154 156.] TIDES IN EQUATORIAL CANAL. 185 



155. Next let us take the case of a canal coinciding with a 

 meridian. Let 6 denote the hour-angle of the moon from this 

 meridian, = pt 4- a, say, and x the distance of any point on the 

 canal from the equator. By an easy application of Spherical 

 Trigonometry, we find for the horizontal disturbing force in the 

 direction of the length of the canal, 



flS 



X= fj, sin 2 - cos 2 



The equation of motion is easily seen to- be of the same form, (16), 

 as before. Substituting then and solving, we find 



.cos2?cos2(^ + c&amp;lt;) ....... (20). 



The first term represents a permanent deviation of the surface 

 from the circular form ; the equation of the mean level being now 



. x 



rj = J - cos 2 - . 

 c~ a 



The fluctuations above and below this mean level are given by the 

 second term -of (20). If, as in the actual case of the earth, c be 

 less than pa, there will be high water in latitudes above 45, and 

 low water in latitudes below 45, when the moon is in the meri 

 dian of the canal, and vice versa when the moon is 90 from that 

 meridian. The circumstances are all reversed when c is greater 

 than pa. 



For a further development of the canal theory of the tides, the 

 student is referred to Airy, I. c. ante. 



Waves in deep water. 



156. When we abandon the assumption that the depth h of 

 the fluid is small compared with the length of a wave, the Eulerian 

 method becomes more appropriate. 



Let the origin be in the undisturbed surface, the axis of & 

 horizontal, that of y vertical and its positive direction upwards. 

 We suppose the motion to take place entirely in these two dimen- 



