NO. 16. 



EFFECT OF SHALLOW WATER. 



39 



the resistance (against 6 different vessels) vertically with an arbitrary unit. As 

 shown by these curves, the resistance was a maximum at a certain critical 

 speed, which Scott Russell found to depend upon the depth of the canal. 

 If the speed was further increased, the resistance rapidly fell down to a 

 minimum and then again increased 1 . 



The decrease of resistance at the critical velocity was accompanied by 

 remarkable changes in the general features of the motion, illustrated by Figs. 

 5 — 7 below, which are reproduced from Scott Russell's paper. Fig. 5 repre- 

 sents the vessel at rest or with a slow motion. When the vessel was forced 



E=7-~- 



Fig. 5. 



Fig. 6. 



Fig. 7. 



up towards the critical velocity (see Fig. 6), the waves aft of the stem, in- 

 creased strongly, and the vessel pushed before her stem a large wave of 

 the type called by Scott Russell "Solitary wave", a single elevation of 

 water travelling along the canal. When the critical velocity was exceeded, 

 the breaking stern-waves disappeared, and the vessel moved on the top of the 

 "solitary wave" (Fig. 7); at the same time her stern, which was before sucked 

 downwards, was now raised so that the vessel drew considerably less water 

 than when at rest. 



The above described, peculiar facts depend on the laws of motion of waves 

 in shallow water. As was discovered by Scott Russell, waves of any length 



Scott Russell believed the existence of a second maximum and of a second minimum 

 of resistance at certain speeds, to be greater than could actually be produced by ex- 

 periments; but the theoretical speculations from which these conclusions are drawn are, 

 as far I can see, entirely erroneous. 



