293 Mr. Challis on the Theory of the 



the velocity pq, \i fp = x, pq=y, y=f{^)- Hence the line fc is 

 given by a single equation, which is always the same whatever 

 be the velocity impressed, and the angle at which it cuts the 

 axis, is independent of this velocity. Also since the particular 

 form of cf must result from the constitution of the fluid, its 

 equation will be 



ttX 



y = m\ sin — . 



or more generally, 



V = wjX Sin —- ± m'K sm—r±m\ sin —77 + &c. 



K K \ 



But as there is nothing from the conditions of the question to 

 determine x, x', X", &c. because they are independent of the im- 

 pressed velocity, and as these quantities cannot be considered 

 arbitrary, since the equation is of a determinate nature, they 

 must be assumed so as to be made to disappear. This will 

 obviously be effected by making each of them indefinitely great. 



Hence, 



y = ■n{m±m! ± m + &c.) x = kx, 



and cf is a straight line. It follows that the extent af over 

 which the shock is felt, varies as the velocity communicated to 

 the particles immediately acted upon. The momentum communi- 

 cated will vary as aj' x the mean of the velocities of the particles, 

 that is, as ac-. Hence if a diaphragm at rest, be suddenly moved 

 with the velocity V, the resistance to be overcome in the first 

 instant, varies as V-. Let af=l, and l=inV ; this quantity n may 

 be determined experimentally. For suppose m- equal to the area of 

 the surface of the diaphragm, /^ equal to its mass, and let it be 

 put in motion by the impact of a mass M, moving with the 

 velocity to, so that the two masses M and \l with the' fluid in 

 contact with the diaphragm, begin to move immediately after 

 the impact with the velocity V. Let I be the density of the 



