36 THE TIDAL PROBLEM. 



over the earth's surface (figures 1 and 2), Afterwards let us consider 

 the phenomena from a more radical point of view founded on the laws of 

 energy and the configuration of the interacting bodies. 



From what has already been said, it is clear that no continuous tides 

 are being dragged around the earth acting as a frictional band. No single 

 tide moves westerly so much as one-half of the earth's circumference, and 

 most of the tides have a much less movement in that direction. On the 

 other hand, many tides move easterly and still others move northerly and 

 southerly. The position of these relative to the moon is various, and the 

 attraction of the moon upon them may be accelerative or neutral as well as 

 retardative, so far as instantaneous attraction while in the given positions 

 is concerned. A wave starting in the Southern Ocean and moving north 

 through the Atlantic for more than a day will run the whole gamut of 

 positional relations to the moon and sun, and will, considered simply as an 

 attached protuberance, be retardative, neutral, and accelerative in turn. 

 In the case of waves that move to and fro across the water-bodies in seiche- 

 like fashion, it is obvious that the positional relations may be various. 

 The most interesting cases are those of water-bodies whose periods of 

 oscillation are nearly commensurate with the periods of the tidal forces. 

 The breadth and depth of a water-body may be such that a wave started 

 under the moon when it passes over the eastern margin will cross to the 

 western side and return to the eastern just in time to fall under the moon's 

 next crossing of the eastern margin, and so be reinforced by every return. 

 In a body a little wider or a httle shallower, the return of the wave would 

 fall behind the moon's arrival and at its turn tend to retard the moon's 

 motion, while in a body a little less wide or a little deeper the turn will 

 come before the moon's arrival and the wave, at its turn, will tend to 

 accelerate the moon's motion. But if either of these waves were to be 

 followed through its whole course and its relations to the moon observed, 

 it would be found to be accelerative, retardative, and neutral at different 

 points. 



Pursuing this line of inspection, it may be seen that the waves developed 

 in the basins of the lithosphere must have a wide range of periods, some 

 longer, many shorter, than the period of the tidal forces. Their rotatory 

 influence on this basis of treatment is thus extremely difficult to analyze 

 and evaluate, and the algebraic sum of all such influences is quite beyond 

 mathematical determination. 



The case is even more complicated when we consider amphidromic 

 systems and those whose oscillations lie in lines oblique to the axis of 

 rotation and to the moon's course. In the case of a stationary oscillation 

 neither forward nor backward drag seems to be predicable as a total result, 

 on this basis of treatment. 



When all of the multitudinous phases are considered, it is clear that 

 the case becomes so extremely complex that it can not be solved with any 

 assurance of a rehable conclusion by analyzing the rotational effects of 

 individual cases and summing the results. Some more basal method, so 

 chosen as to escape these complications and the uncertainties of their 

 interpretation, is required. 



