HYDRAULIC INVESTIGATIONS. ] 15 



Iii the last three experiments, the diameter of the pip* Remarks. 

 Was two inches. The radius of curvature is not ascertained 

 within the tenth of an inch, as Dubuat has not mentioned 

 the thickness of the pipes. The mean errour of his formula 

 iu fifteen experiments, and of mine in twenty, is T V 0I tne 

 whole. 



III. Of the Propagation of an Impulse through an Elastic 



Tube. 



The same reasoning, that Is employed for determining Propagation, of 

 the velocity of an impulse, transmitted through an e^j^C through an 

 solid or fluid body, is also applicable to the case* of an in- elastic tube, 

 compressible fluid contained in an elastic pipe; the magni- 

 tude of the modulus being properly determined, according 

 to the excess of pressure which any additional tension of the 

 pipe is capable of producing; 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 co- 

 lumn of air enclosed in a tube, or through an elastic solid. 

 If the nature of the pipe be such, that its elastic force va- Propositions. 

 ries as the excess of its circumference or diameter above the 

 natural extent, which is nearly the usual constitution of 

 elastic 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 im- 

 pulse will be at every point equal to half of that which is 

 due to the height of the point above the base; and the velo- 

 city of an impulse ascending throeigh the pipe being every 

 where half as great as that of a body falling through the 

 corresponding point in the modular column, the whole time 

 of ascent will be precisely twice as great as that of the de- 

 scent of the falling body ; and in the same manner if the 

 pipe be inclined, the motion of the impulse may be com- 



I 2 pared 



