Earthquake waves through the earth. 355 



of the relief of pressure until the limit of expansibility of the 

 liquid is reached, after which gas will be extruded as the pressure 

 continues to fall. 



We will consider the simplest case, i.e. of a column of unit 

 section filled with the liquid in a state just saturated with the gas. 

 Let r be the constant volume of gas held in solution in unit 

 volume, where r will be independent of pressure. 



o 1 1 



M N 



M' N' 



Let OM = x be the distance from the origin of a particle in 

 the magma in the undisturbed and saturated condition, and let 

 the corresponding pressure be P. 



Let OM' be its distance in the disturbed condition. 



Let the density of MN = D. 



The density of M'N' is different, on account of the expansion 

 of the liquid and of the vesicles of gas which are liberated owino- 

 to the relaxation of pressure. 



Let p be the pressure of the liberated gas at M'. Then this 

 pressure will be transmitted throughout the magma, so that the 

 pressure of the mixed gas and liquid at M' will be p, which will 

 act upon the expanded mass M'N', and it will be observed that 

 the mass of M'N' is the same as that of the original mass MN. 



Let MN = Bx, OM' = x + %. 



Then M'N' = ~ (x + £) Bx + Q8x"- = Bx + ^ Bx + QBx 2 . 



Now consider a volume V of the undisturbed and saturated 

 magma, and let S be what the density of the gas dissolved in it 

 would be at pressure P. Let s be the density of the same at the 

 pressure p. Then because at the pressure P this gas is wholly 

 absorbed, its total volume at the pressure P would be rV. 



S 

 Hence its total volume at the pressure p would be rV - , which 



s 



p 



by Boyle's law =rV — . 



Suppose that at the pressure p some of the gas is set free so 

 as to form vesicles. Then we should have 



volume of free gas + volume absorbed = total volume. 



