COMPRESSIBILITY OF METALS. 179 



the coil was calibrated against the freezing point of mercury at 0° at 

 sufficient intervals to insure the accuracy of the pressure measurements. 

 After the readings had been made of the potentiometer setting as a 

 function of pressure over the entire pressure range, and the various 

 corrections applied to these readings, the points were plotted, potentio- 

 meter setting against pressure. This plot is nearly a straight line. A 

 straight line was now passed by computation through the zero point 

 and the point at the highest pressure, and the intermediate points on 

 the line computed corresponding to the intermediate observed pres- 

 sures. It was necessary to use computation for the intermediate 

 points, as graphical construction would not have been accurate enough. 

 The difference between the linear values and those actually observed 

 was now found by subtraction, and these differences were plotted on 

 an enlarged scale. A smooth curve was now passed through these 

 difference points. This curve could be drawn with sufficient accuracy 

 in most cases free hand. In most cases this curve was symmetrical 

 about the mean pressure (6000 kg.), and could be represented within 

 the limits of error by a parabolic formula. This means that within 

 the limits of error the change of volume is given by a two constant 



AV 

 formula of the type used for iron above, namely -p~ = — (a + bp)p. 



The change of volume under 12000 kg. was next computed, using as 

 the most probable value of the change of resistance that obtained from 

 the smoothed curve of departures from linearity. In computing this 

 change of volume all the corrections were applied. The initial rate at 

 which the volume changes with pressure was also computed. This 

 initial rate was the average rate to 12000 corrected by a factor ob- 

 tained from the smoothed difference curve. The correction factor was 

 usually given with sufficient accuracy by doubling the ratio of the 

 deviation at the mean pressure to the mean ordinate, and applying the 

 result as a correction factor to the average rate to 12000. If the 

 deviation from linearity was so great as to make this procedure in- 

 accurate, the change of volume was calculated directly at several 

 intermediate pressures. Having thus obtained the initial rate of 

 change of volume, and the change under 12000, the constants of a 

 formula like that above were at once determined. For several sub- 

 stances, particularly sodium and potassium, the deviation from 

 linearity was so great that it was necessary to calculate from the 

 smoothed curve the changes of volume at even thousand intervals of 

 pressure, and tabulate these, instead of trying to reproduce the results 

 by a single formula. 



