400 N. L. BOWEN 
to simple systems. Ziegler discusses two three-component systems 
in which there is no solid solution and points out that ‘‘there is no 
recurrence of the substance first crystallized in either case. If 
substances are capable of forming solid solutions they do not 
affect the above in any way.” Yet Vogt," following Schreinemakers 
has shown beyond doubt that, even in relatively simple systems, 
solid solution may bring about precisely the result denied it by 
Ziegler, viz. recurrent crystallization. 
In many respects it is entirely unsafe to fall back on analogy 
with simple systems. The average igneous rock is far from a 
simple system, neither was it formed under simple conditions. 
In the finally crystallized product important quantities of borates, 
fluorides, chlorides, water, CO., etc., are not represented. The 
early portion of the crystallization of a rock magma (the beginning 
of crystallization) is undoubtedly due chiefly to the cooling-down 
of the magma, whereas the addition of the final layers to the crystals 
(cessation of crystallization) may be, in part, due to a process 
which approaches an evaporation during which the above volatile 
substances are removed. The complications are such that it is 
entirely unsafe to extrapolate from simple systems investigated 
under simple conditions. 
For this reason Bowen, in the original paper, avoided theoretical 
discussion, since it must necessarily be on the basis of such extra- 
polation, and turned to the evidence of the rocks themselves. 
Thus, certain conclusions were arrived at concerning the order of 
beginning of crystallization based on the consideration of volcanic 
rocks as the quenched equivalents of plutonic rocks. Ziegler 
doubts whether this method is justifiable and points out that the 
difference of conditions under which volcanic and plutonic rocks 
crystallize, taking the specific cases of granite and rhyolite, might, 
theoretically, bring about a different order of crystallization. 
Certainly, if theoretical considerations were all the light on the 
subject available, the question would have to remain in this con- 
dition of doubt, but there exists other evidence. In nature, rocks 
occur which have been formed under every conceivable gradation 
of conditions intermediate between those characteristic of the 
tT.M.P.M., XXVII, 141-55. 
