XIV 



CONTENTS. 



ART. PAGE 



178, 179. Tides in equatorial canal, and in a canal parallel to equator ; 



semi-diurnal tides . . . , * . . . . 287 



180. Canal coincident with a meridian ; change of mean level ; 



fortnightly tide 290 



181, 182. Waves in a canal of variable section. General laws of 



Green and Lord Rayleigh. Problems of simple- 

 harmonic oscillations in a variable canal. Exaggera- 

 tion of tides in shallow seas and estuaries . . 291 

 183, 184. Waves of finite amplitude. Change of type. Tides of 



the second order 297 



185. Wave-propagation in two horizontal dimensions. Equa- 



tions of motion and of continuity . . . .301 



186. Oscillations of a rectangular sheet of water . . . 303 



187. 188. Circular sheet of uniform depth ; free and forced oscilla- 



tions ; Bessel's Functions 304 



189. Circular sheet of variable depth 312 



190-193. Sheet of water covering a symmetrical globe; free and 

 forced oscillations. Effect of the mutual attraction 

 of the particles of water. Case of an ocean limited 

 by meridians or parallels ; transition to plane pro- 

 blem 314 



194-198. Equations of motion relative to rotating axes. Adaptation 

 to case of infinitely small relative motions. Free 

 oscillations ; * ordinary ' and * secular ' stability. Forced 

 oscillations . . . . . . . . .322 



199, 200. Application to Hydrodynamics. Tidal oscillations of a 

 rotating sheet of water. Plane sheet of water; 

 general equations 331 



201-205. Examples : long straight canal ; circular sheet ; circular 



basin of variable depth 334 



206-208. Tidal oscillations on a rotating globe. General equations. 

 Case of small ellipticity. Adaptation to simple- 

 harmonic motion 343 



209-211. Tides of long period. Integration of the equations. 



Numerical results 348 



212. Diurnal tides. Evanescence of diurnal tide in a^spherical 



ocean of uniform depth . . . . . 355 



213, 214. Semi-diurnal tides. Special law of depth. Laplace's 



solution for uniform depth ; numerical results . . 356 

 215. Stability of the ocean . . . , . , . . . 362 



APPENDIX : On Tide-generating Forces 



364 



