407 



lunar and solar tides is not constant, but varies with the 

 depth of the sea. 



It would take too long to enter into all the applications 

 of this theory to oceanic tides. If we could consider the 

 Atlantic as a canal running nearly north and south, the 

 tides in it would be nearly stationary. This is certainly 

 not the case. The South Sea might be considered as a 

 canal running east and west ; in that case there would be 

 a forced tide wave travelling along it. The only advan 

 tage of this theory in its application to oceanic tides, is 

 the simplicity of its analytical processes. It is even pos 

 sible to consider the effect of friction. The seas to which 

 we apply its results are not canals, but we only use them 



as suo-crestive of the general characters of the motion. 



i 

 The theory is most successful in determining the tides 



in rivers. The water at its mouth being disturbed by 

 the tides formed in the open sea, that disturbance will be 

 propagated, with unaltered period, up the river with a 

 velocity proper to the depth, viz., the square root of pro 

 duct of the mean depth and the force of gravity (32-18 ft.) 

 This disturbance is a long wave ; when the top part of 

 the wave passes any point, it forms high water, and when 

 the lower part, low water at that place. The length of 

 the wave of course depends on the distance up the river 

 travelled by the front part of the wave formed at the 

 mouth of the river, while the other parts are being formed. 

 There may even be many high and low tides on the same 

 river at once. Thus La Condamine observed about 

 twenty places on the Amazon where there was high 

 water with low water at the same time at intermediate 

 places. It is also possible, as this long wave is propa 

 gated up the river, that the low water at some place a 

 considerable distance up the river may be higher than 

 the high water at the sea. This occurs on the Thames 

 and most rivers. 



This propagation of the tide is not the transference of 

 a body of water up the river, but the motion of a form. 



D D 4 



