ON WAVES. 365 



and 30 feet. By these means it will be easy for observers to verify or correct 

 these numbers. 



These waves are very peculiar in this respect, that they exhibit little or no 

 tendency to lateral diffusion ; the breadth of a wave does not apparently ex- 

 ceed the length of a wave, and is often much smaller. When a stream enters 

 a large pool, its path across the pool is marked by these waves very distinctly, 

 and the diminishing length of the waves accompanies the diminishing velocity 

 of the stream, and at the same time indicates the extreme slowness with which 

 diffusion takes place. 



The motion of the particles of water, as observed by a body floating on the 

 surface, is this, the motion is retarded at the top of each wave and accelerated 

 in the bottom, thus oscillating about the mean motion of the stream. The 

 motion, as far as it can be observed by bodies floating near the surface, is a 

 simple combination of a circular with a rectilineal motion. The disturbing 

 body, the stone at the bottom, gives to the particles which pass over it the 

 motion of eddy as indicated, Plate LV. fig. 2, and this being continued down- 

 wards, and combined with the rectilineal motion of the particles, presents 

 the cycloidal form of the wave. 



If we conceive a uniform revolving motion in a vertical plane communi- 

 cated to a particle of water, the centre of the circle of revolution being at 

 the same time carried uniformly along the horizontal line, Plate LVI., then the 

 path of the particle liaving these two motions is marked out by the cycloidal 

 line 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 joining these points, and if every suc- 

 cessive particle of the fluid have the same motions communicated to it, the 

 simultaneous places of successive particles will give the line 1, 2, 3, 4, 5, 6, 

 7, 8, &c. as the form of the surface of the fluid. It is to be observed that at 

 A and C the direction of the motion of revolution is opposite to the motion 

 of transference, and .•. the absolute velocity of the particle is diminished by 

 the oscillating motion, while at B and D it is increased by an equal amount, 

 and in the intermediate positions 3 and 9 it is neither increased nor dimi- 

 nished. It is also to be observed, that when the motion of the water in the 

 direction of transference is slowest (f. e. when the motion of oscillation is 

 opposite to the motion of transference), the transverse section of moving 

 fluid is greatest, and when the motion of transference and of oscillation 

 coincide, and the motion is quickest in the direction of transference, the trans- 

 verse section of the fluid is greatest. Thus we see how dui-ing a change of 

 form the dynamical equilibrium of the fluid may be unchanged. 



The fluid may thus be conceived as moving with varying velocity along 

 a channel of variable section, its upper surface being conformable to the 

 outline of the wave. Hence we might infer that a rigid channel of varying 

 area, of the form of this standing wave, would not interfere with the free 

 motion of the fluid. 



And hence it may follow, that when the area of a pipe conveying fluid is 

 to undergo a change, the best form of pipe or channel is indicated by the 

 form of this wave. Thus the velocity has undergone a change between and 

 1 4 which the form of a close pipe might render permanent. 



In the examples already given, a solid impediment has generated the waves 

 I on the surface of the fluid. At the confluence of streams I have observed 

 j the same waves generated by the oblique action of one current on another 

 I meeting it in a different direction. 



I The height and hollow of the fluid and the change of velocity are to be 

 i regarded as reciprocally the cause and effect each of the other. The obstacle 

 I firtit retards the velocity of the fluid, so as to accumulate it above the obstacle, 

 j the water rises to a height due to this diminished velocity, and as all the 



