362 PROCEEDINGS OF THE AMERICAN ACADEMY. 



to entirely fill the cracks. The total volume of the piezometers was 

 1 or 2 cm.' for water and 3 Or 4 cm.^ for mercury. These small dimen- 

 sions were necessary to keep the size of the apparatus down within 

 reason, as it was necessary to have the walls of the retaining vessel 

 very heavy in order to withstand the pressures. The cylinder in which 

 the piezometers were placed had a hole 9/16 inches in diameter and was 

 4 inches on the outside. The small volume of the piezometers places no 

 restriction on the accuracy of the results, however. The weight of the 

 mercury involved in the compression might rise to 3 or 4 gm. for the 

 higher pressures. Weighings were made to 0.0001 gm., so that any 

 error in the weighings is entirely negligible. 



Pressure measurements were made with an absolute gauge. This 

 gauge and the various precautions to be observed in its use are 

 described in a previous paper. 



Compressibility of the Steel Piezometers. 



The experimental determination of the correction for the compressi- 

 bility of the steel piezometer demands special consideration. The fact 

 must be emphasized that there is no method of determining compressi- 

 bility in which the compressibility of all the substances concerned can be 

 determined directly, that is, by the application of hydrostatic pressure. 

 There is always a residuum, whatever the method. Thus in the present 

 work, the compressibility of both the water and the mercury involve the 

 compressibility of the steel containing vessels. If an attempt were 

 made to determine by independent experiment the cubic compressi- 

 bility of the steel, the compressibility of the vessel in which the steel 

 was contained would turn up as a new unknown. The difference of the 

 compressibility of two substances is all that it is possible to get by 

 direct experiment. To get the absolute compressibility of either, the 

 compressibility of the other, the unknown residuum, must be determined 

 by some indirect method. To ensure the greatest accuracy, this resid- 

 uum should be so chosen as to be as small as possible in comparison 

 with the compressibility in question. Steel, as has been mentioned, is 

 an admirable substance from this point of view. 



There are a variety of methods open for the indirect determination 

 of compressibility, all of which depend in some way on the theory of 

 elasticity. A method frequently adopted is to measure two inde- 

 pendent elastic constants of a material, such as Young's modulus, or 

 the torsion coefficient, or the bending modulus, and from these to cal- 

 culate the compressibility by the identical relations of the theory of 

 elasticity. In applying the identical relations, the assumption must 



