BREAKING OF WAVES. J 19 



anovular point advancing on each side upon the inclined sur* 

 face with a velocity which is at tirst equal to that which is 

 due to half the depth, and is afterwards uniformly retarded; 

 so that the angle is twice as long- in travelling- over the whole 

 surface of the wave, as it would otherw ise have been. The 

 centre descends at first more rapidly than the part nearer 

 the margin, so that the wave becomes concave in the mid- 

 dle, instead of being flat, as it would be if the depth of the 

 fluid were very great. In the mean time the margins of the 

 wave advance with a velocity, which continues to be um« 

 formly accelerated, until the angle reaches it; and this ve- 

 locity is as much smaller than that of a body falling by its 

 weight, as the height of the wave is smaller than half the 

 breadth : for the whole horizontal pressure acting on any 

 vertical section of tlie wave is every where proportional to 

 the quantity of ttie fluid beyond it, and as long as the deeper 

 parts retain their form, they will urge forward the shallower 

 with a constant force. But if any part of the surface of the 

 wave be concave, the velocity thus produced in its upper 

 parts will cause them to advance more rapidly than the 

 lower, and the surface will become more and more inclined 

 to the horizon: if on the contrary it be convex, the lower 

 parts will be protruded, and the convexity will be diminish- 

 ed. Beside the case of a wave advancing in consequence These reason- 

 of its gravitation on a flat shore, these considerations aie Jq^'^Jq^^q^qji 

 also applicable to that of a drop of oil, spreading, by the spreading on 

 force of cohesion, on the surface of a vessel of water. ^* ^^' 



I am. Sir, 



Your very obedient servant, 

 W Sept. 1807. HYDROPHILUS. 



ANNOTATION, 



MY correspondent not having gone at large into the usfe' 

 and application of the tide table annexed, Plate IV, a little 

 more particular detail on the subject will probably be ac- 

 ceptable to many of my readers. The small shaded circle Manner of fit- 

 in fig. 1 being cut out, a damp wafer is to be put in its u^ng Jte^iide 

 place, and over it fig. 2; which is likewise to be cut out, table, 



and 



