233 
Earthquakes through the Earth. 
and a ^ 7r will be the greatest value of ~~ 
x = - , i.e. at half the wave’s length. 
A 
which will occur when 
If at this juncture the pressure has fallen to the point at which 
gas begins to be evolved, it is clear that the greatest value possible 
p - n 
for a IX will be . . And since e, which is the coefficient of 
1 477-e 
voluminal compression at the pressure P, is a very large quantity, 
therefore a/X will be a very small ratio, and the characteristic of 
the wave will be a very slight disturbance and flatness. 
In like manner, if we assume the wave of the second phase due 
to the evolution of gas, to be expressed by 
y 7-273- 
l = — b sm — x, 
P 
observing that II is the highest pressure at which gas is evolved, 
we have 
. 27 r &27r 27 r II — p 
b cos — x = r — „ , 
g g g 11 
consequently the greatest value of r 
n - 
n 
p 
IS 
birr 
P 
which will occur 
when x = ^\ i.e. at half the wave’s length. 
Hence we have the proportion 
b a II — n P — 11 
g : x ::r IT : T~ 
re P — n 
n ’ n — p ' 
From (3) and (4) we know that re/Tl gives the ratio of the 
squares of the velocities of the two phases of wave, viz. (ll/5’2) 2 or 
4 3 nearly, as observed at distant stations. 
Therefore - : 4*3 : 0 . 
g X YY—p 
P — n being the extreme fall of pressure which corresponds to 
the limit of elasticity of the magma, it follows that, if the fall of 
pressure does not exceed this, only the elastic wave would be pro- 
duced, and it seems probable that it might die out before reaching 
a distant station. But if the fall of pressure at the origin of 
disturbance exceeds P — n, a gaseous wave will be also produced, 
and to whatever distance this may be propagated, an elastic wave 
will be started in front of it, but the magnitude of the latter can 
never exceed — 7 — — . 
47re 
VOL. XIV. PT. III. 
16 
