324 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tion is to change the effective area of the piston and so to change the 

 total thrust exerted on the piston by a given hydrostatic pressure. 

 As previously explained, this correction is calculated mathematically 

 and is merely a rough approximation. Its justification is that the 

 correction is in any event exceedingly small, and that no easy experi- 

 mental method of determining it directly presents itself The cor- 

 rection is to be made by finding the change in the mean area of the 

 cylinder and the piston at the lower and the upper ends, and taking 

 the mean of these two changes. This gives the change in the effective 

 area of the cross-section as was proved in the former paper. 



The stress system on the piston and cylinder is as follows. On the 

 piston there is the longitudinal thrust produced by the action of 

 hydrostatic pressure on the end at A, and the equal and opposite 

 thrust of the equilibrating forces at B. This thrust is uniform 

 throughout the length of the piston. In addition there is the normal 

 pressure on the curved surface exerted by the liquid which is slowly 

 flowing out through the crack between piston and cylinder. At A 

 this pressure is equal to the total hydrostatic pressure, and regularly 

 decreases from here outward to zero at B. On the cylinder there is 

 externally a uniform hydrostatic pressure over nearly the entire length ; 

 internally the same distribution of pressure as acts on the piston. At 

 the inner end A the resultant of these two systems of stress is effect- 

 ively a uniform hydrostatic pressure on both piston and cylinder, under 

 which both shrink uniformly. If r and R are the radii of piston 

 and cylinder initially, and / and R' the corresponding values under 

 pressure, we have evidently : 



At the lower end r = r i 1 — ^ j 



..= «(i-4). 



New effective radius = — ^ = — r— ^ ( 1 — — V 



2 2 \ '6 J 



Effective area changed by ~- 



= — 4X1 f )-^ X p 



p is pre 



k = compressibility = G X 10 



p is pressure in kgm./cm.'^ "j 



