450 PROCEEDINGS OF THE AMERICAN ACADEMY. 



of the material of the lower cylinder. This is due to the fact that the 

 upper cylinder was kept at the constant temperature of 8° instead of 0°. 

 For example, let us suppose that the contents of the lower cylinder ex- 

 pand 1 per cent when the temperature is raised from — 20° to 0°. This 1 

 per cent passes from the lower cylinder at 0° to the upper cylinder at 

 8°, and in so doing experiences an additional increase of volume due to 

 the extra 8". The error introduced by assuming the piston displace- 

 ment to give the dilatation will be, therefore, in this example, about 

 0.5 per cent on the dilatation. This error was not corrected for in the 

 present work, since the accuracy of the largest dilatation found, judg- 

 ing only from the number of significant figures, was not over 2 per cent. 



One experimental source of error did require correction. This is due 

 to the wearing away of the packing material of the piston by the enor- 

 mous friction during the advance of the piston. The effect is evidently 

 the same in its results as a leak, although there was absolutely no leak 

 of the liquid and only this wearing away of the packing during actual 

 motion of the piston. The effect was corrected for by making two 

 runs at every temperature with increasing and decreasing pressure, and 

 taking the mean. The discrepancy between the displacements during 

 increasing and decreasing pressure gave the amount of wearing of the 

 packing. This was of the order of 0.01 inch on a total stroke 3 inches. 

 The maximum correction was 0.013 inch. This correction was applied 

 to the next run at higher temperature. The correction so determined 

 incidentally covers the effect of hysteresis, elastic after-working, or of 

 viscous yield in the steel, all of which must be very small at these 

 comparatively low pressures. 



The method used in making the calculations from the data was a 

 combination of arithmetic computation with graphical representation. 

 The graphical representation alone would not have been accurate 

 enough. This is because the changes of volume due to temperature 

 are very small in comparison with those due to changes of pressure in the 

 region in question, so that it was necessary to retain all the significant 

 figures given by the measurements. Piston displacement was measured 

 to 0.0001 inch on a total of 3 inches, but since the pressure measure- 

 ments were sensitive to only 1 part in 3000, the displacement readings 

 were retained only to 0.001 inch. The method was to pass the best 

 parabola through the experimental points at the various constant tem- 

 peratures ; calculate the displacement given by the parabola at the pres- 

 sure of the experiment ; plot on an enlarged scale the difference between 

 the observed displacement and the calculated displacement; pass a 

 smooth curve through these difference points ; and finally by combin- 

 ing the results given by the smooth deviation curve with the computed 



