Dr. Young’s Hydraulic Investigations. 
1*76 
III. Of the Propagation of an Impulse through an elastic Tube. 
The same reasoning, that is employed for determining the 
velocity of an impulse, transmitted through an elastic solid or 
fluid body, is also applicable to the case of an incompressible 
fluid contained in an elastic pipe ; the magnitude of the modulus 
being properly determined, according to the excess of pressure 
which any additional tension of the pipe is capable of pro- 
ducing ; its height being such, as to produce a tension, which 
is to any small increase of tension produced by the approach 
of two sections of the fluid in the pipe, as their distance to its 
decrement : for in this case the forces concerned are precisely 
similar to those which are employed in the transmission of an 
impulse through a column of air enclosed in a tube, or through 
an elastic solid. If the nature of the pipe be such, that its 
elastic force varies as the excess of its circumference or dia- 
meter above the natural extent, which is nearly the usual 
constitution of clastic bodies, it may be shown that there is a 
certain finite height which will cause an infinite extension, and 
that the height of the modulus of elasticity, for each point, is 
equal to half its height above the base of this imaginary 
column ; which may therefore be called with propriety the 
modular column of the pipe : consequently the velocity of an 
impulse will be at every point equal to half of that which is 
due to the height of the point above the base ; and the velocity 
of an impulse ascending through the pipe being every where 
half as great as that of a body falling through the correspond- 
ing point in the modular column, the whole time of ascent 
will be precisely twice as great as that of the descent of the 
