72 



Royal Society. 



the air in E C. It is evident therefore that, according to the received 



theory, no change can, under the circumstances above supposed, take 



place in the density of either mass of air. 



If, however, the density in A F remain unchanged, we have already 



seen that every particle in E C will in the time t 1 describe a space 



ft 2 

 equal to^-J-; and if the density in E C remain unchanged, we have 



equally seen that every particle of A F will have remained at rest 

 during t x ; which is a contradiction. It appears therefore that in 

 the case we have been considering the received theory 

 leads us to an absurd result. 



It can with still more facility be shown that the 

 received theory leads to an absurd result in the fol- 

 lowing case. 



ABCD is such a tube as before described ; but in 

 the present case we shall suppose it filled below the 

 piston with air of uniform density in equilibrium, 

 the pressure of the air being such as to exactly sus- 

 tain the weight W 2 of the piston. As before, a 

 vacuum is supposed to exist above the piston, and the 

 air is assumed to be unaffected by gravity. 



If a second weight W 2 be placed upon the piston, 

 we know that the equilibrium will be destroyed. 

 But if it be true, as the received theory asserts, that 

 the pressure of an elastic fluid depends solely on its 

 density, the pressure of the air on the lower surface 

 of the piston will be exactly the same after W 2 has 

 been introduced as it was before W 2 was introduced ; and, since 

 action and reaction are equal and opposite, whatever be the pressure 

 of the air in the piston, the same will be the pressure of the piston 

 on the air ; so that the pressure downwards of the piston on the air 

 beneath will be the same after W 2 was introduced as it was before ; 

 and the system therefore will continue in equilibrium after W 2 has 

 been introduced ; which is absurd. 



By an argument too elaborate to be indicated within the limits of 

 this abstract, the cause of the failure of the existing theory in the 

 instance first above considered is shown ; and it is proved that in the 

 second case the effect of the introduction of the weight W 2 is instan- 

 taneously to propagate through the air to a definite distance below 

 the piston a finite increase of pressure ; such increase of pressure 

 having its maximum immediately underneath the piston, and thence 

 gradually diminishing till, if the tube be long enough, it finally 

 vanishes. The depth to which the instantaneous increase of pressure 

 will extend will be defined by means of two considerations : — 1st, that 

 the effective force on every particle of the piston and weight must be 

 exactly the same as that on the air immediately below it ; and 2nd, 

 that the aggregate moving force developed in the piston W, the 

 weight W 2 , and the 'portion of the air in the tube through which the 

 instantaneous pressure extends, must be equal to the moving force 

 developed by gravity in W 2 when free to move in vacuo. 



