TWO-PHASE CONVECTION IN IGNEOUS MAGMAS 493 
square, with sides as long as the depth of the magma chamber; and 
further, if the liquid in one vertical side of the square is kept more 
dense than the rest, circulation will occur. The formula for viscous 
or direct flow is* 
where Q is the quantity passing a certain place in unit time, (p,— Pp.) 
the difference in pressure, R the radius of the tube, LZ the length of 
the tube, and v the viscosity of the liquid. With a constant radius 
of 10 meters and the added relation that the length of the tube is 4 
times that of the column giving the pressure, the formula reduces to 
ee » 31,250 TK?(d; —d,) 
where d,; and d, are the as gravities of the two upright columns. 
The rate of flow can be derived from this by the quantity per 
second per unit cross-section: 
(d,—d,) 
V 
X=31,250 
Comparison of estimates.—Tables II and III show the results 
in compact form. 
5 TABLE II 
ESTIMATED CONVECTION RATE, BY DIFFERENT METHODS, IN METERS PER Hour 
Viscosity | 
(Water at Phases Settling Spheres! Flow in Pipe Observed* 
.OIIS) | 
| 
= | 
5 Hot and cool magma 1,000 2,200 tere Snr Le 
5 Magma and gas bubbles 2,500 12,000 | 2,000-5 ,000 
Fy Magma and average crystals 1,700 6,600 [PRN STA GNA 
5 | Magma and heavy crystals 2,500 12,000 | Neale a aes shay 
ts | | 
300 Hot and cool magma 1,000 | 40 emerson ele 
300 -Magma and gas bubbles 2,500 220 lee area aes 
300 Magma and average crystals 1,700 aging} lee era we cate cs lene 
300 Magma and heavy crystals 2,500 220 | SEO TRG OeHRENE 
*R. A. Daly records the apimeniion in a crater lake as 2 ie fe Rilometers per hour in “The 
Nature of Volcanic Action,” Proc. Am. Acad. Arts and Sci., XLVII, 
The calculated results in other columns are not strictly Loans as they are based on a pressure 
of 200 atmospheres, and the convection in the crater may be more active than that 3,000 feet below. 
t Poynting and Thomson, A Text-book of Physics (1902), p. 200. 
A recent paper by W. K. Lewis, in Jour. of Ind. and Eng. Chem., VIII, 627-32, 
gives a good statement of the present methods of calculation. For small velocities 
the formula for viscous flow applies even to pipes of large diameter. 
