Hydraulic Investigations. T83 



a conical pipe, or diverges spherically from a centre, varies 

 in the simple inverse ratio of the distance from the vertex or 

 centre, or in the inverse subduplicate ratio of the number of 

 particles affected, as might naturally be inferred from the 

 general law of the preservation of the ascending force or im- 

 petus, in all cases of the communication of motion between 

 elastic bodies, or the particles of fluids of any kind. There 

 is also another way of considering the subject, by which a 

 similar conclusion may be formed respecting waves diverg- 

 ing from, or converging to, a centre. Suppose a straight 

 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 mu- 

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

 properties of the centre of inertia. Now, if Instead oi one 

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

 very acute angle, the wave will be elevated higher and higher 

 as it approaches the angle : and if its height be supposed to 

 be every where in the inverse subduplicate ratio of the di- 

 stance 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 opposite 

 surface, which will not happen if the elevation vary inversely 

 in the simple ratio of the distance, or in that of any other 

 power than its square root. This mode of considering the 

 subject affords us therefore an additional reason for assert- 

 ing, that in all transmissions of impulses through elastic 

 bodies, or through gravitating fluids, the intensity of the 

 impulse varies inversely in the subduplicate ratio of the ex- 

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

 reasoning may without doubt be applied to the case of an 

 elastic tube. 



There is, however, a very singular exception, in the case 

 of waves 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 



