580 JAMES ASTON 
rock magmas, three or more constituents will be present. This 
greater number of components will admit of the possibility of greater 
multiplication of the solid phases forming and results in a very much 
more complicated problem. Unfortunately, there have been pub- 
lished the results of but very few investigations along this line, and 
these only for very simple cases. ‘To represent the equilibrium of a 
three-component mixture we make use of the property of an equilateral 
triangle that if from any point within perpendiculars be dropped 
upon each of the three sides, the sum of the lengths of these perpen- 
diculars is a constant, and equal to the altitude of the triangle. Con- 
sequently with an equilateral triangle as a base, each apex of which 
represents respectively too per cent. of A, B, and C constituents, and 
temperatures plotted perpendicular to this base, we obtain a space- 
model, with the equilibrium between the solid and liquid phases, 
or, in other words, the locus of the solidification points of each par- 
ticular mixture, represented by a set of warped surfaces, very much as 
topography is represented on a relief map. And just as we represent 
the elevations of this relief map on a plane surface by means of con- 
tour lines of equal elevations, so do we represent the temperatures of 
our space-model of solidification, by contour lines of equal tempera- 
tures, or, as technically called, by isotherms. 
Such a representation is shown in Fig. 8, for the solidification of 
the Bi, Pb, Sn alloys.‘ These have the simplest relations for a three- 
component alloy, since no intermediate compounds are formed, and 
there is complete insolubility between the constituents. The dotted 
lines are the isotherms for the commencement of solidification. The 
altitudes at each angle denote 100 per cent. of each of the elements 
Pb, Bi, and Sn. The triangle is divided into three regions by’ the 
lines GE, TE, and HE, which correspond to our previous freezing- 
point loci representing the primary separation of one of the three pure 
components. Consider an alloy of composition A. The point denot- 
ing this alloy lies in the region Bi, GEI on the isotherm 175°. At 
this temperature, therefore, pure bismuth commences to separate 
out. The alloy becomes successively poorer in bismuth as the tem- 
perature is lowered, and, since the ratio of tin to lead must remain 
1G. Charpy, ‘Study of the White Alloys Called Antifriction,” Metallographist, 
Vol. II, 1899. 
