410 NEWTON S PIUNCIPIA. 



tide on the Dee. On going to a third approximation, 

 triple tides are found possible, and this occurs on the 

 Forth. When there are barriers in the river, as the 

 land at the termination of the Gulf of Fundy, the reflected 

 wave is such that there is no horizontal motion at the bar 

 rier, and that the tidal elevation at the mouth, caused 

 partly by the sea and partly by the reflected wave, shall 

 altogether be equal to the tide in the sea itself. Hence 

 just as in the case of sound waves in a tube, there will be 

 &quot; nodes &quot; and &quot; loops,&quot; if I may so call them. At some 

 places there might be no tide, and at others there will be a 

 rising and falling of the water, but no wave will be pro 

 pagated along the channel. This is called a stationary 

 tide. The usual case is that which corresponds to the 

 &quot; fundamental node.&quot; There will be high water at all 

 parts of the gulf at the same moment, and the tide will be 

 greater the greater the distance from the mouth, and at 

 the termination will be double that at the mouth. But 

 when there is friction in the water, this is not exactly the 

 case. It can be shown that then a tide wave does roll up 

 the river with a velocity different from that proper to the 

 depth, and the end of the flow follows close upon high 

 water. The height of the tide also may or may not in 

 crease as it travels along, according to circumstances. 



In canals adjoining two tidal seas in which high water 

 does not occur at the same moment, the motion of the 

 water must be found by the same kind of reasoning. 

 But as the result is complicated, we shall not consider 

 this case. 



The motion of the tide in channels deeper in the middle 

 than at the sides, as, for instance, the English Channel, 

 has also been considered by Professor Airy. The velocity 

 of the phase is greater in the centre than along the sides. 

 The tide wave will, therefore, become slightly convex, and 

 the velocity being always normal to the front, it will 

 assume such a shape that the part of the normal intercepted 

 between two consecutive positions shall be proportional 

 to the velocity of the wave along that normal. Thus the 



