20 Rankin and Wright — Ternary System CaO-Alfi-SiO % . 



ciate into three solids and then there is no field in which it 

 occurs in equilibrium with solution. 



Of course, in a ternary system there may be any number of 

 compounds, binary and ternary, stable or unstable, but the 

 generalizations which hold for the simple cases are also applica- 

 ble to the complex systems. For this reason we have not 

 taken up all possible cases but merely a few typical examples. 

 A more complete discussion of the possibilities in three-com- 

 ponent systems may be found in " The Phase Rule," by W. 

 D. Bancroft, or " Die Heterogenen Gleichgewichte," Dritte 

 Heft, Erster Teil, by Roozeboom. 



Thus the phase rule together with the theorem of Alkemade 

 enables us to predict how many solid phases we may expect to 

 find at equilibrium under definite conditions, and informs us 

 not only as to the position of maxima on the boundary curves 

 but also as to the direction of rising or falling temperature on 

 those boundaries ; all of which is of assistance in the location 

 of new compounds and in the determination of the conditions 

 under which these compounds exist. The actual location of 

 compounds, the conditions for their existence and their rela- 

 tion to each other (involving the location of quintuple points 

 and. boundary curves), however, can only be determined by 

 experiment. 



EXPERIMENTAL METHODS. 



In work of this kind there are three general experimental i 

 methods of attack, all of which have been largely made use of 

 in the present investigation, though the third one serves our 

 purpose best. 



1. The first method is to ascertain the energy changes occur- 

 ring in the system as registered by the thermoelement, and in 

 this way to endeavor to unravel the phase relations. This 

 method is invaluable, but like all methods employed in the 

 exploration of new fields, it gains strength when employed 

 in conjunction with other methods even though the latter be 

 inferior in the scope of their practical application. With sili- 

 cates as with alloys, it is much easier to interpret the thermal 

 data if one knows the nature of the reacting phases. 



2. The second method is to bake the different preparations 

 for long periods of time at appropriate temperatures in order 

 to allow time for the reactions to become complete and for the 

 growth of crystals of measurable size, thus rendering micro- 

 scopic examination much easier. 



3. The third method has for its object the determination of 

 the boundaries of the various fields in which particular phases 

 have their stable existence, i. e., of the location of the bound- 



