224 Effect upon the Ocean-tides of a Liquid Substratum. 

 And if 28=30°, 



/=0'010316, 

 = jjfe nearly. 



What is meant by such a coefficient of friction may be thus 

 realized. Mr. Heath remarks that it is only necessary to con- 

 sider the friction on the bottom of the canal. The effect is 

 assumed to be to check equally all the liquid in each vertical 

 column, as if it were all directly subject to the action of the 

 bottom (and of the crust at the top also in the case of the 

 substratum). This, as he says, " can hardly be true, though 

 probably the resulting calculation exhibits something closely 

 resembling the case of nature ; for it is the average forward 

 velocity on which the form of the wave depends." But it 

 seems to me that the reciprocatory nature of the motion of the 

 liquid will nearly confine the effect of friction to the two sur- 

 faces, because scarcely will the retardation have been propa- 

 gated far before it will be reversed in direction. The case 

 will be somewhat analogous to the propagation of seasonal 

 variations of temperature into the earth's surface. 



We have then, integrating the equation 



dv 



dt=-J V > 



t= I h.l. -, 



where C is the initial velocity. Whence, if/=O01, such an 

 amount of friction would reduce the velocity to one half in 

 100 x h.l. 2, or 69 - 3 units of time. For instance, if a stream 

 of the material were flowing over level ground with a velocity 

 of one mile an hour, it would be reduced to half a mile an 

 hour in 69*3 hours. As the layer of liquid may, from what 

 has just been said, be likened to a solid layer whose upper and 

 under surfaces are lubricated by a sufficient thickness of the 

 liquid, this would seem to be a low degree of viscosity for such 

 a substance as molten rock. 



In the case of the semidiurnal tide a = 1520 feet per second; 

 and if we put/= 0-01, 28 will be about 87°, and cos 2 28=0-0024. 

 This factor will render the diminution of the ocean-tide prac- 

 tically inappreciable. 



(13) The final result therefore is that, upon the canal theory 

 of the tides, if there be a liquid substratum of 60 miles or 

 more in depth beneath the crust, and resting on a rigid 

 nucleus, upon the supposition (of course impossible) that the 



