NEWTON S PKINCIPIA. 409 



at spring tides is 18 feet, at Swansea 30 feet, at Chepstow 

 about 50 feet.&quot; &quot;At Newnham it is reduced to 18 feet, 

 and it is still less at Gloucester.&quot; 



The form of the wave itself is also changed in its progress 

 up the river, if the channel is so shallow that the height of 

 the wave bears a sensible proportion to the depth. It is 

 in this case necessary to carry our solution of the Hydro- 

 dynamic Equations to a second or third approximation. 

 When this is done we find that the high water travels up 

 the river with a greater velocity than the phase of low 

 water ; the wave becomes steeper in front, and long and 

 gentle in rear. Thus it takes less time for the tide to rise 

 than to fall. &quot; In the St. Lawrence at 40 leagues below 

 Quebec, the rise and fall occupy equal times ; at 6 leagues 

 below Quebec, the rise occupies five hours and the fall 

 seven hours ; at twenty leagues above Quebec, the rise 

 occupies three hours and the fall nine hours.&quot; The rule 

 given by theory is, that the excess of the time of the water 

 falling over the time of rising is six times the product of 

 the time occupied by the tide wave in passing from the 

 open sea to the station under consideration, and the ratio 

 of the rise of the tide above the mean depth to the mean 

 depth. In this change of form we find an explanation of the 

 bore. Two things, says Professor Airy, are necessary for 

 its formation. There must be a large tide rising with 

 rapidity, and the channel of the river must be bordered 

 with a great extent of flat sands near the level of low 

 water. The tide rises rapidly in the centre of the river, 

 but the water is not broken. But, the rise being very 

 rapid, the water is elevated above the sands faster than it 

 can cover them, and therefore rushes over them with a 

 great velocity and a broken front. As the tide proceeds 

 up the river, a still more extraordinary change of form 

 takes place ; the middle of the rear becomes less and less 

 steep ; it is at last horizontal, and finally slopes the other 

 way. Thus for every high tide at the mouth there may 

 be two unequal high tides at a distance up the river. In 

 accordance with this, Mr. Russell has observed a double 



