316 NV. L. BOWEN 
place in the marginal phase that no diffusion into that region can 
occur. One then arrives at a method of formation of a border 
phase that has been suggested by Daly, who regards the border 
phase as a chilled phase having the composition of the original 
magma.* 
FORMATION OF REACTION RIMS 
We have seen in the foregoing that the movement of large 
quantities of material through long distances by diffusion in a 
magma cannot be credited when the relatively rapid rate at which — 
the magma must cool is considered. On the other hand, diffusion 
through short distances is to be expected, and such phenomena as 
the formation of reaction rims about foreign inclusions are readily 
to be attributed to diffusion. At the same time it should be noted 
that a rather wide reaction border will require a very considerable 
period of time for its formation if diffusion alone is active. Figure 7 
enables one to form an idea of the period of time required for the 
diffusion of material from an inclusion to various distances in the 
surrounding medium if the scale of concentrations is reversed, 
that is, if zero is placed at the top and one at the bottom. The 
solution is by no means a rigid one for a small inclusion, but for a 
large slablike inclusion is sufficiently good to enable one to draw 
general conclusions. The figure shows that after sixty-four years 
the effect of the inclusion is barely felt for about 3 m. and is strongly 
felt (one-half saturation) for not more than 1 m. These con- 
siderations suggest that the formation of reaction rims up to 2 m. 
thick, such as those described by Ussing, about inclusions of quart- 
zite in augite syenite at Kangerdluarsuk would require a period of 
time of the order of magnitude of one hundred years if diffusion 
alone were operative.” 
The growth of crystals is itself largely dependent upon diftu- 
sion, but no quantitative estimate of the rate of growth is possible 
without some knowledge of the concentration gradient along 
which flow of material takes place, that is of the degree of super- 
saturation possible in the liquid interstitial to the crystals. The 
t Igneous Rocks and Their Origin, p. 237. 
2 Geology of the Country about Julianehaab, Greenland, p. 362. 
