Abstract
In the investigations which follow, we are concerned with the motion of an elastic fluid in one dimension, say, parallel to
x
. It is implied not only that there are no component velocities perpendicular to
x
, but that the motion is the same in any perpendicular plane, so that it is a function of
x
and of the time (
t
) only. If
u
be the velocity at any point
x, p
the pressure,
ρ
the density, X an impressed force, the dynamical equation for an inviscid fluid is
du/dt + u du/dx
= X - 1/
ρ
dp/dx
. At the same time the "equation of continuity" takes the form
dρ/dt
+
d (pu)/dx
= 0.
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