ON THE THEORY OP HYDRAULICS. . 289 



reflection of a series of waves,which is easily observed, wlien they strike against a 

 steep wall or bank ; and when this reflection is sufficiently reg-ular,it is easy to 

 show, that the combination of the direct with the reflected motions must 

 constitute a vibration, of such a nature, that the whole surface is divided into 

 portions, which appear to vibrate alternately upwards and downwards, without 

 any progressive motion, while the points which separate the portions remain 

 always in their natural level. (Plate XX. Fig. §63.) 



But those series of waves which are usually observable in any broad sur- 

 face, and which constitute a number of concentric circles, are usually re- 

 flected in such a manner as to appear to diverge after reflection from a centre 

 beyond the surface which reflects them, and to be subject to all those laws, 

 which are more commonly noticed in the phenomena of reflected light; but 

 as these laws are of more practical importance in their application to optics, 

 than to hydraulics, it is unnecessary at present to examine their consequences 

 in detail. It may, however, be easily understood, that a new series of waves, 

 proceeding from a centre at the same distance behind the reflecting surface, 

 as the centre of the original series is before it, would produce precisely the 

 same eflfect as a fixed obstacle; consequently the law of reflection at equal 

 angles is a very simple inference from this mode of reasoning. (Plate XX. 

 Fig. 264.) 



When a series of waves proceeds in an equable canal, it is obvious that the 

 centre of gravity of the whole fluid neither rises nor falls; from this analogy, as 

 well as from the general application of thelawof ascending force, it is probable 

 that in all cases of the propagation of waves, the place of the centre of gravity 

 remains unaltered; so that when a circular wave spreads further and further 

 from its centre, its height is not diminished in the same ratio as its diameter 

 is increased, but the square of its height only varies in this proportion ; that 

 is, a wave which is a yard m diameter, and an inch high, will retain a height 

 of half an inch, when its diameter is increased to four yards. ♦ 



Many of the phenomena of waves may be very conveniently exhibited, by 

 means of a wide and shallow vessel, with a bottom of glass, surrounded by 

 sides inclined to the horizon, in order to avoid the confusion which would' 

 arise from the continual reflections produced by perpendicular surfaces, Tha- 



VOL. I. J. p 



