a minimum. A flat molecule with its atoms grouped together nearly in a plane will require more room, when turning with its motions that depend on the temperature, than a spherically shaped molecule with its atoms all crowded together. It is thus explicable, from the differences between molecules that have been described, that different extensions in space may be ascribed to the atoms according to their location in the molecule. The following table contains the results of the different calculations of the molecular volumes : Column I. gives the values of the volume of the sphere of action, taken as spherical, on an arbitrary scale; these were calculated by Lothar Meyer from Graham's experiments on transpiration. We must further remark that the mean molecular weights of the components of air have been employed for the calculation of the number given for air, and also that the number for water-vapour, which I have added, has been deduced from Kundt and Warburg's experiments on viscosity. Column II. contains the values, calculated by Kopp's rules, of the molecular volume in the liquid state. For the volumes of an atom are taken S = 22.6 Cl = 22.8 C = 11.0 H= 5.5 N = 2·3 and it is assumed that O= 7.8 in free oxygen, water vapour, and methyl ether, and 0 = 12.2 in carbon monoxide, nitric oxide, and nitrous oxide; further, that in carbonic acid and sulphurous acid the two atoms together have the value 7·8 + 12·2 = 20·0. Column III. contains the values which result from Lothar Meyer's assumed occupation of space by the atoms. The volumes N77 and H = 30 are assumed, and also 0 = 12.2 in nitrous oxide and for one of the atoms in sulphurous acid, but in all other cases O = 7.8. Columns IV. and V. contain the values as calculated in accordance with Loschmidt's assumptions. In them are put S26, C 14, Cl = 22-8, H = 3.5, and in Column IV. but in Column V. 011, N = 13, 0 = 11, 0, 21, N = 12, CN = 28. = The agreement of the last four columns with the first is not complete, and indeed cannot be if the preceding considerations are justified; for here the sphere of action and the molecular volume are treated as if the same thing, whereas in reality the former is much the smaller. If the theory were worked out with absolute accuracy, we should have to deal with circumstances which depend not only on the volume, but also on the section and shape of the molecular system; hence no perfect regularity of agreement can show itself if the matter is treated one-sidedly as if the volume alone determined the phenomena. But so many cases exhibit a surprisingly good agreement that all idea of the agreement being accidental must be put aside. One will agree with Lothar Meyer in deducing from his figures that the atomic volumes of many elements in their liquid combinations are proportional to the spaces occupied by their atoms in the gaseous state. 114. Influence of the Molecular Heat-motion in Liquids on the Apparent Size of the Molecular Volume One feels oneself tempted to go a step further in this conclusion, and to assume that the volumes in the liquid and gaseous states are not only proportional to, but identical with, each other. Lothar Meyer did not consider this conclusion justified, but he is of opinion that the molecular and atomic volumes are greater in the liquid state than in the gaseous. The weightiest reason that he adduces for this view rests on a conception, like that of our gaseous theory, of the state of motion which the molecules of a liquid take in consequence of their heat. We have to consider the atoms in lively motion not only in the gaseous state, but also in the liquid and solid states. The solid state seems to be characterised by the centroids of the molecules being at rest while the atoms move. Dulong and Petit's law at least points to this, in so far as it establishes a relation for the atomic heat of different bodies into which the molecular heat does not enter at all. We shall probably have to conceive of the liquid state as something between the other two; so that we have to ascribe to the particles of a liquid both molecular and atomic motions. Of whatever kind these motions may be,1 they in any case require space for their performance. In a liquid, therefore, a molecule will, under all circumstances, require a larger space than if it were at rest. The space demanded by a molecule will presumably increase, not only with the kinetic energy but also with the speed itself, in such a way that, of two different kinds of molecules whose energies are equal, the lighter needs a larger space for its correspondingly quicker motion than the heavier and therefore more slowly moving molecule. The same holds good for the atoms. By this consideration Lothar Meyer explains the behaviour, for instance, of hydrogen, for which a much smaller atomic volume results from consideration of its viscosity than Kopp had calculated for it from its liquid compounds; and this was his reason for assigning to hydrogen in gaseous molecules a smaller volume than in molecules of a liquid. Similar considerations may enter into the case of other atoms, even if, perhaps, they are less striking. We may therefore assume it as possible, for the molecules built up of atoms, that their molecular volume in the liquid state is larger than in the gaseous. On this subject further explanations will be found in Clausius' memoir, Pogg. Ann. 1857, c. p. 360; Abhandl. 2. Abth. 1867, p. 236. In spite of all this, we have no reason to believe that the molecules themselves are larger in a liquid than in the vapour of the same substance. For, to explain the difference of the two states of aggregation, the assumption that the motion of the molecules in the two cases is different seems sufficient. If the molecular motion in liquids were known to us just as much as the motion in gases, we should be in as good a position for liquids as for gases to determine in absolute measure the sum of the sections, or any other corresponding property, of the whole assemblage of molecules contained in unit volume, and we could thus by experiment decide the question with certainty whether the difference of the states of aggregation consists only in the motion or also in other properties of the molecules. long as we are without a kinetic theory of the liquid state, we cannot in the determination of the extension in space of the molecules bring into the calculation the influence of their motion, as in the case of gases, and we therefore obtain values which are too high. But so 115. Possibility of Determining the Size of Gaseous Molecules We have succeeded, however, in obtaining limiting values, at least, of the sizes of molecules in absolute measure by comparison of the two fluid states of aggregation. Such a calculation was first attempted and made by Loschmidt,' and then later by Lord Kelvin 2 (then Sir William Thomson) and by Maxwell3 in the memoirs already cited. These calculations assume the sphere of action to be spherical, and they are based on the relation between the mean free path L and the radius s of the sphere of action, which was discovered by Clausius, and is with Maxwell's theory represented by the formula 1 = √/2πs2NL 1 Wien. Sitzungsber. 1865, lii. Abth. 2, p. 395. 2 Nature, 1870, i. p. 551; Silliman's Amer. Journ. 1. pp. 38, 258. |