The Tides in Relation to Geophysical and Cosmic Problems 505 



tide gauge of AA = rj . The order of magnitude of this increase in the ocean 

 is about one-eighth of the original range. 



Let the tide generating forces deform the earth from BB n to B'B' and let 

 us assume that the surface will rise an amount ?? from P to P'. The tide gauge 

 in P will register the same rise, so that P Q becomes P' and the point N on the 

 tide gauge will be at N' , and we have P P' = NN^ = rj . 



I 



B'^ 



Ffg. 208. Tides of the solid earth and oceans. 



However, the surface HH does not rise, because its distance from the 

 centre of the earth is governed by the balance between the tide generating 

 force and gravity (equilibrium between tidal forces and pressure forces). 

 The protuberance of the earth could cause to the utmost a slight change, 

 inasmuch as the lower part of the protuberance of the water is now occupied 

 by solid matter instead of water, which changes to some extent the potential 

 of the attraction of the water protuberance. Figure 208 shows that 



NoA =rj = r}+r] -?] 



(XV. 1) 



Likewise, if a is the gradient of HH against H'H' and a the gradient of 

 B'B against BB , a — a + a —a and the horizontal acceleration will be 



go. =g(a + a -ot ) 



(XVI. 2) 



