30 THE TIDES. 



(of the water) is ultimately not affected by the coefficient 

 /. In fact the retarding force fo is then = \He sin 28. 

 This being premised, I shall now examine the question 

 from the point of view suggested by Airy. 



5. Effect of the changes in the disturbing force due 

 to the displacement of the water. 



By substituting, in the expression for the disturbing 

 force, the altered value of the ordinate of the water for the 

 original value (% + X, for #), Airy finds that the expres- 

 sion contains a constant term dependent on the distance 

 of high water from quadrature. The source of this con- 

 stant term may be understood from the following observa- 

 tion : 



The particles are in their mean place at the moment of 

 high water and at that of low water ; at the former they 

 are travelling W. with their greatest velocity; at the 

 latter they are travelling E., also with their greatest 

 velocity. Now, the place of high water being W. of 

 quadrature, and the water moving W., it follows that 

 when the water reaches quadrature, approaching the moon, 

 it is behind, or west of the place which, without friction, it 

 would have occupied. On the other hand, at syzygy it is 

 in advance, or E. of its place. In both cases the disturb- 

 ing force is diminished by this displacement, the force being 

 greater the nearer the particles are to the middle point of 

 the quadrant. In other words, H sin 2w is diminished 

 throughout, o> being increased when over 45, and dimi- 

 nished when less than 45. In the following quadrant, 

 i.e. after passing the moon, the opposite change takes 



