1S0 Dr. Young's Hydraulic Investigations . 
transmissions of impulses through 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. 
There is however a very singular exception, in the case of 
waves crossing each other, to the general law of the preser- 
vation of ascending force, which appears to be almost suffi- 
cient 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 pre- 
serve its motion and its elevation with respect to the surface 
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 direction, both the height and the 
actual velocity of the particles being doubled, it is obvious that 
the ascending force or impetus is also doubled, since the bulk 
of the matter concerned is only halved, while the square of 
the velocity is quadrupled ; and supposing the double wave 
to be stopped by an obstacle, its magnitude, at the moment of 
the greatest elevation, will be twice as great as that of a single 
wave in similar circumstances, and the height, as well as the 
quantity of matter, will be doubled, so that either the actual 
or the potential height of the centre of gravity of the fluid 
seems to be essentially altered, whenever such an interference 
of waves takes place. This difficulty deserves the attentive 
consideration of those who shall attempt to investigate either 
the most refined parts of hydraulics, or the metaphysical 
principles of the laws of motion. 
