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Now, it can be shown by a simple algebraical argument' that if A, B, C, and D, be any four phases whatever, formed from the same three components, it is possible either (i) to mix three of these, e.g., A, B, and C, in such proportions that the components are present in the mixture in tlie same propor- tions as they are in D, or (ii) to prepare a mixture of A and B, and another of C and D in Buch proportions that the quantities of the three components are the same in both mixtures. In other words, it is possible with these four phases to build up two systems identical with respect to the amounts of eaeh of the three com- ponents, but differing in the nature and composition of the phases composing them, and the condition that the state of the system should be completely defined hy the nmounfs of the components (and tempera- ture and preflBure) can be fulfilled only if one of these alt rnative systems changes spontaneously into tlie other ; that is, if reactions between the phases A+B=C-LD A+B-fC=D ' Van der WaalB, quoted by Rooieboom, Rec. Trav. Chlm. Pays-Bas 6 286. (1887.) 40 KOYAL SOCIETY OF CANADA take place whenever possible, and proceed until one at least of the react- ing pliasee totally disappears. Which of the four will be the firsb to disappear, depends obviously on the direction of the reaction and on the relative amounts of the diiferent phases present. When the number of phases has been reduced to three, the possibility of a reaction of this nature has vanished. The occurrence of reactions of this type, then, is the mechanism by means of which the number of phases in a three-component system is kept down to three. If it fails, the state of the system is no longer defined solely by temperature, pressure, and the masses nf the compo- nents. Experimental evidence of such definition, must therefore be reganled as proof that not more than three phases are present in the (three-component) system. Tiie result predicted by the second theorem is effected by means of reactions of a second type, which can take place in a three-component system of three phases only if one of the three is capable of continuous varir.tion in compo.sition (a solution). By dissolving more or less of the solid phases in the solution it would be possible to construct a whole series of systems— formed of tlie same amounts of the same components— but differing in the com- position of the solutions and in the relative quantities of the solid phases. If only one of these is found to exist in fact, the disappearance of the others must be ascribed to the occurrence of reactions of this second type, which fix the composition of the solution irrespective of the relative quantities of the three phages of which the system is com- Extension of the Method. The two theorems which serve to interpret the experimental results distinguishing between mixtures and single substances, and identifying the chemical individuals in the precipitates, are thus dependent on the occurrence of reactions of two types :-the first (which does not involve change of composition of any of the phases) resulting in the disappear- ance of all phases in excess of three; the second (which involves change of composition of the solution) keeping the composition of the solution constant so long as it is in contact with che same pair of basic salts. The possibility of applying the same method to the study of preci- pitates formed by j.otash in solutions of metallic salts, depends on the discovery of conditions under which a fourth component may be added to the system without interfering with the occurrence of these tiro classes of reactions. [MlLLW * MXKICK] IDENTIFICATION OF BASIC SALTS 4, ments there mu.t be a constant ratio between the amounts o7the fourth component and of the water in the system. If the water is present in large excess, (condition a) the mass of the solution wdl be much greater than that of the precipitate, nrd no reac! |o„ oceurnng in the system can have more than a vvry slight "on ,n,lf .^^^K ^ "°^ .^^''^'^ ^''^ composition of the solution re. ain mialtered), the quantiti^ of the other components eat.ring or leav n" the solution must be still smaller than that of the water; so t at "^ ^Zed " '''' '"^"^ '"^ '''"' '"^^^ "^ '"^^ sol„tion'(p,.a:ti:lli;) If now a fourth component be added, the total amount of which m the solution is unafTectod by the reaction (conduion b), this slight variation m the quantities of the other components in the olut on vil Tct oft ' r ''' ?':'' "' "" '=°"P"'''°" °^'*"« '"»- thatlh effect of the change m checking the progress of the reaction may safely be neglected; so that the prince of the fourth component, under tl«e cond ions, will not interfere with the efficiency o'f re..etions o t"e first type m kee,„ng down the number of phases to three of thoTnf r\°' '^T'""^ *yP« ('°^'«l^^i"g changes in the compositi..,> of the solut.on) are of course just as posslMe when the solution contains soluTons""''^"''^* " "'^^ '' ""^ ""'• ^° °^^-' '— -, th^ solutions over a given pair of basic salts should roach exactly the same composition in diilorent experiments, it is obviously nccessan- tha the concentration of the fourth component in the solution should be h same from case to case. This is provided for by condition c. In exp ri ments on the action of caustic pota.h on solutions of bichloride of copper, for example, H,0, CuO, and CuCl, may be selected a ompo nents with KCl as the "fourth component" of the pre e,l ng pTra graphs; and condition c requires that if the quantity of pota ladlTd nonrKri : f ''IT'' "^"^'^^" ^'^""'"^ vary-from'case to ca!., enongh KCl must 1^ added to keep the total amount of potne.ium per cubic centimetre of water the same in each experiment. ^ 42 ROYAL SOCIETY OF CANADA }-M ?#, Experiments. In the spring and summer of 1899 the writers carried out a lengthy series of experiments on the action of potash and ammonia on the chloride of lead. The less basic of the oxychlorides are formed with remarkable tlowness ; the reaction between n/3 ammonia and lead chloride not coming to a standstill in ten days shaking at 100° C. PbCljSPbO, however, was formed in a few hours in the cold. In the winter of 1900-1901, Mr. Good took up the study of the action of water on antimony tri-chloride, presenting his results as a thesis in competition for the 1851 Exhibition scholarship. His observa- tions may be rejrarded as confirming the individuality of the oxychloridc SSbCl.nSb.Oj ui the powder of Alfiuroth : allliough in this case also equilibrium is often not attained i'Util days after the precipitation. Mr. F. B. Allan, Lecturer on Chemistry in the University of Toronto, has just completed a series of experiments on the action of water (111 the nitrate of bismuth,' which lie has presented as a thesis for the degree of Ph.D. His results, some of which are represented in llic