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V. On the Theory of Pressure in Fluids, By 11. Moon, M.A., 



Honorary Felloiv of Queen's College, Cambridge*. 



I DESIRE to commend the following points in the theory of 

 pressure in fluids to the attention of mathematicians. 



I. Suppose that we have a closed cylinder filled with air, and, 

 for the sake of precision of statement, suppose the axis of the 

 cylinder to be horizontal. Suppose also that at the time t every 

 particle of the air is destitute of velocity, while the density of 

 the air varies on this wise ; viz., the air to the left hand of a ver- 

 tical plane which bisects the axis of the cylinder has the uniform 

 density D, while the air to the right of the same plane has the 

 density 2D. 



Under these circumstances, according to the received theory 

 with regard to the law of pressure in fluids, the air in the right- 

 hand half of the cylinder will exert on the air in the left-hand half 

 exactly double the pressure which the air in the left-hand half 

 exerts on the air in the right-hand half; that is, the law of pres- 

 sure of the received theory contradicts, in this case, the universal 

 principle that action and reaction are equal and opposite. 



II. Suppose that we have a vertical cylinder closed at its 

 lower end, and having an air-tight piston capable of moving 

 freely in the upper part of it. Below the piston the cylinder is 

 filled with air, w r hich is kept in equilibrium by means of a weight, 

 W, resting on the piston, above which there is a vacuum. 



If a second weight, W, be placed upon the piston, we know 

 that the equilibrium will be destroyed. Let us see, however, 

 how, according to the received theory of pressure, a thin stratum 

 of air immediately beneath the piston will comport itself under 

 these circumstances. 



The pressure of the piston upon this lamina and the pressure 

 of the lamina upon the piston must under all circumstances be 

 equal and opposite. 



Consequently, if the principle of the received theory be true 

 (viz. that the pressure varies only with the density), the pres- 

 sure of the air upon the piston (and therefore the pressure of 

 the piston upon the air) must remain unaltered until a change 

 has taken place in the density of the air in the lamina. 



Now to a change in the density of the air in the lamina one 

 thing is essential, viz. relative motion of the particles of which 

 the lamina is composed ; and to such motion of the particles 

 two things are requisite, viz. : — 



(1) A preexisting variation of pressure in the lamina, through 

 the operation of which relative motion of its particles may be 

 generated. 



* Communicated by the Author. 



