GLOBE COVERED WITH WATER. 17 



the surface will be the same as would be produced by a 

 constant force equal to the mean amount of the actual 

 force. The alternate excess and defect of the latter will 

 cause a periodical motion, just as if it were an independent 

 force.* 



First, then, the moon being still supposed to be in the 

 equator, let the earth be uniformly covered with water. 

 The tangential force may be resolved into two compo- 

 nents one touching the parallel of latitude (i.e. east and 

 west), the other meridional. These may be regarded as 

 giving rise to distinct waves one east and west, the other 

 north and south. 



The actual amount of these forces may be found as 

 follows : 



By the previous construction (fig. 4) (ME being moon's 

 force at E) 9 the disturbing force at A is represented by 



- | r sin 2 A M = - H sin 2 A M. 



Resolved along the parallel of latitude, this is 



3r sin AM cos AM sin 0. 

 But by the right-angled spherical triangle (fig. 6) 



sin AM sin = sin MB (hour angle from moon), 

 and cos AM = cos MB cos AB (latitude). 



* If the reader wishes to apply these considerations to the case of an 

 equatorial canal assumed above, it must be observed that there the elevating 

 force is the excess of easterly force acting on any particles of water above 

 that which affects those in advance, i.e. to the east of them. This excess is 

 positive from 45 west of the moon to 45 east (i.e. while the moon passes 

 from 45 east zenith distance to 45 west), then negative for 90, and so on. 



C 



