36 THE TIDES. 



With a depth of 3 miles, h = 483000 nearly .'. W = 233000 

 millions nearly. The value of /u at a temperature of 



10C. = 50 F. is = -013257, 



15 C. = 59F ____ -011503, 



20 C. = 68F ____ -010164. 



If we take the third of these values, we find 



3-82 billions 

 Then sin 23 = tan 2g - 7000 / = 



546000 millions 



If we introduce this value into the formulae for the 

 retardation given above, we arrive at the result that if 

 the displacement is due to friction alone, the consequent 

 retardation would be in fact nil. Supposing, however, 

 that from whatever cause the displacement amounted to 

 15 (and we have seen on p. 34 that over a certain limited 

 region it reaches 30), the formula on p. 32 would give 

 1-15 seconds in 100,000 years. When we consider how 

 far the actual state of things is from the hypothesis of 

 a globe uniformly covered with water 3 miles deep, with 

 the moon always in the equator, the fact that the retar- 

 dation deduced from eclipses is about two-fifths of this 

 is certainly curious. But we cannot attribute much im- 

 portance to this coincidence. 



(With the value of / here given it would take about 

 12,000 years to produce the effect described in 4 so as to 

 make this formula applicable) . 



