SECT. XIII. THEORY OF THE TIDES. 91 



SECTION XIII. 



Tides Forces that produce them Origin and Course of Tidal Wave 

 Its Speed Three kinds of Oscillations in the Ocean The Semidiurnal 

 Tides Equinoctial Tides Effects of the Declination of the Sun and 

 Moon Theory insufficient without Observation Direction of the 

 Tidal Wave Height of Tides Mass of Moon obtained from her 

 Action on the Tides Interference of Undulations Impossibility of a 

 Universal Inundation Currents. 



ONE of the most immediate and remarkable effects of a gravi- 

 tating force external to the earth is the alternate rise and fall 

 of the surface of the sea twice in the course of a lunar day, or 

 24 h 50 m 28 s of mean solar time. As it depends upon the action 

 of the sun and moon, it is classed among astronomical problems, 

 of which it is by far the most difficult and its explanation the 

 least satisfactory. The form of the surface of the ocean in equi- 

 librio, when revolving with the earth round its axis, is an ellipsoid 

 flattened at the poles ; but the action of the sun and moon, espe- 

 cially of the moon, disturbs the equilibrium of the ocean. If 

 the moon attracted the centre of gravity of the earth and all its 

 particles with equal and parallel forces, the whole system of the 

 earth and the waters that cover it would yield to these forces 

 with a common motion, and the equilibrium of the seas would 

 remain undisturbed. The difference of the forces and the ine- 

 quality of their directions alone disturb the equilibrium. 



The particles of water under the moon are more attracted than 

 the centre of gravity of the earth, in the inverse ratio of the 

 square of the distance. Hence they have a tendency to leave 

 the earth, but are retained by their gravitation, which is dimi- 

 nished by this tendency. On the contrary, the moon attracts 

 the centre of the earth more powerfully than she attracts the 

 particles of water in the hemisphere opposite to her ; so that the 

 earth has a tendency to leave the waters, but is retained by 

 gravitation, which is again diminished by this tendency. Thus 

 the waters immediately under the moon are drawn from the 

 earth, at the same time that the earth is drawn from those 



