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

 Now 



ClfJb K 



'" 9 



\ g J a- g 



Substituting for E, and observing that — divides out, we have 



ir 



=?{\-\ \ cos25 2 , (2-i 



(. 5 a. 1 k" a.-\ 



9 a 9 9 ° 9 



This expression is therefore applicable to find the diminution 

 of an ocean-tide of any period, if we give a corresponding- 

 value to a, because the moon's force is not involved in it*. 



(9) The theory of "mountain-roots," described at the com- 

 mencement of this paper, requires that the liquid substratum 

 should be at least about 60 miles deep. Now if « be the velo- 

 city of the semidiurnal tide, — is about 12 miles. Hence k 



2 9 



will be at least five times — . And if we omit the considera- 



9 k 2 a 2 



tion of friction, then cos 2S = 1, and -= — is very small, so that 

 ' > a z g 



The semidiurnal tide would therefore, under these circum- 

 stances, be diminished to one half. 



If the depth of the substratum were, say, 120 miles, the 

 tide, when friction is neglected, would be diminished by ^, or 

 it would have 2 3 of its undiminished value. 



(10) But, no doubt, friction would have a very considerable 

 effect upon a tide of short period in such a substance as molten 

 rock, confined both above and below between a rigid nucleus 

 and the floating crust. The factor cos 2 2S would therefore 

 greatly lessen the term expressing the diminution of the 

 tide. The mountain-roots likewise, following the contour of 

 the land masses of the globe, would so confuse the tidal phe- 

 nomena, both in the substratum and in the ocean, that little 



* " If Q. be the moon's orbital velocity, and I the inclination of the plane 

 of the orbit to the earth's equator, then the part of the tide-generating 

 potential on which the fortnightly tide depends is 



| ™ w> ' 2 siu2 J (3 - cos2 6 ) cos 2 ™" 



■where m is the moon's mass, c her distance, w the mass per unit of volume 

 of the earth, r the radius vector, and 6 the colatitude (Darwin, "On the 

 Bodily Tides," &c, he. tit. p. 15). 



