299-300] 



PERIODIC TIDAL FORCE. 



543 



This might have been obtained directly, as the solution of (2) 

 satisfying the conditions that u = for y = 0, and 



u =f/&amp;lt;r . sin (at + e) 



for large values of (3y. 



The curves J, , (7, Z&amp;gt;, E, F in the accompanying figure represent 

 successive forms assumed by the same line of particles at intervals of 

 one-tenth of a period. To complete the series it would be necessary to add 

 the images of E, D, C, B with respect to the vertical through 0. The whole 

 system of curves may be regarded as successive aspects of a properly shaped 

 spiral revolving uniformly about a vertical axis through 0. The vertical range 

 of the diagram is one wave-length (2?r//3) of the laminar disturbance. 



As a numerical illustration we note that if i/ = 0l78, and 2ir/o- = 12 hours, 

 we find /3~ 1 = 15 6 centimetres. This indicates how utterly insensible must 

 be the direct action of viscosity on oceanic tides. There can be no doubt that 

 the dissipation of energy by tidal friction takes place mainly through the 

 eddying motion produced by the exaggeration of tidal currents in shallow 

 water. Cf. Art. 310. 



