1862.] 245 



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 eifect of the introduction of the weight "W 3 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. 



It is also shown that if instead of the weight on the piston being 

 suddenly increased it were to be suddenly diminished, exactly analo- 

 gous results, miCtatis mutandis, would occur, the effect of the sudden 

 removal of part of the weight being instantaneously to diminish the 

 pressure to a finite distance below the piston such diminution having 

 its maximum immediately beneath the piston, and thence gradually 

 diminishing till, at a certain distance below the piston, the whole 

 pressure will be exactly the same as it was before any part of the 

 weight was removed. 



If the piston were wholly removed, the pressure of the air originally 

 in contact with it at the instant of removal would be zero. 



It is then shown that the addition to or diminution from the weight 

 on the piston in the case last considered will produce no immediate 

 change in the horizontal pressure in the air below the piston. 



It is next shown that in cases where there is no impressed velocity, 



