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formula, but distributed in the second; the former therefore may be presumed to occupy a larger space, the molecular volume, that is, the volume in cubic centimetres occutpled by the molecular weight in grams, actually being IO8 in the ormer, and 103 in the latter case (compare CHEMISTRY! Physical). An analogous remark applies to the boiling-point of isomers. According to the above formula the critical temperature is given by 8aA/5412, and as the critical temperature is approximately proportional to the boiling-point, both being estimated on the absolute scale of temperature, we may conclude that the larger value of b corresponds to the lower boiling point, and indeed the isomer corresponding to the left-hand formula boils at 74°, the other at Il4°. Other physical properties might be considered; as a general rule they depend upon the distribution of negative and positive elements in the molecule. Reversible (dynamical) Isamerism.-Certain investigations on isomerism which have become especially prominent in recent times bear on the possibility of the mutual transformation of isomers. As soon as this reversibility is introduced, general laws related to thermodynamics are applicable (see CHEMICAL ACTION; ENERGETICS). These laws have the advantage of being applicable to the mutual transformations of isomers whatever be the nature of the deeper origin, and so bring polymer ism, metamerism and polymorphism together. As they are pursued furthest in the last case, this may be used as an example. The study of polymorphism has been especially pursued by Otto Lehmann, who proved that it is an almost general property; the variety of forms which a given substance may show is often great, ammonium nitrate, for instance, showing at least four of them before melting. The general rule which correlates this polymorphic change is that its direction changes at a given temperature. For example, sulphur is stable in the rhombic form till 95-4°, from then upwards it tends to change over into the prismatic form. The phenomenon absolutely corresponds to that of fusion and solidification, only that it generally takes place less quickly; consequently we may have prismatic sulphur at ordinary temperature for some time, as well as rhombic sulphur at 100°. This may be expressed in the chosen case by a symbol: “ rhombic sulphur 9% prismatic sulphur, ” indicating that there is equilibrium at the so-called “ transition-point, ” 9 5-4°, and opposite change below and above. This comparison with fusion introduces a second notion, that of the “ triple-point, ” this being in the melting-phenomenon the only temperature at which solid, liquid and vapour are in equilibrium, in other words, where three phases of one substance are co-existent. This temperature is somewhat different from the ordinary melting-point, the latter corresponding to atmospheric pressure, the former to the maximum vapour-pressure; and so we come to a third relation for polymorphism. ]ust as the melting-point changes 'with pressure, the transition-point also changes; even the same quantitative relation holds for both, as L. ]. Reicher proved with sulphur: aT/a.P=A'vT/q, 'v being the change in volume which accompanies the change from rhombic to prismatic sulphur, and q the heat absorbed. Both formula and experiment proved that an increase of pressure of one atmosphere elevated the transition point for about o-o4°. The same laws apply to cases of more complicated. nature, and one of them, which deserves to be pursued further, is the mutual transformation of cyanuric acid, C3H3N3O3, cyanic acid, CHNO, and c yam elide (CHNO)=; the first corresponding to prismatic sulphur, stable at higher temperatures, the last to rhombic, the equilibrium-symbol being: c yam elide I§ cyanuric acid; the cyanic acid corresponds to sulphur vapour, being in equilibrium with either c yam elide or cyanuric acid at a maximum pressure, definite for each temperature.

A second law for these mutual transformations is that when they take place without loss of homogeneity, for example, in the liquid state, the definite transition point disappears and the change is gradual. This seems to be the case with molten sulphur, which, when heated, becomes dark-coloured and plastic; and also in the case of metals, which obtain or lose magnetic properties without loss of continuous structure. At the same time, however, the transition point sometimes reappears even in the liquid state; in such cases two layers are formed, as has been recently observed with sulphur, and by F. M. ]ager in complicated organic compounds. Thus the introduction of heterogeneity, or the appearance of a new phase, demands the existence of a fixed temperature of transformation.

On the basis of the relation between physical phenomena and thermodynamical laws, properties of the polymorphous compounds may be predicted. The chief consideration here is that the stable form must have the lower vapour pressure, otherwise, by distillation, it would transform in opposite sense. From this it follows that the stable form must have the higher melting-point, since at the melting-point the vapour of the solid and of the liquid have the same pressure. Thus prismatic sulphur has a higher melting-point (I2o°) than the rhombic. form (116°), and it is even possible to calculate the difference theoretically from the thermodynamic relations. A third consequence is that the stable form must have the smallei solubility: J. Meyer and ]. N. Bronstedt found that at 251), ro c.c. of benzene dissolved o-25 and Q-18 gr. of prismatic and rhombic sulphur respectively. It can be easily seen that this ratio, according to Henry's law, must correspond to that of vapour-pressures, and so be independent of the solvent; in fact, in alcohol the figures are o-oo66 and o-oo52. Recently Hermann Walther Nernst has been able to deduce the transition point in the case of sulphur from the specific heat and the heat developed in the transition only. This best studied case shows that a number of mutual relations are to be found between the properties of two modifications when once the phenomenon of mutual transformation is accessible.

In ordinary isomers indications of mutual transformation often occur; and among these the predominant fact is that denoted as tautomerism or pseudomerism. It exhibits itself in the peculiar behaviour of some organic compounds containing the group -C-CO-C-, e.g. CH3CO-CHX-CO2C2H5, derivatives of acetoacetic ester. These compounds generally behave as ketones; but at the same time they may act as alcohols, i.e. as if containing the OH group; this leads to the formula H3C~C(OH): CX~CO2C2H5. In reality such tautomeric compounds are apparently a mixture of two isomers in equilibrium, and indeed in some cases' both forms have been isolated; then one speaks of desmotropy (Gr. 660'/J/68, a bond or link, and Tpovrii, a turn or change). Nevertheless, the relations obtained in reversible cases such as sulphur have not yet found application in the highly interesting cases of ordinary irreversible isomerism.

A further step in this direction has been effected by the introduction oi reversibility into a non-reversible case by means of a catalytic agent. The substance investigated was acetaldehyde, C2H4O, in its relation to par aldehyde, a polymeric modincation. The phenomena were first observed without mutual transformation, aldehyde melting at -118°, par aldehyde at 13°, the only mutual influence being a lowering of melting-point, with a minimum at- 1 20° in the eutectic point. When a catalytic agent, such as sulphurous acid, is added, which produces a mutual change, the whole behaviour is different; only one melting point, viz. 7°, is observed for all mixtures; this has been called the “ natural melting-point.” It corresponds to one of the melting-points in the series without catalytic agents, viz. in that mixture which contains 88% of par aldehyde and 12 % of acetaldehyde, which the catalytic agent leaves unaffected. Such an introduction of reversibility is also possible by allowing sufficient time to permit the transformation to be produced by itself. By R. Rothe and Alexander Smith's interesting observations on sulphur, results have been obtained which tend to prove that the melting-point, as well as the appearance of two layers in the liquid state, correspond to unstable conditions. (J. H. vAN'T H.)

ISOTHERM (Gr. ifeos, equal, and 0ép;.m, heat), a line upon a

map connecting places where the temperature is the same at sea-level on the earth's surface. These isothermal lines will be found to vary from month to month over the two hemispheres, or over local areas, during summer and winter, and their position is modihed by continental or oceanic conditions.