244 



[Recess, 



masses of fluid has changed. Hence change in the density of the 

 air in A F must precede change in the density of E C. 



On the other hand, so long as the pressure of the air in E C on 

 the air in A F remains unchanged, the air in A F will remain at rest, 

 and will therefore undergo no change of density. But as, according 

 to the received theory, the pressure of the air in E C on the air in 

 A F depends on the density of the part of the air in E C which abuts 

 on the common boundary of the two masses of air, it follows that 

 change in the density of the air in E C must precede change in the 

 density of the air in A F. 



But we have before proved the exact contrary, viz. that change in 

 the density of the air in A F must precede change in the density of 

 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 l describe a space 



ft 2 

 equal to*^-i; and if the density in EC remain unchanged, we have 



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

 during ^ ; 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 following case. 



A B C D 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 x 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 A 



