299 



taken from Dubuat and Gerstner, with some of his own, the results 

 of which are compared with the velocities calculated according to the 

 formulae of Dubuat and of the author. 



The next section treats of the resistance occasioned by flexure of 

 the channel. In this case Dubuat directs the squares of the sines of 

 the angles of flexure to be added together and multiplied by the 

 square of the velocity, and considers the quantity thus obtained pro- 

 portional to the height necessary for overcoming the resistance. But 

 since the magnitude of this quantity is evidently dependent on the 

 number of parts into which the angle is arbitrarily divided, the au- 

 thor prefers attending merely to the aggregate angle of flexure as 

 expressed in degrees to which the resistance is proportional, but va- 

 ries also inversely as the radii of curvature, or more nearly as that 

 power of the radius which is expressed by -J-. A table which follows 

 shows the comparative correctness of the author's formula with that 

 of Dubuat. 



Dr. Young next considers the propagation of impulses through 

 tubes, the elasticity of which supplies the want of elasticity of the 

 fluid contained, and admits the same mode of reasoning that is em- 

 ployed in the case of elastic fluids or solids ; for if the elastic force 

 of the tube be as the increase of its circumference, a certain finite 

 height may be assigned, which would cause infinite extension, and 

 which may be called the modular column. The velocity of an im- 

 pulse at any point will be equal to half that which is due to the 

 height of this point above the base of such a column, and hence the 

 time of ascent of an impulse will be twice as great as that of a fall- 

 ing body ; and if the pipe be inclined, the ascent of an impulse will 

 bear the same relation to that of a body moving along an inclined 

 plane. 



The magnitude of diverging pulsations is next examined, and the 

 conclusions of Euler, Lagrange, and Bernouilli, who have demon- 

 strated that the velocity of each particle of an elastic fluid is as its 

 distance from the centre of impulse, are supported by a new method 

 of considering the subject. 



When a wave is reflected from two surfaces distinctly opposed to 

 each other, they evidently sustain equal pressures ; and if to one of 

 these surfaces two others be opposed converging at the acute angle, 

 the wave will be elevated higher as it approaches the angle ; and if 

 the height be supposed in the inverse subduplicate ratio of the cor- 

 responding subtense of the angle, the pressure will then be equal to 

 that upon the single surface opposed : and hence is an additional 

 reason t for inferring, that in all transmissions of impulses the in- 

 tensity is in the inverse subduplicate ratio of the [extent of parts 

 collaterally affected, and this in conformity to the law of the ascend- 

 ing force ; but in the case of intersecting waves, there is observed to 

 be a paradoxical deviation, which isdeserving of further consideration. 



From considering the effect of bodies moving along an open canal, 

 the author infers, that by means of a contraction moving progressively 

 along an elastic pipe, the quantity of fluid impelled will be very 



