IPPLICATIOX OF EQUILIBRIUM LAW TO SEPARATION OF CRYSTALS. 265 



experimentally, the phase rule itself giving no assistance in this part of 

 the inquiry : in fact, the only purpose it serves is to limit the number 

 of the equilibrators. 



Case IV. — All cases in which other salts are added to a reciprocal 

 Bait pair resolve themselves into the general case of x substances occur- 

 ring in X + 1 phases, and therefore requiring x — \ equilibrators. The 

 number of substances which can act as equilibrators may be very large, 

 and of course can only be ascertained by experiment : when their 

 number is determined the various ways of associating them, taken x — 1 

 at a time, are readily deduced. Experiment is then again required to 

 eliminate those which are incompatible. In special cases a simplifica- 

 tion may be introduced by taking one or more salts as always present 

 among the equilibrators. Thus, in the case of sea water. Sodium 

 chloride and Calcium sulphate are always taken as two of the equilibrators. 



Experimental Methods. 



The data required in drawing diagrams to represent the composition 

 of saturated solutions and the order in which salts are deposited from 

 them are arrived at by means of determinations of solubility. As a 

 knowledge of the character of the substances which can exist sepai'ately 

 is essential, a preliminary investigation must often be carried out to 

 determine the conditions under which given double salts or hydrates are 

 stable, or the synthesis of such compounds may have to be effected for 

 the first time. A variety of methods are made use of in this part of the 

 inquiry, the determination of volume-change by means of the dilatometer, 

 and of vapour-pressure by means of the tensimeter, being of special 

 importance in establishing transition points. 



The precautions to be observed in determining solubilities are often 

 insufficiently appreciated. The exact method followed in van't Hoff's 

 laboratory may therefore be described. 



The determinations have hitherto been made at 25°, this temperature 

 being both easy to reach in the laboratory and to maintain constant, 

 whilst probably not so very far removed from that which may have 

 prevailed at the time the Stassfurt deposits were laid down. 



A large water-bath is used as thermo-regulator, its temperature being 

 kept constant by means of a modified Ostwald Calcium chloride regulator, 

 whilst for smaller baths a regulator on the same principle tilled with 

 toluene is used. It is essential to use weighed quantities of everything, 

 so that the approximate composition of the solution may be ascertained 

 by calculation at any moment. 



The determinations are made in a large test tube, about .3 cm. 

 broad and 30 cm. long, immersed as deeply as possible in the bath. 

 The contents are kept in violent agitation by means of a screw-shaped 

 glass stirrer passing though a piece of glass tubing inserted in the 

 tightly fitting stopper of the test tube : this stirrer is actuated by a small 

 motor. If the tube be selected so that the rod of tlie stirrer just fits ib, 

 and a little grease be inserted, no loss of water by evaporation is to be 

 feared. 



The solubility determinations are carried out by stirring weighed 

 quantities of the substances with a known quantity of water, an excess of 

 solid being always used. When approximately saturated, the solution is 

 cbaracterisediin some way, e.g., by ascertaining its density. In determining 



