HYDRAULIC INVESTIGATIONS. ]0<J 



the contraction approaches to the natural velocity of an im- 

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

 still smaller than in on open canal ; that is, it must be ab- 

 solutely inconsiderable, unless the contraction be very great 

 in comparison with the diameter of the pipe, even if its ex- 

 tent be such as to occasion a friction, which may materially 

 impede the retrograde motion of the fluid. The appllca- Motim of th« 

 tion of this theory to the motion of the blood in the arteries 

 is very obvious, and I shall enlarge more on the subject 

 when I 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, Resistance to a 

 might in spme cases be calculated in a similar manner: but floating body. 

 the principal part of this resistance appears to he usually 

 derived from a cause which is here neglected ; that is. the 

 force required to produce the ascending, descending, or la- » 



teral motions of the particles which are turned aside to make 

 way for the moving body; while in this calculation their di- 

 rect and retrograde motions only are considered. 



The same mode of considering the motion of a vertical Velocity or a. 

 lamina may also be employed for determining the velocity wave, 

 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 



eed ~ r. But the final velocity in this space is the 



2a + 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 



-, and half this velocity is i m «/ ( j, which 



2a + \2c + by 



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

 wave describes the space c + d, and its velocity is greater 



c 

 than that of the lamina in the ratio of ~ -f 1 to 1, that is 



a 



2a + b\ la . . . /a \ 



- — ,— ■ — V 1 or -T- + 2 to 1, becoming m ( r + 1 ) 



b 



