i860.] On the Translation of Waves of Water. 271 



a current is markedly increased by compression, which on the con- 

 trary, retards the translation of a wave through friction. 



21. It is now necessary to trace the connection between the phe- 

 nomenon of the flooding of the Indus, and the preceding laws ; in 

 fact, to answer the question which has been proposed on the assump- 

 tion of the cause being some obstruction above. Why may not all 

 the water which was heaped up above the dam be supposed to have 

 come down the river as a huge cataract when the barrier was overborne : 

 without taking the formation of a wave at all ? 



22. To this it may, I believe, be answered. 1st. That it is impos- 

 sible according to the laws of fluids, that a variation of level, however 

 it may have been caused, should do otherwise than alter its position 

 by wave motion, (excepting in the case noted in a succeeding section.) 

 The huge superincumbent mass must necessarily force up the water 

 about and beyond it, far more rapidly than its own particles could 

 run down the declivity for the following reasons. 



Let A B C be a portion of a river flowing towards the sea on a 

 slightly inclined plane, and let there be a barrier at B which has so 

 completely shut off the water above it, that by the accumulation of 

 rain, melted snow, &c. it has risen several feet above the level of the 

 river below it. Now, let us suppose the barrier B to be suddenly 

 destroyed, what will be the motion of the waters ? 



The triangle A B D is then evidently, for all purposes of calculation, 

 a ready formed wave, which will follow the laws of a wave in the 

 mode of its translation. A small portion of the water near to B will 

 of course topple over upon the water below it in foam through lateral 

 pressure, but this will only continue so long as a sufficient slope is 

 forming, to support the wave unbroken. The great body of the water 

 will follow a different course. 



Let us take the column of water x y z ; each particle under x is 

 pressed downwards, but finds no outlet in that direction ; and as 

 fluids press equally in all directions, the forces towards A and B are 

 equal ; but from A it is also shut out, and it is consequently directed 

 towards B with a force proportional to the differential gravitation 

 of x z and F z, but beyond B E the particles will be pushed upwards 

 as well as forwards, causing the water to be heaped up successively 

 at F H J, &c. thus translating a protuberance above the level of the 



