16 THE TIDES. 



moment that the force changes its direction. Thus a 

 pendulum is moving fastest at the lowest point of its 

 oscillation. 



2. Secondly, the velocity (diminishing under the coun- 

 teraction of the force) continues to be in the same direction 

 until this counter force has undone all the work accom- 

 plished in that direction by the previous force. If the 

 circumstances are alike in both directions, this will be 

 when the force has done half its work. This again is 

 precisely the case of the common pendulum. For the 

 present case this will be at efgh, fig. 3. 



3. Thirdly, in the case before us, the water rises when 

 the particles behind are moving faster than those before. 

 The rate of rise is greatest when this difference is greatest ; 

 but as the effect is cumulative, the whole amount of the 

 rise is greatest at the moment when the difference = 0, and 

 is about to change to the opposite. 



4. Fourthly, as in 2, this difference ceases to increase 

 (i.e. is greatest) when the force (or difference of forces) 

 producing it ceases to act ; but it is not reduced to until 

 the opposite force has done half its work. At this moment 

 the accumulation is greatest. 



5. Fifthly, in the case which we are now considering, 

 the effective force depends on the form of the surface, and 

 vice versa. If, then, when this form is spherical the dif- 

 ference mentioned in 3 were always in the same direction, 

 it would continue to act until a certain permanent alte- 

 ration was produced. If the difference were constant, 

 a state of equilibrium would be attained ; but if it alter- 

 nately increases and diminishes, then the mean form of 



