NEWTON S PRINCIPIA. 395 



series of long waves propagated along it. If h and b be 

 the variable depth and breadth, the result arrived at is 

 that the altitude of the wave varies * 



inversely as v^ . A/. 



Professor Airy has demonstrated that waves cannot be 

 propagated, strictly speaking, along a canal of variable 

 depth. He shows that if it were possible, we would be 

 led to an equation that cannot be satisfied. Hence, &quot; one 

 at least of the two conditions on which the equations of 

 Hydrodynamics are founded must fail. These are the 

 continuity of the fluid and the equality of pressure in all 

 directions. While the continuity holds, the equal pres 

 sure must exist, from the nature of the fluid. There 

 fore the continuity must cease, or the water become 

 broken. This appears to be the explanation of the broken 

 water which is usually seen on the edge of a shoal, or a 

 ledge of broken rocks, although the whole is covered, 

 perhaps deeply, with water.&quot; The* Astronomer Royal 

 mentions the instance of Newfoundland, where, when the 

 waves are high, there is a surf caused by the breaking of 

 the waves over the edge of a shoal 500 feet deep. A 

 similar breaking is observed about the line of &quot; no sound 

 ings &quot; (that is, where the water suddenly becomes deeper 

 than 600 feet, which at some distance borders the British 

 isles (Encyc. Met., art. Tides and Waves). The wave, 

 on reaching a part of its course where the depth changes 

 suddenly, breaks, because the velocity of the top part for 

 ward and of the hollow backwards, is too great to travel 

 with the velocity proper to the new depth. The top part 

 therefore, tumbles forwards into the hollow. The degree 

 of breaking is less and less the longer the wave and the less 

 the change of depth. If the depth alter very slowly, the 

 wave may be considered as only slightly breaking, and is 

 propagated as a changing wave. 



* Green on the Motion of Waves, Trans. Camb. Phil. vol. vi. 



