442 Umlélsxiba AOI 
We are able to obtain a more detailed determination of the 
individualization boundary by studying a series of porphyritic 
rocks, with phenocrysts of plagioclase when this mineral is in 
excess, and of pyroxene when the ferromagnesian silicate is in 
excess. I am, however, far from having sufficient material for 
such a precision-determination. 
Because of physicochemical considerations we must draw the 
conclusion that the individualization boundary here shown is a 
eutectic boundary between pyroxene and plagioclase. And our 
individualization boundary shows almost exactly the same course 
as the eutectic boundary curve between diopside and Ab+An, 
determined by Bowen at a pressure of one atmosphere. 
If we imagine a quartary system, consisting of Ab, An, 
CaMgSi,O¢ (Diops), and CaF eSi,O. (Hed), this system will sepa- 
rate into two fields, each consisting of a continuous mix-crystal. 
Ab+<An surely, and Diops+Hed almost certainly, belong to type I. 
The difference between this quartary system and the ternary 
system Ab+An:Diops (Fig. 6), or Ab+An:Qu (Fig. 5), is chiefly 
that for the melting-plane of the independent component in the 
ternary system (ex. Qu on Fig. 5) is substituted a melting-plane 
of a binary mix-crystal combination (Diops+Hed). 
The eutectic boundary between basic plagioclase and hyper- 
sthene I term the “‘noritic,’”’ between basic plagioclase (labradorite, 
exceptionally bytownite) and monoclinic pyroxene (diallage) 
the ‘“‘gabbroidic,’ and between somewhat more acid plagioclase 
(andesine, in some cases oligoclase) and the ferromagnesian constitu- 
ent, the “‘dioritic’”’ eutectic boundary. We shall calculate the 
composition of this boundary on the assumption that it has the fol- 
lowing course with varying proportions of Ab and An: 
45 per cent hypersthene (or diallage):55 per cent AbaoAngo 
Ao per cent hypersthene (or diallage):60 per cent Ab;;Ang6; 
35 per cent hypersthene (or diallage):65 per cent Abs:Anso 
33 per cent Augite (or diallage):67 per cent Ab;;An,; — 
27 per cent Augite (or diallage):73 per cent AbgoAnyo 
20 per cent Augite (or diallage) :80 per cent Ab7;Anz; 
For hypersthene we assume: 48 MgSiO;, 30 FeSiO;, 5 MgALsiOs, 
A MgFe.SiO«, 13 CaFeSizOc= 51.2 per cent SiO., 2.5 Al.O;, 2. 5 Fe.O;, 2.9 CaO, 
20.1 FeO, 20.8 MgO. And for the plagioclase respectively An;sAb,sOr,, 
Ang.Ab;.Ore, and An,;Ab,,Ore. 
