80 



KNOWLEDGE. 



[Ai'RiL 1, 189G. 



waves my favourite post of observation is the bridge near 

 the Magazine ; whilst for a near view, and to observe the 

 "wave profile" of the duck, I prefer to walk by the edge 

 of the water in St. James's I'ark, where one is sure to be 



Fig. 3. — Ducks swimming, showing Echelon Waves. 



accompanied at one's own pace by a duck on the look-out 

 for food, the ducks in St. James's Park being both tamer 

 and greedier than those of the Serpentine. The wavelets 

 or ripples which form a fringe in front of the bow wave 

 should be noticed ; also the rise of water at chest and tail 

 and its sinking " amidships " when the duck darts forward 

 for a piece of bread. Very pretty also is the interlacing 

 of the wave tracks when a whole fleet of ducks moves off 

 together, especially when the sun is low and the slanting 

 rays give lights and shadows to the waves. 



In canals, the heavily-laden barges dragged by horses 

 move too slowly to generate a system of waves ; but when 

 there is steam navigation upon a canal, or when Hghter 

 boats travel more quickly than the laden barges, a train of 

 waves may be seen to follow the vessel. With higher 

 speeds the wave-length increases, and the disturbance due 

 to an even moderate velocity reaches the bottom of the 

 canal. The surface particles can then no longer swing 

 freely in a circular orbit, for they feel the effect of the 

 bottom, communicated through the water particles which 

 swing in their respective orbits at intermediate depths. As 

 the motion of the swinging particles departs more and 

 more from the original circular, uniform movement, the 

 rear of the procession of waves travels at a rate more 

 nearly equal to that of the boat. This is due to the fact 

 that, as the motion of the swinging particles increases in a 

 horizontal direction relatively to the vertical motion, the 

 proportion of the energy of motion which is handed on at 

 each swing is increased. When the wave-length has 

 increased until the vertical motion of the swinging particles 

 is very small in comparision with the horizontal motion, 

 practically the whole of the energy is transmitted. For a 

 canal of any given depth there is a particular wave velocity 

 corresponding to this condition. If by any means there 

 be instituted a train of waves following one another with 

 this velocity there will be no lengthening out of the train 

 of waves, for the energy does not fall behind the wave, but 

 is transmitted with the velocity of the wave itself. Each 

 wave crest travels on with undiminished height, except for 



the inevitable loss of energy which takes place through 

 friction. Such a wave is termed a s(dit<inj wave, because it 

 is capable of existing by itself without giving rise to a 

 group of waves. When the critical velocity has been 

 reached there is no distinction between the group velocity 

 and the wave velocity. Perhaps it would be more correct 

 to say that when the critical velocity is reached there is no 

 such thing as a group of waves, since each single impulse 

 creates only a single wave ; and if a number of such waves 

 be created by a succej;sion of impulses each wave remains 

 " solitary," for it neither parts with nor does it receive 

 energy to or from the following or preceding waves. 



To return to our canal boat. As the velocity is increased 

 the rear of the group of waves moves more and more 

 nearly at the rate of the boat itself. At a greater velocity 

 the boat is followed by a shorter train of higher waves. 

 At the critical velocity the wave created by the bow of the 

 boat moves along with the boat ; the energy of the wave 

 does not fall behind so as to create a train of waves, and 

 if the boat continue to move at the proper speed no new 

 waves are formed. This fact was discovered many years 

 ago, on the Glasgow and Ardrossan C'anal, through the 

 accident of a horse taking fright and bolting with a light 

 canal boat in tow. When the horse galloped off with the 

 boat it was observed that the foaming surge which used to 

 devastate the banks had ceased, and that the vessel was 

 carried on through comparatively smooth water witli <i 

 greatly diminislud resistance. The value of the discovery 

 was at once perceived, and fly-boats, as they were called, 

 were introduced upon the canal for the rapid conveyance 

 of passengers. The boat, which was drawn by a pair of 

 horses, was started slowly : at a given signal it was by a 

 sudden jerk drawn up onto the top of the bow wave ; and 

 the horses were then kept at a trot or gallop, going from 

 seven to nine miles an hour, the boat riding smoothly 

 and easily upon a lump or hillock of water. Wave- 

 making resistance was done away with ; the horses had 

 only to overcome skin resistance. After the critical 

 velocity has been attained the only thing like a wave 

 which is to be seen is the solitary hump or hillock of water 

 upon which the boat rides. If the boat be stopped this 

 hillock of water travels on as a free wave. Mr. Scott 

 Russell has described the occurrence as follows : — " When 

 the boat stopped . . . the mass of water . . . 

 accumulated round the prow of the vessel in a state of 

 violent agitation ; then suddenly leaving it behind rolled 

 forward with great velocity, assuming the form of a solitary 

 elevation — a rounded, smooth, and well-defined heap of 

 water, which continued its course along the channel 

 apparently without change of form or diminution of speed. 

 I followed it on horseback and overtook it rolling on at a 

 rate of some eight or nine miles an hour, preserving its 

 original figure, some thirty feet long and a foot to a foot 

 and a half in height. Its height gradually diminished, 

 and after a chase of one or two miles I lost it in the 

 windings of the channel." 



This is the free solitary wave, which is most generally 

 known in the form of the low, foaming ridge which slides 

 in upon a flat beach after the bursting of a breaker, as 

 shown in our illustration in the February number of 

 Knowledge. Here, by the shore, may be seen the more 

 rapid progress of the solitary wave in deeper water, for the 

 hinder ridges are constantly catching up those in front, 

 which are in shallower water. 



It remains to explain why the critical velocity of a 

 canal boat depends upon the depth of the canal, being 

 greater for greater depths. The change from oscillating 

 wave to solitary wave depends upon the change from a 

 circular swing of the water to a backward and forward 



