598 



ROSSITEB 



[chap. 16 



Table II 

 The Equilibrium Form of the Long-Period Tides 



The question as to whether long-period tides will obey the equilibrium law 

 has been open to doubt, partly due to the presence of land- masses on the face 

 of the earth (Laplace's equilibrium theory postulates an ocean covering the 

 entire earth), and partly because it has long been known that steady tidal 

 motions can exist (tides of the "second class") which are not related to the tide- 

 generating forces (Lamb, 1932, §214). 



Consider first the effect which land-masses may introduce to produce the so- 

 called "corrected" equilibrium tide. Darwin and Turner (1886) showed theo- 

 retically that, for long-period tides in general, if the equilibrium form is 

 proportional to 



(i-sin2 8)(i-sin2A), 



where S is the declination of the moon above the equator and A denotes latitude, 

 then the "corrected" equilibrium tide would be proportional to 



(^ — sin2 8)(sin2 Aq — sin^ A), 



where Ao is a latitude (possibly imaginary) determined by the geographical 

 distribution of land-masses. Numerical integration of the area of dry land by 

 Turner led to a value of approximately 34° for Ao, suggesting that land-masses 

 have only a minor influence upon the distribution of long-period tides. 



Consider next the tides of the second class. Their possible existence prevents 

 the assumption of the equilibrium tide. Darwin (1886) pointed out that Laplace 

 had simply assumed that, owing to the action of dissipative forces, the equili- 

 brium law was valid; Darwin argued that the frictional forces arising from 

 these currents would be infinitesimally small. Now Bowden (1953) has shown 

 that the friction affecting any tidal constituent is not simply a function of the 

 current associated with that constituent, but depends upon the product of that 

 current with the total current ; Proudman (1960) has used this fact to show that 

 this product is so much larger than what was assumed by Darwin and Lamb 



