84 PROCEEDINGS OF THE AMERICAN ACADEMY. 



vesicalation should be the rule at one atmosphere of pressure and non- 

 existent at one hundred or one thousand atmospheres ; it is all a ques- 

 tion of the degree of saturation with gas. The two-phase convection 

 hypothesis rests on this unproved assumption, but its merit is great, as 

 it explains the essential facts of circulation in Halemaumau. The hy- 

 pothesis also explains the periodicity of " Old Faithful." Throughout 

 the years 1908 and 1909 its geyser-like uprush occurred, on the 

 average, once every 35 seconds or thereabouts. This pulsatory effect 

 is expected as a result of the mechanism of two-phase convection. 



Cooling by Rising Juvenile Gas. — As a fifth hypothesis it might be 

 conceived that the heat is kept up in the lake through the rise of 

 bubbles oi free juvenile gas from the magma chamber, the bubbles 

 arriving at the surface with some excess of temperature above that re- 

 quired to give the lava of the lake its observed fluidity. But the 

 feeble explosiveness of the emanating gas at Kilauea shows that any 

 unit mass of it, arriving at the surface, is already nearly expanded to the 

 volume appropriate to one atmosphere of pressure, and therefore that 

 the gas is in nearly perfect thermal equilibrium with the enclosing lava 

 at the surface. Such bubbles, as they rise and expand, must thereby 

 tend to cool the magma. 



The cooling effect is very great, as may be shown by the following 

 calculation. In an adiabatic expansion of a perfect gas: let T' be the 

 initial absolute temperature, and T the final absolute temperature ; let 

 p be the initial pressure, and }) the final pressure; and let y{= 1.4) 

 be the ratio of the specific heat of the gas at constant pressure to its 

 specific heat at constant volume. Then 



r _ (py-^ 



T ~\p] ' 



At about 37 meters below the lake surface the pressure is 10 atmos- 

 pheres. If the bubble, after expanding adiabatieally, is to arrive at 

 the surface at a temperature of 1200°C., it must have at the depth of 

 37 meters a temperature of about 3700°C. (assuming no dissociation of 

 the gas). Evidently the free-moving gases have a cooling effect on 

 the upper part of the lava column. That this effect is actually small 

 is, of course, due to the small mass of gas emitted in a unit of time and 

 to the fact that y is much less than 1.4 for the actual (not "perfect ") 

 gases while rising through the deeper levels. IMoreover, it has been 

 noted that the rise of a bubble must be exceedingly slow if its mass is 

 anything like that in the average vesicle of frozen lava. So slow is 

 the transfer that the rapid heat wastage at Halemaumau cannot pos- 

 sibly be compensated by any residual superheat in the emanating gas. 



