EFFECT OF DISPLACEMENT OF WATER. 3L 



place, since the particles enter it E. of the place they 

 would otherwise occupy, and leave it W. of their place. 

 Now, the former quadrant is that in which the moon's 

 force is accelerating, the latter that in which it is retarding. 

 The same observation applies to the other two quadrants. 

 Thus the accelarating and retarding forces are no longer 

 in equipoise, the latter predominating. 



To calculate the effect : The maximum excursion of 

 the water without friction in the case of a canal three miles 

 deep would he about 136 feet. For the greatest velocity 



= - (feet per second). Now if this continued for one- 

 o2 



fourth of a day the space passed over would be ^ = 430 



nearly. With the varying velocity ^ cos 2o> the space 



traversed is less than this in the proportion of 1 to -^TT (as 

 in the calculation of the velocity in p. 11). It is therefore 

 = 272 feet nearly. This is the double excursion. There- 

 fore the maximum excursion on either side is 136 feet. 

 Assume that this is undiminished ; and assume, as before, 

 that it is high water 45 W. of quadratures. Then we 

 may assume the displacement at each point to be 136 cos 2w ; 

 and the moon's force being H sin 2o>, the change in the 

 disturbing force due to this displacement 



2H cos 2w x cos 2(o per second. 



r 



I O 



The constant part of this = H 



Putting for H its value OCKAAJ an( i calculating the 



