DEDUCTIONS FROM THE TIDES. 43 



that for waves of the class corresponding in his terminology to n = 0, in 

 waters of abj^smal depths, the modulus of decay (to 0.368 value) is 42.6 

 years; for the class corresponding to n = l-, 31.7 years; while for that 

 corresponding to n = 100, it is 4.8 years. The types, n = 0, n = l, represent 

 the longest and strongest waves; while those in which n has a high value 

 represent waves of much shorter and feebler type and hence those first 

 to be reduced to the limit named, as indicated by the moduli. In a case 

 where the depth is 200 meters — the prevailing depth on the edge of the 

 continental shelf — the moduli of decay for the types w = and n= 1 are 4.5 

 and 3.3 years, respectively. For waves of 100 meters amplitude in water 

 with a depth of 1 meter, the modulus of decay is about 80 minutes, bottom 

 friction included. If there were no friction at the bottom, the modulus of 

 decay would be about 2.25 years. In summation Hough says: 



These results indicate how little can be the effects of viscosity upon the motion of 

 the sea, except possibly in usually confined waters. It seems that wherever the depth 

 exceeds a very moderate amount, say 100 fathoms, the rise and fall of the waters due to 

 the Sim and moon will not be appreciably affected by friction.' 



These determinations have a significant bearing upon the question how 

 much of a given tidal wave is due to the force that has just been acting 

 upon it during the current tidal period, and how much to the residual 

 motion inherited from previous tides. If the motion of the waters when 

 once generated requires these long periods for subsidence, it is obvious 

 that each tidal wave may be perpetuated so as to cooperate with a long 

 series of forcing actions in succeeding periods, if its period is commensurate 

 with these. This supports the view, previously discussed, that the waves 

 observed in those portions of the ocean most favorable for sympathetic 

 accumulation are the products of a considerable series of forcing actions. 

 This means that, at least in such cases, the element added with each tidal 

 period is not measured by the actual waves observed, but by some minor 

 fraction of it, and hence that the tidal friction which is daily exerted on 

 the earth is by no means the amount necessary to reduce the observed 

 tidal movement to zero, but merely that which is necessary to offset the 

 daily increment, or its equivalent, the daily factor of decay. A wave of 

 the type n = in water 200 meters deep, if commensurate action were per- 

 fect and dissipation, by giving rise to derivative waves, were wholly absent, 

 would need to have less than Y^tij of its value added to it daily to maintain 

 its value. This must not be taken as representing an actual case, but it 

 appears from considerations of this kind that the total energy of motion 

 expressed by the tides daily is by no means a safe basis for estimating 

 the energy lost through them. This must be computed directly from the 

 water- movements under the conditions that actually affect them. 



There is a check on carrying considerations of this kind too far, in the 

 fact that the spring and neap tides and other special tides that depend on 

 variations in the relations of the tide-producing bodies pass through their 

 climacteric phases within one or two days of the astronomical configura- 

 tions that give origin to them. They increase and die away with a relative 



» Loc. cit., p. 287. 



