402 FRANK F. GROUT 
action of crystallization as compared with the separation of the 
gases and liquids in deep-seated magmas. All magmas crystallize 
before they are found exposed as deep-seated types, for geological 
investigation. During the process of crystallization important 
changes in the aggregate density are likely to occur locally, and 
the quantitative importance of the change may be estimated. It 
will be assumed for the calculation that the early crystals are of 
average density. The specific-gravity increase when crystal- 
lization occurs will be 6 to 1o per cent. As outlined above, the 
viscosity is not enough to interfere with eruption if 40 per cent of 
the mass is crystalline. To make a conservative estimate— 
Assume that 20 per cent of the mass is crystalline. 
On the crystallization of one-fifth of the magma the specific gravity of the 
aggregate will rise from 2.70 to 2.73. 
The density difference for any magma is at least .03. 
The final rate of motion of a sphere of 10 meters radius is nearly 1,700 
meters per hour. 
The mineral composition of the early formed crystals may now 
be included in the calculation. If magnetite crystallizes, the 
change in specific gravity is estimated as .26 (see Table I); for 
olivine and augite the change in specific gravity is .19. These, 
when compared with the change in average gabbro used in calcu- 
lation (.03), indicate that if the early minerals are magnetite and 
olivine or augite the specific-gravity difference should be greatly 
increased, though the change in density of the residual magma 
would of course be in the reverse direction. With other con- 
tributing factors the specific gravity may change as much as .c6— 
twice as much as was assumed. ‘The rate of motion might be even 
greater than would result from deep-seated vesiculation. 
Combination effects—It is known that two minerals may 
crystallize together, and that gas may separate from a magma 
during crystallization; even the separation of immiscible fractions 
during crystallization is a possibility. These combinations may 
retard or reinforce the general convection tendency due to simple 
thermal changes in density. 
Use of the formula for flow of liquids through pipes.—If a cylin- 
drical pipe of 10 meters radius be imagined as bent approximately 
Age al 
