BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 325 



At the end B, the piston is exposed merely to the thrust p. It will 

 be assumed that the strain is the same as that under a thrust p uni- 

 form throughout the entire length. 



Then at B ,-' = ^^1+^^ 



= r (1 + 1.4 X 10-'' X p), 



where o- is Poisson's ratio, assumed = 0.28, and E = Young's modulus, 

 taken as 2 X 10^ kgm./cm.^. 



This correction for the distortion of the piston is not open to serious 

 question, because of the smallness of the diameter compared with the 

 length. But the calculation of the distortion of the cylinder at the 

 upper end is open to much more serious question, because the irregular 

 shape and unknown action of the packing produce an unknown stress 

 system in the mass of metal about the upper end. In place, then, of 

 a calculation, the experimental fact was used that in all probability the 

 crack between piston and cylinder would not completely disappear at 

 less than 15,000 kgm., since the piston still possessed some freedom of 

 motion at 13,000. Discussion of this experimental fact is given later. 

 It will be assumed, then, simply that the distortion is proportional to 

 the pressure, and that the combined distortion of cylinder and piston 

 will produce complete closing at 15,000. The initial size of the crack 

 was determined experimentally, by measuring the piston and the 

 effective area, to be 0.00035 inch. 



This gives at the upper end R' = R {\ — ap). 

 When the crack closes r' = R' 



or r (1 + 1.4 X 10-'^ x jt?) = (r + 0.00035) (1 — ap). 



Substituting r=l/16, 



we find = 2.3X10"''. 



At B R!- R{\- 2.3 x 10"' X />). 



Whence / + i^' = r + i? + ^^^ [(1.4 - 2.3) X 10"^ X p\ 



Effective radius, ^^^^ = ^"t^ (1 " 0-45 X 10"^ X p). 



Effective area decreased by 0.90 X 10"'' X p. 



The average change of effective area, top and bottom, which is the 

 correction desired, is therefore — 2.4 X 10"^ X ^. 



