78 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Pressure. Specific Gravity. 



1. 2. 



200 2.688 2.7495 



1000 2.736 2.74975 



2000 2.742 2-74997 



A single standard bubble replacing the liquid in each cubic centi- 

 meter of gas-free basalt would lower the specific gravity to the amounts 

 shown, again approximately, in Col. 2. 



This last table illustrates possible ranges of buoyancies induced by 

 vesiculation at the three depths chosen. The actual buoyancy attained 

 may often be much higher. It will be seen that the buoyancy pro- 

 duced by only a small extra vesiculation of a local mass of magma 

 must occasion a rapid uprise of that mass. 



The bubbles themselves, as independent bodies, must rise with com- 

 parative slowness. The experiments of H. S. Allen have shown that 

 small spherical bubbles, rising in a liquid, attain their terminal velo- 

 city according to the formula previously deduced by Stokes for the 

 rise of light solid spheres of very small radius. ^^ 



Let r represent the radius of a bubble ; d' , its density ; d, the density 

 of the surrounding magma ; v, the coefficient of viscosity of the magma ; 

 g, the acceleration of gravity ; and x, the terminal velocity of the rising 

 bubble, that is, the velocity when the motion is steady. The Stokes 

 formula applies if the product dxr is small compared with v. This is 

 clearly true for the standard bubble in liquid basalt with the viscosi- 

 ties appropriate to pressures of 200 to 2000 atmospheres. We have, then, 



o 2/^^ -A 



Computing the values of x when the magmatic viscosity is assumed 

 to be constant and only 100 times that of water at 15° C. (0.0115) or 

 1.15 in C. G. S. units, we have, at the three illustrative pressures : 



31 H. S. Allen, Phil. ]\Iag., 50, 323 and 519 (1900). G. G. Stokes, Cam- 

 bridge Phil. Trans., 9 (2), 8 (1850). 



