28 Mr. R. Moon on the Theory of 



(2) An interval of time during which such variation of pres- 

 sure may act. 



But while it has thus been seen that variation of density in 

 the lamina must be preceded by variation of pressure in and 

 upon the lamina, the received theory asserts that these two things, 

 viz. variation of density and variation of pressure, are necessarily 

 coexistent. 



Hence in the case just stated, since at the time t, when the 

 second weight is introduced, there is no variation in the density 

 of the air in the lamina immediately beneath the piston, it fol- 

 lows, according to the received theory, that when the second 

 weight is introduced there will be no variation of pressure in the 

 lamina, and therefore nothing to generate that which, according 

 to the received theory, is the essential mark and test of a change 

 of pressure, viz. variation of density. According to the received 

 theory, therefore, the equilibrium will be maintained after the 

 second weight has been introduced, which is absurd. 



It is clear that in the case just considered, the effect of the 

 introduction of the second weight will be to propagate instanta- 

 neously into the air beneath the piston a pressure of finite amount, 

 extending to a finite distance below the piston — such additional 

 pressure having its maximum immediately below the piston, and 

 thence diminishing gradually till, if the portion of the cylinder 

 below the piston be long enough, it will finally vanish. If the 

 portion of the cylinder below the piston be small, as compared 

 with the magnitude of the weight resting upon the piston and 

 with the density of the air, such additional pressure will extend 

 throughout the entire mass of air beneath the piston ; and we 

 shall have, besides, an additional pressure of finite amount ex- 

 erted simultaneously upon the base of the cylinder. 



III. Suppose that we have a vertical cylinder having its lower 

 end closed and resting upon a solid pier, and having, as before, 

 an air-tight piston capable of moving freely in the upper part of 

 it. Above the piston is a vacuum, while below it the cylinder is 

 rilled with air which at the time t is destitute of velocity, but of 

 which the density varies according to the following law, viz. 



p = I>s ax t 



where x denotes the vertical distance from the base of the tube. 

 Gravity is supposed not to act; but a constant downward pres- 

 sure is exerted upon the piston equal in amount to the pressure 

 which, according to the received theory, would be due to the air 

 immediately beneath the piston at the time /. 



Under these circumstances the effective force which, according 

 to the received theory as to the pressure in fluids, will be exerted 

 upon each particle of the air at the time t will be uniform. As- 



