234 
Mr Fisher , On the transmission of 
The case of the second phase — the gaseous wave — will be 
different. Its greatest magnitude as measured by h/p will be 
r(U—p)/4<7rU, and will accordingly be proportional to the fall 
of pressure below that at which gas begins to be evolved. 
The above proportion shows that if the further fall of pressure, 
11 — p, is no greater than that which has produced the elastic 
wave, i.e. if II — p equals P — II, even then the second phase would 
be four times as large as the first. 
It would appear from the above that, if the theory is true, for a 
given distance of the origin the preliminary tremors ought to be no 
greater for great earthquakes than for lesser ones, but the magni- 
tude of the second phase ought to be in proportion to the strength 
of the shock. 
The purport of my former paper was primarily to meet the 
argument for rigidity of the earth’s interior based upon the 
assumption that the waves of the second phase are distortional. 
In this connection, if we take into account the total expansion of 
the magma arising both from elasticity and the extrusion of gas, 
and if we assume for illustration the resulting wave to be of the 
type expressed by 
• 27T, V 
c sm — (ut — x), 
X 
where u = 
equation (6) 
eP 
D (er + P) ’ 
7 eP 27 r 
P — p — 
we obtain in like manner as in 
• 27 r 
c versm — (ut — x). 
er + P X 
This function satisfies the condition 
d 2 (P~p) _ d 2 (P — p) 
dt 2 dx 2 5 
and therefore represents a single wave of stress, propagated with 
/ eP 
the velocity u, or au< ^ notl f°U° we d by another*. 
The disturbance of pressure having been once started, its 
propagation through the medium would depend upon the physical 
properties of the medium, which in the case supposed are expressed 
by r, e , and D ; and we see that its velocity u would be less than 
rp 
D that of the elastic wave, or than that of the gaseous 
wave. 
It results that the original impulse would be propagated as a 
solitary wave through the magma, which would excite two series of 
* See Airy’s Undulatory Theory of Optics, 1877, p. 19, note. 
