BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 209 



and accordingly the effective diameter was determined in another 

 way, to be described later. 



The second correction is a correction for the distortion of the gauge 

 under pressure, and increases in percentage value directly with the 

 pressure. This correction, of course, varies with the type of gauge, 

 but in the types of gauge described above, and the pressure gauge 

 employed, the correction is practically negligible. A rough calcu- 

 lation showed that at 3000 kgm. the correction in Amagat's mano- 

 meter is about to per cent. Since, however, it was desired in this work 

 to reach an accuracy of T V per cent, and since the pressure range is 

 6800 kgm., some approximate evaluation seemed desirable. 



No easy experimental method of determining this correction sug- 

 gested itself, so recourse was had to a calculation, using the theory of 

 elasticity. This was done only as a last resort, because of the doubt- 

 ful accuracy of the mathematical theory at these pressures, and of the 

 fact that the solution obtained is only an approximation, instead of a 

 rigorous mathematical solution. In fact, the general problem involved 

 has not been solved mathematically, and even if it could be, its applica- 

 tion here would be doubtful, because slight irregularities in either 

 cylinder or piston would destroy the ideal boundary conditions of the 

 mathematical problem. In spite of all these objections, however, the 

 magnitude of the approximate correction turned out to be so slight, 

 tV per cent, that the calculated value can probably be applied with a 

 fair degree of confidence. 



The facts used in the following calculation are taken from the most 

 elementary parts of the theory of elasticity, and may be found stated 

 in any book under the calculation of the strains produced in a cylinder 

 by external or internal hydrostatic pressure. It will be noticed that 

 the correction for distortion found below includes the effect of the 

 friction of the escaping liquid. 



The strain in the piston can be broken up into two components. 

 The first is that due to the longitudinal compression of the piston by 

 the hydrostatic pressure at one end and the equilibrating weights at 

 the other, and is uniform throughout the piston. The radius increases 

 from this effect by the amount 



3 k — 2 a 

 Ar = X r X P, 



LbfJLK 



where P is pressure in kgm. per sq. cm., k the compressibility modu- 

 lus, and fi the shear modulus. These elastic constants vary only 

 slightly in different grades of steel. If we assume as average values 

 that 



