190 Hydraulic Investigations. 



contraction moving along an elastic pipe. In this case, an 

 increase of the diameter does not increase the velocity of the 

 transmission of an impulse; and when the velocity of the 

 contraction approaches to the natural velocity of an impulse, 

 the quantity of fluid protruded must, if possible, be still 

 smaller than in an open canal ; that is, it must be absolutely 

 inconsiderable, unless the contraction be very great in com- 

 parison with the diameter of the pipe, even if its extent be 

 such as to occasion a friction which may materially impede 

 the retrograde motion of the fluid. The application of this 

 theory to the motion of the blood in the arteries is very ob- 

 vious, and I shall enlarge more on the subject when 1 have 

 the honour of laying before the Society the Croonian Lecture 

 for the present year. 



The resistance, opposed to the motion of a floating body, 

 might in some cases be calculated in a similar manner : but 

 the principal part of this resistance appears to be usually de- 

 rived from a cause which is here neglected ; that is, the force 

 required to produce the ascending, descending, or lateral 

 motions of the particles, which are turned aside to make way 

 for the moving body; while in this calculation their direct 

 and retrograde motions only are considered. 



The same mode of considering the motion of a vertical 

 lamina may also be employed for determining the velocity 

 of a wave of finite magnitude. Let the depth of the fluid 

 be a, and suppose the section of the wave to be an isosceles 

 triangle, of which the height is b, and half the breadth c: 

 then the force urging any thin vertical lamina in a horizon- 

 tal direction will be to its weight as b to c; and the space d, 

 through which it moves horizontally, while half the wave 

 passe* it, will be such that (c—d). (a + \b) = ac, when, 



be 



ced = r. But the final velocity in this space is the 



'la -f b J r 



same as is due to a height equal to the space, reduced in 



the ratio of the force to the weight, that is, to the height 



-7, and half this velocitv is £ m J ( — • — 7 ), which is 



la + b ' \2a -j- 0/ 



the mean velocity of the lamina. In the mean time the wave 



describes 



