118 HYDRAULIC INVESTIGATIONS. 



wave to be reflected backwards and forwards in succession, 

 by two vertical surfaces, perpendicular to the direction of its 

 motion ; it is evident that in this and every other case of 

 such reflections, the pressure against the opposite surfaces 

 must be equal, otherwise the centre of inertia of the whole 

 system of bodies concerned would be displaced by their 

 mutual actions, which is contrary to the general laws of the 

 properties of the centre of inertia. Now if, instead of one 

 of the surfaces, we substitute two others, converging in a 

 very acute angle, the wave will be elevated higher and 

 Jiigher as it approaches the angle : and if its height be sup- 

 posed to be every where in the inverse subdu plicate ratio of 

 the distance of the converging surfaces, the magnitude of 

 the pressure, reduced to the direction of the motion, will 

 be precisely equal to that of the pressure on the single op- 

 posite surface, which will not happen if the elevation vary 

 inversely in the simple ratio of the distance, or in that of 

 Jn tensity of the anv other power^han its square root. This mode of consir 

 inversely Iruhe Bering the subject affords us therefore an additional reason 

 eubduplicate for asserting, that in all transmissions of impulses through 

 teii^affeaedr elastic bodies, or through gravitating fluids, the intensity of 

 the impulse varies inversely in the subduplicate ratio of the 

 extent of the parts affected at the same time; and the same 

 reasoning may without doubt be applied to the case of an 

 elastic tube. 

 Waves crossing There is however a very singular exception, in the case of 

 each other. wa ves crossing each other, to the general law of the pre- 

 ' servation of ascending force, which appears to be almost 

 sufficient to set aside the universal application of this law to 

 the motions of fluids. It is confessedly demonstrable, that 

 each of two waves, crossing each other in any direction, will 

 preserve its motion and its elevation with respect to the sur- 

 face of the fluid affected by the other wave, in the same 

 manner as if that surface were plane : and, when the waves' 

 cross each other nearly in the same d rection, both the 

 height and the actual velocity of the particles being dou- 

 bled, it is obvious, that the ascending force or impetus is 

 also doubled, since the bulk of the matter concerned is only 

 halved, whiie the square of the velocity is quadrupled; and 

 supposing the double wave to be stopped by an obstacle, its 



magnitude 



