34 THE TIDAL PROBLEM. 



incompatibility with the theory of direct attractional action on the water 

 itself; indeed, the concrete features of Harris's theory seem to have been 

 developed largely by a study of these remarkable features, and to be an 

 attempt to give them a dynamical expression in terms of the direct-action 

 hypothesis. Whatever shall be the final judgment regarding particular 

 aspects of this theory, whose author claims for it only a partial explana- 

 tion of the tides, it seems eminently probable that commensurate oscilla- 

 tion is a vital factor in building up the waves of the actual tides. The 

 attempt to work out a concrete theory of the tides from their specific phe- 

 nomena is greatly to be commended, for by concrete application alone are 

 the proximate sources of the tides likely to be determined. This may be 

 said without derogation of the value of the more general theories. 



Concerning the insufficiency of simple attraction without sympathetic 

 intensification to explain the actual tides, Harris says: 



In approaching the question of the actual causes of the tides, upon which so much 

 labor has been expended and concerning which so much has been written, one may well 

 surmise that the subject does not admit of accurate or complete treatment. It is there- 

 fore natural to consider, in the first place, only those sources which would seem to account 

 for the dominant tides in any given region under consideration, and to postpone, perhaps 

 indefinitely, the consideration of those sources whose importance in the production of the 

 tides must be relatively small. Considering the actual distribution of land and water a 

 few computations upon hypothetical cases will suffice to convince one that as a rule the 

 ocean tides, as we know them, are so great that they can be produced only by successive 

 actions of the tidal forces upon oscillating systems, each having as free a period, approxi- 

 mately the period of the forces, and each perfect enough to preserve the general character 

 of its motion during several such periods were the forces to cease their action.* 



In another place he says: 



Unless the free period of a body of water, or of some portion of this body, approxi- 

 mately agrees with the period of the tidal forces, the tide in the body proper must be small, 

 and generally smaller than the theoretical equilibrium tide for the body in question. But 

 in many parts of the oceans, the tide is several times greater than that which could be 

 raised by the forces, even if we could suppose sufficient depths and sufficiently complete 

 boundaries for enabUng equihbrium tides to occur. Hence regions the dimensions of 

 which approach critical values must exist in the oceans and account for the principal tides. 



That stationary oscillations of unexpectedly large amplitude exist in the oceans there 

 is abundant evidence. In fact, a glance at the charts will show regions of large ranges 

 over each of which the time of the tide varies but little. As a nodal line is approached the 

 range diminishes, and the time of the tide changes rapidly in a comparatively short distance. 

 Moreover the dimensions of the oceans are such that areas having nearly critical lengths 

 can be readily discovered; these respond well to the forces, and their tides must be the 

 ruling semi-diurnal tides of the ocean.^ 



Harris has attempted to detect those portions of the oceans whose 

 lengths, depths, and relations make them susceptible to the development 

 of free oscillations whose periods are sufficiently near to the periods of the 

 tidal forces, or to some simple fraction of them, to permit cooperation in 

 building up effective stationary systems of oscillations. Of the major 

 order, he finds a northern and a southern system in the Indian Ocean, a 

 South Atlantic system, a North Atlantic system, and two systems in the 

 Pacific, as well as a large number of systems of the minor order. Diagrams 

 and details of the main systems are given in the original paper. 



* Loc. cit., p. 624. ' Nature, Feb. 22, 1906, p. 388. 



