32 THE TIDES. 



effect continued for one lunar day (89280 seconds), we 

 have 



11 136 100 



n x - > or 7^ ^rr - > nearly. 

 46 r 65 millions 



This acts on the whole mass of the canal. Introducing 

 the moments, as in p. 27, we have as the acceleration for 

 one day 



200 mass of canal 



_ V -- - ' - - . 



65 millions mass of equatorial section of earth x r 

 With the assumed depth of sea, the latter factor = 



Hence the daily angular acceleration 



1 1 



~ 325000 X 3300 x r' 



Multiplying by the lunar days in 100,000 years (about 

 33 millions) we have nearly as before . This gives a 



retardation of about 1'83 seconds in 100,000 years. Adding 

 the solar tide we have as the total 2*6 seconds. This is 

 on the hypothesis that the elevation is not diminished. 

 Introducing the necessary correction we have, as in p. 28, 

 2-6 sin 48. 



For the reason before stated, it is unnecessary to multiply 

 this by the coefficient of friction. 



There is a third way of viewing this cause. Owing to 

 the displacement of the place of high water, since that is 

 the point where the water is moving fastest westward, the 

 water is a longer time in the retarding quadrants than in 

 the others, e.g. on the previous hypotheses it is 136 feet 

 behind its place on entering the accelerating quadrant, 



