352 PROCEEDINGS OF THE AMERICAN ACADEMY. 



To correct for the distortion of the containing vessel only indirect 

 methods are open, as direct observation of the vessel under high pressure 

 is out of the question. All of those indirect methods which are primary, 

 that is, which do not assume the correctness of the work of some other 

 observer, endeavor to determine in one way or another the compressi- 

 bility of the material of the containing vessel. This may be done by 

 measuring Young's modulus and the bending or the torsion coefficient, 

 and from these calculating the cubic compressibility by the identical 

 relations of the theory of elasticity ; or it may be done with the introduc- 

 tion of less questionable assumptions by measuring the linear compres- 

 sibility and then multiplying by three for the cubic compressibility. 

 This latter method in somewhat different forms has been adopted by 

 Richards ^ and the author. ^ Once the compressibility is known, the 

 change of volume of the vessel is found immediately by multiplying 

 the compressibility by the pressure. This assumes that the contain- 

 ing vessel changes volume without changing shape. This assumption, 

 which is made universally, seems necessary and unavoidable. There can 

 be little question, however, that the assumption is not entirely j ustified. 

 There are outstanding discrepancies between the determination of the 

 same compressibility by different observers, or by the same observer 

 with different apparatus, or indeed by the same observer with the same 

 apparatus on different occasions, that are beyond the limits of error of 

 the measurements. For instance, four very careful determinations of 

 the compressibility of mercury by de Metz "^ differed among themselves 

 by 5 per cent. The containing vessels were all of the same kind of 

 glass, and the elastic constants had been determined by direct exper- 

 iment. The only explanation of these discrepancies seems to be that 

 the distortion of the containing vessel is irregular, so that there is 

 change of shape as well as change of volume. The irregularities in 

 the results introduced by irregularities in the piezometer will, of course, 

 be proportional to the total correction introduced by the envelope, and 

 will be greatest in the case of the most incompressible liquids. Thus 

 for mercury in a glass envelope, the correction for the envelope is 60 

 per cent of the whole effect, while for water it is only o per cent. 



There can be no doubt that these irregularities are due to lack of 

 homogeneity in the containing vessel, either imperfect annealing or 

 actual variation in the constitution of the material from point to point. 

 It is inconceivable that a perfectly homogeneous body of any shape, 



^ Richards, loo. cit., 1907. 



* Bridgman, These Proceedings, 44, 255-270 (1909). 



' De Metz, Wied. Ann., 47, 706-742 (1892). 



