Chapter IX 



Theory of the Tides 



1. The Equilibrium Theory 



In order to visualize the effect of the tide-generating forces on an ocean 

 covering uniformly the whole earth, we can use the presentation of the hori- 

 zontal components given in Fig. 111. Under the action of this system of 

 forces, the water tends to flows towards the points Z and TV and accumula- 

 tion of water occurs at these convergence points, while at the great circle 

 with a distance of 90° from these points the sea level lowers. These flood 

 protuberances originating in the zenith and nadir increase only until there 

 exists an equilibrium between the tide-generating forces and the horizontal 

 forces provided by the differences in pressure. Then the flood protuberance 

 at the surface has a fixed position in the direction of the moon (Fig. 117). 



Fig. 117. Flood protuberance caused by the action of the tide generating forces on an 

 ocean covering the entire earth. 



Newton, who developed the equilibrium theory of tide, was conscious of the 

 fact that treating the tides as a static problem was only a rough approxima- 

 tion of the phenomenon. The equilibrium theory of the tides was completed 

 50 years later when the Paris Academy of Science asked for the best ma- 

 thematical and physical explanation of the tides. Bernoulli, Euler and 

 MacLaurin (1741) were among the contestants. The work of Bernoulli is 

 of quite some interest still today. 



In the equilibrium theory of the tides, the free surface is assumed to be 



