42 THE TIDAL PROBLEM. 



and other special situations, that give quite notable movements, but the 

 proportion of these to the whole is easily exaggerated. From a simple 

 inspection of this kind it may be seen that the actual movement of the 

 water, as distinguished from the wave-form, is of a low order and hence the 

 friction is relatively small. 



If one were to entertain the thought that the energy of movement of 

 the tides arrested by the continents is a factor of much value in rotation, 

 it should be recalled that the arrest of the easterly moving tides is to be 

 set over against that of the westerly moving tides, and in the case of tides 

 moving obliquely to the earth's axis there are easterly components to 

 offset the westerly components. We have previously noted that the tides 

 on the eastern sides of the Atlantic and Pacific average higher than those 

 on the western side, so that, on the face of things, the balance of influence 

 would, if the reasoning were fundamentally sound, favor rotational accel- 

 eration. But an analysis of the action shows that it results chiefly in a 

 return wave, and this throws the problem back upon the dissipation of energy 

 through friction. Some part of the energy of impact is not recovered in 

 the return wave either through elastic resilience or the increased head which 

 actuates the tidal ebb, but if the return wave is computed as though it were 

 equal to the advance wave the loss will be covered. 



Hough has made an important contribution to the frictional phase of 

 the tidal problem by an investigation of the influence of viscosity on tidal 

 waves and currents,^ in which he included stationary oscillations as well 

 as progressive waves. He considered separately the tides whose wave- 

 lengths are large in comparison with the depth of the water-body and 

 those in which the wave-lengths are small. If attention were confined to 

 the main tidal phenomena, it might be thought that the wave-lengths 

 small in comparison with the depth of water would have no representatives 

 in tidal action, since the greatest depths of the sea are small compared with 

 the ampHtude of typical tidal waves, but, on consideration, it is apparent 

 that these waves of great ampHtude, by their various interactions upon 

 one another, by the modifications which they suffer in their approaches 

 to the shores, their arrests and their retreats, as also by their multitudinous 

 interactions with wind-waves, sea-currents, etc., give rise to an indefinite 

 number of waves of lesser ampHtude, and that the length of these second- 

 aries may be short compared with the oceanic depths. Hough did not 

 consider the special effects of the irregularities of coasts and some other 

 modifying conditions and these must be recalled in interpreting his extra- 

 ordinary results. When these various agencies of modification are duly 

 considered, it seems probable that after a very few days the original tidal 

 oscillations largely lose their primitive ampHtudes and take on shorter 

 ones, and that in this way they pass beyond observation long before they 



actually die out. 



Hough did not attempt to determine the complete destruction of the 

 tidal waves by friction, but merely the time required for their reduction 

 to the value represented by lie, or 0.368 of their original value. He found 



» Proc. Lond. Math. Soc, vol. 28, pp. 264-288. 



