406 PROCEEDINGS OF THE AMERICAN ACADEaiT. 



had been broken. The seasoning of the upper cylinder was done more 

 carefully, and is described elsewhere. The set must have been nearly 

 all removed by this seasoning, but any subsequent set would still affect 

 only those results for increasing pressure. 



In view of all these considerations, the course actually adopted 

 seems justified ; namely, to retain only those values found during melt- 

 ing, that is, during decreasing pressure. In consequence, in some two 

 or three of these last determinations, and in many of those on water, 

 the experimental determination with increasing pressure was entirely 

 omitted. 



Elastic Deformation. — It has already been stated that the only way 

 in which elastic deformation, that is, a deformation depending only on 

 the pressure, enters, is in the correction for the change of cross-section 

 of the upper cylinder. Although the value finally adopted for this 

 correction is small, only 1.8 per cent at 10,000 kgm /cm.*^, still it must 

 be admitted that the greatest uncertainty in the work is precisely in 

 determining this correction. The difficulty comes because of the very 

 high pressure employed, which renders doubtful the calculation by the 

 ordinary theory of elasticity. If the maximum pressure used in the 

 experiment, 12,000 kgm., were the greatest pressure involved, the case 

 would not be so doubtful, because the elastic limit of the steel is not 

 greatly exceeded here. Indeed, if it were possible to harden the steel 

 uniformly throughout its mass, reaching to a depth of 1 1/2 inches, the 

 elastic limit would not be reached until about 15,000 kgm., and there 

 would not be much question in applying the ordinary equations of 

 elasticity. But it is impossible to raise the ela.stic limit throughout 

 the metal by quenching, and the interior of the cylinder always shows 

 some set at 12,000. Since the accuracy of the whole method depends 

 on accurate knowledge of the cross-section it was necessary to remove 

 every vestige of set in this part of the apparatus. This was done by 

 subjecting the cylinder initially for five or six hours to a pressure of 

 24,000 kgm. This was sufficient to stretch the inside of the cylinder 

 from its initial value of 1/2 inch to nearly 9/16 inch. The cylinder 

 was then reamed out to 9/16 inch for its entire length, and this was the 

 form in which it was finally used. The effectiveness of the treatment 

 is shown by the fact that the cylinder has shown no further change of 

 so much as 0.0001 inch on the internal diameter. 



The present condition of the cylinder is therefore far from one of a 

 state of ease ; there are certainly internal strains. But it should be 

 noticed that this fact in itself is not sufficient to destroy the applica- 

 bility of the equations of elasticity. Provided only that the metal 

 shows no further set after the first application, and that strain remains 



