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and this velocity increases as the temperature is raised. Even at lower temperatures, e.g. at the ordinary temperature, the velocity of transformation is increased under the influence of light,^[69] or by the presence of certain substances, e.g. iodine,^[70] just as the velocity of transformation of white tin into the grey modification was increased by the presence of a solution of tin ammonium chloride (p. 40). At the ordinary temperature, therefore, white phosphorus must be considered as the less stable (metastable) form, for although it can exist in contact with red phosphorus for a long period, its vapour pressure, as we have seen, is greater than that of the red modification, and also, its solubility in different solvents is greater^[71] than that of the red modification; as we shall find later, the solubility of the metastable form is always greater than that of the stable.

      The relationships which are met with in the case of phosphorus can be best represented by the diagram, Fig. 11.^[72]

      In this figure, BO₁ represents the conditions of equilibrium of the univariant system red phosphorus and vapour, which ends at O₁, the melting point of red phosphorus. By heating in capillary tubes of hard glass, Chapman^[73] found that red phosphorus melts at the melting point of potassium iodide, i.e. about 630°,^[74] but the pressure at this temperature is unknown.

      At O₁, then, we have the triple point, red phosphorus, liquid, and vapour, and starting from it, we should have the vaporization curve of liquid phosphorus, O₁A, and the fusion curve of red phosphorus, O₁F. Although these have not been determined, the latter curve must, from theoretical considerations (v. p. 58), slope slightly to the right; i.e. increase of pressure raises the melting point of red phosphorus.

      

Fig. 11.

      When white phosphorus is heated to 44°, it melts. At this point, therefore, we shall have another triple point, white phosphorus—liquid—vapour; the pressure at this point has been calculated to be 3 mm.^[75] This point is the intersection of three curves, viz. sublimation curve, vaporization curve, and the fusion curve of white phosphorus. The fusion curve, O₂E, has been determined by Tammann^[76] and by G. A. Hulett,^[77] and it was found that increase of pressure by 1 atm. raises the melting point by 0.029°. The sublimation curve of white phosphorus has not yet been determined.

As can be seen from the table of vapour pressures (p. 46), the vapour pressure of white phosphorus has been determined up to 500°; at temperatures above this, however, the velocity with which transformation into red phosphorus takes place is so great as to render the determination of the vapour pressure at higher temperatures impossible. Since, however, the difference between white phosphorus and red phosphorus disappears in the liquid state, the vapour pressure curve of white phosphorus must pass through the point O₁, the melting point of red phosphorus, and must be continuous with the curve O₁A, the vapour pressure curve of liquid phosphorus (vide infra). Since, as Fig. 10 shows, the vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures, the "break" between BO₁ and O₁A must be very slight.

      As compared with monotropic substances like benzophenone, phosphorus exhibits the peculiarity that transformation of the metastable into the stable modification takes place with great slowness; and further, the time required for the production of equilibrium between red phosphorus and phosphorus vapour is great compared with that required for establishing the same equilibrium in the case of white phosphorus. This behaviour can be best explained by the assumption that change in the molecular complexity (polymerization) occurs in the conversion of white into red phosphorus, and when red phosphorus passes into vapour (depolymerization).^[78]

      This is borne out by the fact that measurements of the vapour density of phosphorus vapour at temperatures of 500° and more, show it to have the molecular weight represented by P₄,^[79] and the same molecular weight has been found for phosphorus in solution.^[80] On the other hand, it has recently been shown by R. Schenck,^[81] that the molecular weight of red phosphorus is at least P₈, and very possibly higher.

      In the case of phosphorus, therefore, it is more than possible that we are dealing, not simply with two polymorphic forms of the same substance, but with polymeric forms, and that there is no transition point at temperatures above the absolute zero, unless we assume the molecular complexity of the two forms to become the same. The curve for red phosphorus would therefore lie below that of white phosphorus, for the vapour pressure of the polymeric form, if produced from the simpler form with evolution of heat, must be lower than that of the latter. A transition point would, of course, become possible if the sign of the heat effect in the transformation of the one modification into the other should change. If, further, the liquid which is produced by the fusion of red phosphorus at 630° under high pressure also exists in a polymeric form, greater than P₄, then the metastable vaporization curve of white phosphorus would not pass through the melting point of red phosphorus, as was assumed above.^[82]

      We have already seen in the case of water (p. 31) that the vapour pressure of supercooled water is greater than that of ice, and that therefore it is possible, theoretically at least, by a process of distillation, to transfer the water from one end of a closed tube to the other, and to there condense it as ice. On account of the very small difference between the vapour pressure of supercooled water and ice, this distillation process has not been experimentally realized. In the case of phosphorus, however, where the difference in the vapour pressures is comparatively great, it has been found possible to distil white phosphorus from one part of a closed tube to another, and to there condense it as red phosphorus; and since the vapour pressure of red phosphorus at 350° is less than the vapour pressure of white phosphorus at 200°, it is possible to carry out the distillation from a colder part of the tube to a hotter, by having white phosphorus at the former and red phosphorus at the latter. Such a process of distillation has been carried out by Troost and Hautefeuille between 324° and 350°.^[83]

Relationships similar to those found in the case of phosphorus are also met with in the case of cyanogen and paracyanogen, which have been studied by Chappuis,^[84] Troost and Hautefeuille,^[85] and Dewar,^[86] and also in the case of other organic substances.

      Enantiotropy combined with Monotropy.—Not only can polymorphic substances exhibit enantiotropy or monotropy, but, if the substance is capable of existing in more than two crystalline forms, both relationships may be found, so that some of the forms may be enantiotropic to one another, while the other forms exhibit only monotropy. This behaviour is seen in the case of sulphur, which can exist in as many as eight different crystalline varieties. Of these only monoclinic and rhombic sulphur exhibit the relationship of enantiotropy, i.e. they possess a definite transition point, while the other forms are all metastable with respect to rhombic and monoclinic sulphur, and remain so up to the melting point; that is to say, they are monotropic modifications.^[87]

      E. Liquid Crystals.

      Phenomena observed.—In 1888 it was discovered by Reinitzer^[88] that the two substances, cholesteryl acetate and cholesteryl benzoate, possess the peculiar property of melting sharply at a definite temperature to milky liquids; and that the latter, on being further heated, suddenly become clear, also at a definite temperature. Other substances, more especially p-azoxyanisole and p-azoxyphenetole, were, later, found to possess the same property of having apparently a double melting point.^[89] On cooling the clear liquids, the reverse series of changes occurred.

      The turbid liquids which were thus obtained were found to possess not only the usual properties of liquids (such as the property of flowing and of assuming a perfectly spherical shape when suspended in a liquid of the same density),

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