44 THE TIDAL PROBLEM. 



promptness which shows that no tidal agency perpetuates its special effects 

 in a special phase for a very long period. 



There is a minor qualification of Hough's results that is worthy of 

 passing notice. He took for his coefiicient of viscosity 0.0178, which is 

 one of the determinations for 0° C. The viscosity of water is much in- 

 fluenced by temperature. The coefficient for 17° C. is 0.0109. As this is 

 about the average temperature of the surface of the earth, it may be taken 

 as roughly, though not accurately, the average temperature of the ocean 

 water. Salinity increases the viscosity. While I do not know of any direct 

 determinations on sea-water, the determinations for normal solutions of 

 sodium chloride imply that the viscosity of sea-water at 17° C. would be 

 about 0.012, which makes Hough's results very conservative, so far as affected 

 by the coefficient of viscosity used. This, however, is not so much the point 

 as is the difference in the viscosity of the bottom and the surface water, 

 respectively, in the low latitudes, that of the deep water being somewhere 

 about 0.0195, while that of the surface in the tropics is about 0.0099, 

 or but little more than half as great. This difference must increase rela- 

 tively the motion of the water on itself and reduce that upon the bottom. 

 It will thus substitute a distributive movement within the water, in which 

 the friction is very low, for a more concentrated movement between the 

 film of w^ater attached to the bottom and that immediately above it, in 

 which the friction is relatively high. The total effect is to reduce the fric- 

 tional value. 



Radical as are the suggestions of Hough's inquiry, a way to apply them 

 directly, so as to secure a numerical expression of the total value of the 

 friction of the tides in terms of work done, has not been found, and I have 

 therefore tried to shape the problem so that it could be treated by the 

 method of the engineer, as a given mass of water, with a given amount of 

 flow, in a given time, under assigned conditions. To do this it seems neces- 

 sary to substitute for the actual ocean an equal body of water in a more 

 tractable form, but subject to equivalent friction. In doing this I have 

 endeavored to give to the movements of the substitute ocean at least as 

 great friction as that of the actual ocean. For the purposes of frictional 

 treatment the ocean may be regarded as consisting of three portions, (a) 

 the shallow water between the coast and the edge of the continental shelf, 

 (6) the water on the slope between the edge of this shelf and deep water, 

 and (c) the deep portion. 



(a) The coast line is taken at 120,000 miles, which is nearly double the 

 simple outlines of the ocean and about 5 times the earth's circumference. 

 The depth of water on the outer edge of the continental shelf is taken at 

 600 feet, the accepted depth. The water is made to deepen uniformly 

 from the coast to the edge of the shelf, which very greatly exaggerates its 

 shallowness near the shore, where the friction is relatively greatest. The 

 area is taken at 12,000,000 square miles, or 20 per cent more than Murray's 

 estimate for this part of the actual ocean. 



(5) The portion b is given a width of 50 miles, a descent from 600 to 

 9,000 feet, and an aggregate length of 120,000 miles. This length is much 

 greater than the actual length of the continental margin, the excess being 



