4 THE TIDES. 



I. Without friction it would be loiv ivater under the moon, 

 and high icater in quadratures. 



I suppose the moon to be fixed, and the earth rotating 

 in the direction ABCD, carrying the ocean with it. That 

 the ocean is so carried is a fact of experience. 



Now, in the course of one lunar day every particle of 

 the ocean is subjected to precisely the same forces, acting 

 in the same order of succession and for the same periods, 

 being accelerated for about one quarter of a day, viz., 

 while passing from B to C ; then retarded for a quarter, 

 from C to D, and so on. The variation in the amount of the 

 force does not concern us, being the same for every particle. 



This being so, it is obvious that those particles will be 



Fig. 2. 



moving faster which have been for a longer time acted 

 on by an accelerating force, and the velocity will be a 

 maximum when the accelerating force has acted during 

 its full period, viz. through one quadrant. On the other 

 hand, those particles will be moving slower which have 

 been longer acted on by a retarding force, and the 

 absolute velocity will be a minimum when the retarding 

 force has acted during its full period, or through one 

 quadrant. The maximum velocity is therefore at A and 

 (7, the minimum at B and D. 

 Secondly, it is clear that the tide will be rising where 



