10 THE TIDES. 



fg, throughout which the water is moving faster than 

 the earth, has its middle point at C ; and the following 

 quadrant in which it is slower has its middle point at D. 

 These quadrants are, therefore, equally divided between the 

 accelerating and the retarding quadrants. With friction, 

 the middle points being displaced to n and o respectively, 

 the water is moving faster than the earth through more than 

 half the quadrant BC, and slower through more than half 

 the quadrant CD ; and similarly in the opposite quadrants. 

 But BC, DE are the accelerating quadrants, and CD, AB 

 the retarding quadrants. Therefore the water is exposed 

 for a longer time to the retarding than to the accelerating 

 force. 



We have here, therefore, a vera causa which may pos- 

 sibly be effective in retarding the earth's rotation. An 

 attempt will presently be made to estimate the maximum 

 amount of this effect. 



On the Quantitative Valuation of the Tidal Disturbance. 



To determine more precisely the magnitude of the dis- 

 turbing force : 



The moon's attraction at x : force of gravity : : 



moon's mass earth's mass 1 



- -, or nearly = : 81J ; there- 



fore the whole attraction of the moon (represented in fig. 1 

 by ME] = i . But on the same scale the greatest 



o 



tide-producing force is represented by-r (the greatest value 



