CONSTANT WESTWARD CURRENT. 9 



retarding ; in the latter it is accelerating ; therefore the 

 retarding force exceeds the accelerating, and produces a 

 permanent westward motion. 



Secondly, the water having reached its mean place at n, 

 and passed it with its greatest eastward velocity, it is, when 

 it reaches (7, eastward of its mean place, i.e. it is nearer to 

 g. On the whole way before reaching g it is nearer to 

 that point than if there were no friction ; but on passing g 

 it begins to move westward ; but its eastward excursion 

 having been shortened by friction, it begins this motion to 

 the west of where it would otherwise be. At o it again 

 arrives at its mean place, which, without friction, it would 

 not reach until D. Thus, in the whole quadrant CD, the 

 particles are nearer to g than if friction had not operated. 

 But the tangential force is greater the nearer the particles 

 are to g, being proportional to sin 2 (angle from moon) 

 = cos 2 (angle from/ or g) ; hence the force in the quadrant 

 CD, which is a retarding force, is increased. After passing 

 its mean place at 0, the water going westward is, on arriv- 

 ing at Z), west of its mean place ; and until it reaches h 

 it continues to be west of the place which it would have 

 occupied had friction not operated, i.e. friction withdraws 

 it from h. At h its westward excursion is stopped, and it 

 begins to return eastward. But now from h to A. it is east- 

 ward of the place due to it without friction. Thus through- 

 out this quadrant the particles are brought farther from h 

 by friction. But here the force is accelerating. Therefore 

 the force in the accelerating quadrants is diminished, while 

 that in the retarding quadrants is increased, and hence 

 again a balance of retarding force, and therefore a current 

 westward. Or thus : Without friction, the quadrant 



