232 
Mr Fislier, On the transmission of 
effect of this reaches M the magma beyond it will expand, and M 
will be urged towards the origin. 
Let P be the pressure at M in the undisturbed state : p that 
at M'. Let OM' — x — £ — £, where f is the expansion at M' due 
to the elasticity, and £ that due to the evolution of gas. Let e be 
the coefficient of voluminal compression of the magma. Also let 
II be the pressure corresponding to the limit of elasticity at which 
gas will begin to be evolved. 
Referring to the paper of 1903 it will be seen that for the 
first and second types of waves we shall have respectively the 
equations 
1 dp _ d 2 % ^ 
and 
the differential 
respectively 
and 
e dx dx 1 ’ 
r dp _ c? 2 £ 
II dx dx 2 ’ 
( 2 ) 
equations to the two types of wave being 
D<H 
e dtf 
rD d 2 £ 
II dt 2 
dx 2 ’ 
dff 
dx 2 ’ 
(3) 
( 4 ) 
where D is the density and r the ratio of the volume of gas which 
can be held in solution in accordance with Henry’s law. 
For the sake of illustration we may suppose the waves to be of 
the harmonic form. Then 
. 2-7T 
£ = — a sin — - x, 
A 
(5) 
£ being negative because M' is urged towards 0. Then a is the 
maximum displacement, and X the wave’s length, so that ajX will 
be the ratio of the maximum displacement to the wave’s length. 
Then 
d% 27t 2tt 
Also from (1), 
dx 
dj 
dx 
— — a 
cos 
p 
+ 0, 
r 2i t 27 r 
- — U = a — cos — x. 
e XX 
P 
When f = 0 there will be no disturbance, and p will have the 
undisturbed value P. Then by (5) x = 0. 
2tt a2ir 2i r P—p . . 
a— — cos-— x = — , (o) 
Hence 
X 
