THE TIDES 119 



water, and the depth of this water to be the same throiigh the 

 whole extent of any parallel of latitude. The motion of the 

 water which forms the variable élévations of the tides at 

 différent parts of the earth miist be conceived to be principally 

 a horizontal oscillation, the water on both sides of the highest 

 point at any time having- run towards that point in order to 

 raise the surface there, and consequently, since the highest 

 point occupies différent positions at différent times, the water 

 at any particular place runs sometimes in one direction and 

 sometimes in another. Combining this with the gênerai resuit 

 of the equilibrium theory of the tides (semi-diurnal) — namely, 

 that the water is equally raised at two opposite points — it 

 follows that if a canal were traced through the water forming 

 a great circle of the earth it would (in certain positions of the 

 Sun and moon) be divided into four parts, in two of which the 

 water is running in one direction, and in the other two it is 

 running in the opposite direction. 



The mathematical exposition of Laplace's theory is given 

 in détail by Airy.* 



A marked advance both in theory and practice was 

 registered by the canal theory of Airy. In it the motion of 

 the tidal waters is supposed to be that of ordinary waves in 

 canals. This theory does not apply to ail places in the sea, 

 and is therefore to that extent imperfect. Still, it does apply 

 strictly in many cases, to rivers without exception ; to arms of 

 the sea where their breadth is smaller than their length and 

 where the irregularities of the coast are not very remarkable; 

 and it applies without sensible modification to other cases of 

 open seas, where the whole may be conceived divided into 

 parallel canals in which the circumstances are nearly similar. 



As will be deduced from the preceding account of waves, 

 a wave in continuons motion does not imply that the water is 

 continuously moving in the same direction. It ,is only the 

 motion of a shape. The motion of a wave has been explained 

 by considération of the oscillatory motion of the particles, 



* "Waves and Tides," Sections 72-127, 



