256 



The Tide-generating Forces 



Ln 



(VIII. 1) 



and the summation should extend over all the particles of mass of the earth. 

 Although this relation is always fulfilled for the earth considered as a whole, 

 this does not prove that for each point of the earth there is equilibrium 

 between the attractive forces and the centrifugal forces acting at the point 

 in question. In fact, this could hardly be expected, because the two forces 

 obey different physical laws. Comparing these forces at any arbitrary point 

 of the earth, we find residual forces, and these are the tide-producing forces. 

 When the moon stands in the zenith, the forces of attraction are greater than 

 the centrifugal forces in a point Z on the earth closest to the centre of the 

 moon; both act in the direction of a line joining the centre of the earth with 

 the centre of the moon. The resultant is the tide-producing force at the 

 point Z; here it is directed against the moon (see Fig. 108). At the opposite 



Fig. 108. Determination of intensity and direction of the tide generating forces resulting 

 from the difference between attractive and centrifugal forces. >, open arrows: attractive 



forces; 2ZZZZ77>, hatched arrows: centrifugal forces; ""^ , black arrows: tide generating forces. 



point N, where the moon stands in the nadir, the force of attraction is 

 smaller than in Z and smaller than the centrifugal force. For this reason, 

 the tide-producing force is directed away from the moon. Consequently, 

 in both cases there is a force directed from the centre of the earth towards 

 the outside. Thus, for any point on the earth's surface, we can compute the 

 direction and the intensity of the resultant between the forces of attraction 

 and the centrifugal force. The total sum of all these resultants all over the 

 earth is zero, but at no point does this tide-generating force become zero, 

 and it has everywhere a definite direction and force. A schematic drawing 

 of the distribution of the tide-generating force in a meridional section in 

 the direction earth-moon is shown in Fig. 108. 



