D topside — Forsterite — Silica. 231 



done in fig. IT. The space between the boundary curve, for- 

 sterite-pyroxene, and the pyroxene conjugation line, has been 

 widened, relatively, and the three-phase-boundaries, LK, RF, 

 etc., have been made to cross this space less obliquely than 

 they should if drawn to true scale. A glance at figs. 14 and 

 15 will convince one that the geometrical relations could not 

 be followed if the boundary curves and the three-phase-boun- 

 daries were drawn in their proper relative positions. The dis- 

 torted figure illustrates the principles involved equally well, 

 besides facilitating the discussion. 



Crystallization with Perfect Equilibrium between Liquid 

 and Solid Phases. — If a liquid of composition M (fig. IT) is 

 allowed to cool, forsterite begins to crystallize at the tempera- 

 ture of the isotherm through the point M and continues to 

 crystallize until the temperature of the point K on the boun- 

 dary curve is reached. In the meantime the composition of 

 the liquid has changed from M to K along the straight line 

 AMK. Since liquid K is saturated with pyroxene that phase 

 then begins to crystallize, and since we now pass into a three- 

 phase-area the composition of the pyroxene can be found by 

 drawing the three-phase-boundary through the point K, i. e., 

 KL, and L represents the composition of the pyroxene. When 

 the temperature is further lowered pyroxene continues to crys- 

 tallize and forsterite begins to redissolve. The composition of 

 the liquid now changes along the boundary curve and the com- 

 position of the pyroxene in the act of crystallization, as well as 

 that of the pyroxene which has already separated (if there is 

 perfect equilibrium), changes toward S. When the tempera- 

 ture of the point JN" is reached, the liquid finally disappears and 

 the whole consists of pyroxene of composition P and forsterite, 

 ISTP being the three-phase-boundary for the temperature of the 

 point N. The proportion of pyroxene to forsterite is as 

 MA : MP. 



If the composition of the original liquid had been that of the 

 pyroxene P, forsterite would crystallize first as before, and the 

 whole course of crystallization would be precisely as given 

 above. At the temperature of the point N, in this case, the 

 last of the liquid and the last of the forsterite are used up simul- 

 taneously and the whole consists simply of pyroxene of com- 

 position P. 



If the composition of the original liquid was that of the 

 point D, forsterite would crystallize first as before and crystal- 

 lization would follow the same course as in the two preceding 

 cases until the temperature of the point F is reached. At this 

 temperature the last of the forsterite has dissolved and the 

 mixture consists of liquid of composition F and pyroxene of 

 composition R, FR being the three-phase-boundary through 



