Pressure in Fluids. 29 



sume this force to he f, then at the end of the time t + dt each 

 particle of the air will have acquired a velocity /«?/, and will have 



described a space^- 



Moreover, since the motion during the time dt (being such as 

 has been described) can in no way have altered the density, it is 

 clear that at the end of the second interval dt each particle will 

 have acquired a velocity 2fdt, and will have described a space 

 2fdt 2 , the density remaining unaltered. 



Reasoning from step to step in the same manner, at the end 



of the finite time t l} each particle will have acquired a velocity ft lt 



ft 2 

 and will have described the space -—• 



It is obvious, however, that no such effects as those above de- 

 scribed, and which, if the received theory of pressure be univer- 

 sally true, must necessarily take place, can occur in the case we 

 are considering. At the end of the time t + t v equally as at the 

 end of the time £ + dt, the particles in contact with the base of the 

 cylinder will have described no space, they can have acquired no 

 velocity. 



It is clear, in fact, that any theory of pressure which, under 



dz) 

 the above circumstances, would render the value of -j- other than 



zero, as the received theory on the subject does render it, must 

 be erroneous. 



IV. Suppose that we have a vertical cylinder, closed at both 

 ends and resting on a solid pier, filled with air which is in equi- 

 librium, gravity being supposed to act. 



Suppose that at the time t a second force begins to act, which 

 is equal to the force of gravity and acts in the same direction. 



Under these circumstances, either the law of pressure in the 

 air in the cylinder will be instantaneously altered or it will not. 



If it be instantaneously altered, the received theory as to the 

 law of pressure is contradicted ; for it is impossible that the den- 

 sity of the air in the cylinder can be altered instantaneously, 

 change of density implying motion, for which lapse of time is in- 

 dispensable. 



But if the pressure throughout the air be not instantaneously 



altered, the following consequence will occur; viz. each particle 



of the air will be acted upon (1) by the forces which acted upon 



it before the time t, which forces destroy each other, since before 



/ the air was in equilibrium ; (2) by the constant force g. Hence 



at the end of the time t -j- dt each particle will have acquired the 



qdf 

 velocity gdt, and will have described the space -ks no change 



taking place in the density of the air. 



