370 NEWTON S PBINCIPIA. 



nomena occurred, and the boat rode on the anterior surface 

 of a &quot;forced wave,&quot; with its prow depressed below its stern. 

 If the boat were suddenly stopped, the wave became im 

 mediately &quot;free,&quot; and was propagated forwards with the 



velocity ^gh. If the velocity of the boat were equal to 

 that of a free wave, the boat rode on the top, with its prow 

 and stern much more out of water than its middle part. 



By making the vessel move with a velocity = &quot;Sgh, the 

 depth of water is increased by the height of the wave, and 

 it is found that by this artifice boats can be carried without 

 grounding over shallow parts of the canal. Professor 

 Airy has offered an explanation of the phenomena, to which 

 we shall allude when we come to discuss waves. 



As may be expected, these waves considerably affect 

 the resistance offered to the boat. Accordingly Scott 

 Russell found that the resistance does not follow the ratio 

 of the square of the velocity, except when the velocity is 

 small and the depth of the fluid considerable. 



The resistance was found to increase quicker than in 

 the ratio of the square of the velocity, as the velocity ap 

 proached a certain quantity determined by the depth of 

 the fluid. After this point of maximum, the resistance 

 actually decreases as the velocity increases, until the ve 

 locity is equal to the velocity of propagation of a free 

 wave, and the resistance is here less than that due to the 

 square of the velocity. After this the resistance increases 

 with the velocity, but in a ratio slower than that due to 

 the square of the velocity. According to the law of pro 

 gression established, the resistance would reach a second 

 point of maximum when the velocity shall have attained a 

 certain quantity, greater than any obtained in the ex 

 periments. 



The best velocity for a boat to travel at in a canal is 



therefore ^gh. That the resistance should be less for this 

 velocity than for any other is clear, for then the boat rides 

 on the top of the wave, and the water is moving in the 



