152 154.] TIDES IX EQUATORIAL CANAL. 183 



Since (16) does not contain Y, it appears that the horizontal 

 disturbing force is much more effective than the vertical one in 

 producing waves. This might be anticipated from the hydro- 

 statical theorem that a liquid is in equilibrium when, and only 

 when, the surfaces of equal pressure coincide with those of equal 

 potential. The latter being everywhere perpendicular to the lines 

 of force, it is plain that the addition of a small horizontal force 

 would make them deviate from their original horizontal arrange 

 ment far more than the addition of a small vertical force. 



154. We will follow Airy* in applying equation (16) to illus 

 trate the theory of the tides. Let us investigate the tides which 

 would be produced in a uniform equatorial canal, the moon being 

 supposed to describe a circle in the plane of the equator. Let x 

 denote the undisturbed distance, measured along the equator, of 

 a particle of water from some fixed meridian, x + f the value of 

 the same quantity, for the same particle, at the time t. If n be 

 the angular velocity of the earth s rotation, the actual displace 

 ment of the particle at the time t is f + nt ; so that the tangential 



j*t 

 acceleration will be -~ . If we suppose the centrifugal force to 



be as usual allowed for in the value of g, the processes of the 

 previous articles will apply without further alteration. Also, we 

 have f, approximately 



where 



M = the mass of the moon in astronomical units, 

 a = the radius of the earth, 



D the distance between the centres of the earth and 

 the moon, 



6 = the hour-angle of the moon at the station x, 



= pt--+*&amp;gt; 

 a 



* Sect. vi., &quot;Tides and Waves.&quot; 

 t Thomson an&amp;lt;l Tait, Art. 804. 



