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THE most serious difficulty of the Phase Rule for begin-viduals as defined above; # the number of physical maniners lies in the definition of the word "component," of which many varying definitions have been given by various authorities. Of these most are entirely legitimate, although they may lead to different choices as to the number of components in special cases (see, for example, "The Phase Rule," by Alex. Findlay, London, 1904, p. 12). The difficulty lies in the fact that the restrictions imposed often cause the number of "components" to be different from the number of individual chemical substances taking part in the reaction. No attempt will be made here to give all the varying definitions or explain the limitations which must be imposed upon them. The object of this note is to advocate briefly a different method of treatment, perhaps more generally acceptable to chemists and more easily comprehensible by beginners than most of the others. Doubtless it has been used before, but it does not seem to have been clearly stated or commonly recognised. The idea is this : Instead of stating the Phase Rule in a very simple equation and placing all the burden of incomprehensibility upon the component, this method abandons the complex older idea of the component and substitutes another, that of the chemical "individual" or "constituent," which is easily understood by the chemist, and places all the necessary restrictions in definite form in a somewhat more complex but easily comprehensible equation defining the Phase Rule. Ι in which F the actual variance, or the number of degrees of freedom in the special case; ; the number of indifestations of energy (mechanical, thermal, electrical, &c.) which are brought into play in the reaction; the number of phases; and, the number of independent recircumstances of the case but not included in the definistrictions or fixed conditions which are determined by the tion of the individuals. Each quantity is of course a small whole number. This method of statement separates sharply the characteristics (ni and nɛ) tending to increase the variance from those (no and ny) tending to diminish the variance, and seems to me to place the whole subject in a clearer light. Ordinarily, where only mechanical and thermal energy come into play, n = 2. Then the equation for the Phase Rule becomes This is, of course, the ordinary statement of the Phase Rule, with the addition of n,, the number of restrictions, as a last term. Equation 2 thus given is used in the subsequent exemplification. Because all the subtlety of the Phase Rule is concentrated in the last new term, nr, one must be especially careful in studying each case to be sure that the value of this term is properly estimated; in other words, to be sure that one has counted correctly all the independent restrictions. Moreover, each restriction (especially those concerning concentration, which apply to a variable phase) must be carefully examined in order to show that it is really not involved in another previously determined upon or in the definition of the individuals. This procedure of course involves thought, but I know of no method by which the Phase Rule can be applied properly to any but the simplest cases without thought according to any definition. One must remember, of course, that no restriction can be applied to the quantity of any phase; a drop of a solution in true equilibrium is as effective as a bucketful for the purposes of the Phase Rule. Thus in the case of calcium carbonate, discussed below, a limitation of the quantity of the carbon dioxide to that of the lime is not a real restriction. Adding more lime has no effect on the equilibrium. Note.-Except for the fact that in most minds conversant with the subject the term "component” indissolubly involves restrictions it would be better to retain this old term, giving it the new and simpler meaning. Prof. Lash Miller convinced me that on this account the change of meaning is undesirable. The word "individual," however (suggested in conversation by Prof. A. B. Lamb), seems to answer the requirement. The word "constituent " would be almost as good, but not quite so definite and distinctive. This, then, might be used; indeed it has already been used in a sense not very different from the present by Trevor (Fourn. Phys. Chem., 1896, i., 22), but his use of the word was somewhat freer than that needed here, as was also Bancroft's ("The Phase Rule," 1897, 227). The qualification given above, "undecomposed in the In most cases no great difficulty arises in the interpretareactions concerned," is a very important one for the tion of the new term ny. So far as I can discover it may present purpose, although it does not appear in the earlier include only two different classes of restrictions; on the definitions. According to Bancroft's application n, would one hand, the intensity factor of some form of energy may sometimes be a minus quantity (p. 230 "The Phase be restricted or kept constant; on the other hand, one inRule," a suggestive book which did much to promote dividual may (either from chemical necessity or arbitrary study of the subject). The interesting very recent treat-choice) be kept in definite weight-ratio to some other indiment of Washburn ("Principles of Physical Chemistry," vidual or at definite concentration in a variable phase. N.Y., 1915) is yet different, involving another idea called (The requirement that a given volume of gas shall contain the "composition number," although of course the funda- a given weight is a valid restriction in this sense). This mental idea is the same, as indeed it must be in any sound duality of type might be indicated if desired by substitreatment of the Phase Rule. This present method of tuting for ny its equivalent ny+n", in which the two statement adopted above makes no attempt to define the modified subscripts represent the two different types. A kinetic mechanism needful for achieving the result. It new restriction belonging to either of these types adds one records simply the facts, and may be made subject to any to their sum ny. For example, if temperature and pressure interpretation applicable according to any other formula- are both fixed, but no other fixed requirements exist, tion which likewise expresses the facts. Reference may nr 2 and ny"=0, therefore ny =2. If neither temperabe made to the interesting papers of Wegscheider (Zeit. ture nor pressure is fixed, but one individual must always Phys. Chem., 1903, xliii., 89; 1903, xlv., 496; 1904, 1., bear a definite quantitative relation to another, my =o 357; 1905, lii., 171). and ny; therefore nr 1. According to this plan the definition of the chemical "individual" is as follows:-The INDIVIDUALS of any | It will be noted that the usual definition of the number of "components" makes this number equal to (ni — nr'). |