Dr. Young’s Hydraulic Investigations . 179 
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 
impetus, 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 diverging 
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 reflec- 
tions, 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 ac- 
tions, which is contrary to the general laws of the proper- 
ties 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 higher as it ap- 
proaches the angle: and if its height be supposed to be every 
where in the inverse subduplicate ratio of the distance of 
the converging surfaces, the magnitude of the pressure, re- 
duced 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 asserting, that in all 
A a 2 
