408 NEWTON S PRINCIPIA. 



We have seen that when a wave travels, along a uniform 

 channel, that the water is moving in the direction in 

 which the wave travels, so long as the water is above its 

 mean level, and in the opposite direction so long as it is 

 below its mean height. This is also the case with the 

 tide, except so far as this circumstance may be modified 

 by the varying depth, breadth, &c., of the river. It is a 

 common error to suppose that the flow up the river ceases 

 when the tide begins to fall. The flow in a uniform canal 

 continues for three hours after tide. But if the depth 

 and width be decreasing, if there be any friction among 

 the particles of water, if there be any impediments to 

 the progress of the wave, as a barrier or a series of 

 bridges, the theory shows that this interval will be much 

 less, and observation confirms the result, for the mean 

 interval at which slack water follows high or low tide at 

 Deptford has been shown* to be thirty-seven to forty 

 minutes. 



The height of the tide wave also experiences many 

 alterations due to the varying circumstances of the river. 

 If the tide be stopped by a barrier, or if we are consider 

 ing the tides in a gulf like the Bay of Fundy, theory 

 shows that there will be tide waves reflected from 

 the barrier, and the height of the tide at the extremity 

 may be greatly increased. If the breadth or depth de 

 crease, the height of the tide will be increased, particularly 

 by any decrease of the former. On entering any river, 

 then, we may expect the tide to be greatly increased. The 

 magnitude of this change depends on the breadth of the 

 wave, and this again depends on whether the tide be 

 formed by the sun or moon ; hence the ratio of the tides 

 formed by the two luminaries will not be exactly the same 

 at all places. But when the tide has entered the river, the 

 friction of the particles of water causes the disturbance to 

 diminish in geometrical progression as it goes up the river. 

 &quot; At the entrance of the Bristol Channel the whole rise 



* Phil. Trans. 1842. 



