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 =fl<r . sin (crt + e) 



for large values o 



The curves A, B, (7, Z), 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 (2ir//3) of the laminar disturbance. 



As a numerical illustration we note that if i/ = '0l78, and 27r/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. 



