&90 LECTURE XXIII. 



waves may be excited by the vibrations of an elastic rod or wire, loaded 

 ■with a weight, by means of which its motions may be made more or less rapid 

 at pleasure; and the form and progress of the waves may be easily observed, 

 by placing a light under the vessel, so that their shadows may fall on a white 

 surface, extended in an inchned 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 pro- 

 portion to its own breadth, into the surface of a part of the water which is 

 at rest, it diverges from the aperture as from anew centre; but when the 

 aperture is considerably wider than the wave, the wave confipes 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 waves, proceeding from centres near 

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

 othei', 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 ob- 

 served, 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 ap- 

 plication 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 evi- 

 dence of the truth of some facts, which are capable of being applied to the ex- 

 planation of some of the most interesting phenomena of acustics and optics. 



