220 Rev. 0. Fisher on the Effect upon the Ocean-tides 



moon, and when k > — there will be high tide under the moon. 



In the case of the semidiurnal tide — is about 12 miles. 



a 2 . 9 



When k= — the result fails; for c becomes infinite, which 

 9 

 is contrary to the assumptions on which the solution has been 

 obtained. 



(7) Let us now look to the effect of a tide in the crust of the 

 earth upon the ocean-tide, to see whether the tide formed in a 

 liquid substratum would so far diminish the ocean-tide that the 

 observed amount of the ocean-tide would disprove the existence 

 of a liquid substratum. The manner in which such a dimi- 

 nution of the ocean-tide would be produced in an extreme case 

 appears thus: — Suppose that the earth were liquid, and that 

 there were an extensible film within it at a depth from the 

 surface equal to the ocean depth. Then, on the equilibrium 

 theory, the entire sphere would be deformed as a whole, and 

 the measurable tide would be merely the excess of the defor- 

 mation at the surface beyond that at the depth at which the 

 film lay; which excess would be inappreciable. 



In considering this question, it is necessary to take account 

 of the attraction upon the ocean of the part of the tidal earth- 

 spheroid exterior to the sphere to which it is tangential. The 

 problem has been worked out by Mr. Gr. H. Darwin in part ii. 

 of his paper " On the Bodily Tides of a Yiscous Spheroid"*. 

 He considers the moon as moving uniformly in the equator 

 and raising tide-waves in a narrow equatorial canal. The 

 greatest range of the bodily tide is taken as 2E; and it is sup- 

 posed to be retarded after the passage of the moon by an 



angle -' which corresponds to 8 in this paper. The expression 



at which he arrives for the motion of the wave-surface of the 

 ocean relatively to the bottom of the canal (observing that he 

 measures the ordinate downwards instead of upwards as I 

 have done), when the symbols arc replaced by those here 

 used, becomes 



K+ «^l{(¥ cos2o-^E)cos(2. + 2S) 



+ ^sin 28 sin (20)4-28)}. 

 The apparent tide relatively to land can therefore be written, 

 * Phil. Trans. Roy. Soc. part i. 1879, p. 22. 



