220 LECTURE XXIII. 



may fall on a white surface, extending in an inclined position above. In 

 this manner the minutest inflections of the surface of the water may be 

 made perfectly conspicuous. (Plate XX. Fig. 265.) 



By means of this apparatus, we may examine the manner in which a 

 wave diverges, when a portion of it has been intercepted on either side or on 

 both sides. Thus, if a wave is admitted, by an aperture which is very 

 narrow in proportion to its own breadth, into the surface of a part of the 

 water which is at rest, it diverges from the aperture as from a new centre ; 

 but when the aperture is considerably wider than the wave, the wave con- 

 fines its motion in great measure to its original direction, with some small 

 divergence, while it is joined on each side by fainter circular portions, 

 spreading from the angles only. (Plate XX. Fig. 266.) 



When two equal series of circular w r aves, proceeding from centres near 

 each other, begin their motions at the same time, they must so cross each 

 other in some parts of their progress, that the elevations of the one series 

 tend to fill up the depressions of the other ; and this effect may be actually 

 observed, by throwing two stones of equal size into a pond at the same 

 instant ; for we may easily distinguish, in favourable circumstances, the 

 series of points in which this effect takes place, forming continued curves, 

 in which the water remains smooth, while it is strongly agitated in the 

 intermediate parts. These curves are of the kind denominated hyperbolas, 

 each point of the curve being so situated with respect to its foci, as to be 

 nearer to one than the other by a certain constant distance. (Plate XX. 



Fig. 267.) 



The subject of waves is of less immediate importance for any practical 

 application than some other parts of hydraulics ; but besides that it is 

 intimately connected with the phenomena of the tides, it affords an elegant 

 employment for speculative investigation, and furnishes us with a sensible 

 and undeniable evidence of the truth of some facts, which are capable of 

 being applied to the explanation of some of the most interesting phenomena 

 of acustics and optics. 



It may be shown, by steps nearly similar to those by which the velocity 

 of the motions of waves is investigated, that a fluid which is contained in an 

 elastic pipe, and which receives an impulse at any part of the pipe, will 

 transmit its effects with the same velocity as a wave would have in a 

 reservoir, of that depth which measures the elasticity of the pipe, that is, 

 with half the velocity which a body would acquire in falling from the 

 height at which a portion of the fluid connected with the contents of the 

 pipe, would stand in a vertical tube. It is in this manner that the blood is 

 transmitted, by means of the impulse given to it by the heart through the 

 blood vessels ; the pulse moves on with great rapidity, the elastic force of 

 the vessels being considerably assisted by the temporary actions of the mus- 

 cular coats of the arteries, which cause a contraction more rapid than the 

 dilatation ; while the whole mass of the arterial blood continues at the same 

 time to advance with a much smaller velocity ; like the slow stream of a 

 river, on the surface of which undulations are continually propelled with 

 motions independent of its own. 



