UNIVERSITY 



EFFECT ON LENGTH OF DAY: 25 



attributes the retardation to the moment of the moon's 

 disturbing force on the tidal prominences. He started 

 from the assumptions that without friction it would be 

 high water under the moon and anti-moon, and that friction 

 retards the time of high water. Both these assumptions 

 were erroneous ; but they so far counteracted one another 

 as to leave the place of high water in the same quadrants 

 as the true theory, viz. in the quadrants east of the 

 moon and anti-moon, in which the moon's force is 

 retarding. 



Sir George Airy corrected these errors, and working out 

 the equations, found two terms which indicate a constant 

 current westward one term (the smallest) depending on 

 the vertical, and the other on the horizontal, displacement 

 of the water.* 



In my own Essay on the Theory of the Tides (Quarterly 

 Journal of Mathematics, 1872, and Philosophical Magazine), 

 the effect of friction was indicated, but there was no at- 

 tempt to estimate it quantitatively. I am not aware that 

 any attempt has been made to solve this problem ;f and 

 indeed it would be absurd to pretend to do so with any 

 degree of accuracy. "What I propose to do is to estimate 

 the effect so far as to enable us to form a judgment as to 

 the actual importance of the tides as a cause retarding the 

 earth's rotation. 



It will be convenient first to prove the following propo- 

 sition respecting the effect of obstacles : 



* Monthly Notices of the Royal Astronomical Society, 1866, p. 221. 



t See, however, Lord Kelvin, Philosophical Journal, 1866, p. 533. 

 He mentions also a Paper by Wm. Fernel, Astronomical Journal of 

 Cambridge, U.S.A., December 8, 1853, which I have not seen. 



