FKICTION ACCELERATES HIGH WATER. 7 



II. Friction accelerates the times of high and low water. 



The theorem that the effect of friction is to accelerate 

 the time of high and low water admits of an equally 

 simple proof. As the water approaches (7, the tangential 

 force diminishes gradually to zero at C. Therefore it 

 must have been equal to the force of friction at some point 

 n (fig. 1), after which friction prevails and the velocity 

 diminishes. It is therefore low water at n. Approach- 

 ing D, the ocean is moving slower than the earth ; there- 

 fore here friction tends to accelerate it, while the retarding 

 force is decreasing to zero. The two forces, then, must be 

 equal at same point 0, after which the velocity again 

 increases. It is high water therefore at o. 



It sounds paradoxical to say that friction " accelerates " 

 high water. The paradox is only apparent. Friction 

 checks the motion, so that the water stops rising or falling 

 sooner than it otherwise would ; and thus we may speak 

 of the phase of high or low water being accelerated. 



The preceding proof assumes that the ocean is carried 

 round by the earth in its rotation. This amounts to 

 supposing that it has not assumed a position of equili- 

 brium.* 



* It is important to observe that we are not entitled to assume that when 

 the tide is rising fastest the water is flowing in from both sides. This is 

 by no means evident. The rate of rise depends on the difference in velocity 

 between two successive parts of the ocean, and this may be greater when 

 the two velocities have the same sign than when they have different 

 signs. Taking into consideration the rotation of the earth, the assumption 

 amounts to this that the tide is rising fastest where the velocity of the 

 ocean is just equal to that of the earth. This is certainly not evident : in 

 fact it would not be true if the tangential force did not decrease at the same 

 rate on both sides of each of the four maxima. It ought not, therefore, to 

 be assumed, but deduced. 



