BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 25 



corresponding to a rise of temperature from 20° to 40°, CD from 40° 

 to 60°, and EF from 60° to v80°. These displacements correspond to 

 slightly different values of the mean pressure. The piston displace- 

 ments at constant pressure obtained from a diagram like Figure 2 

 were then plotted against pressure on another diagram, the points 

 for the two independent series of measurements on the same liquid 

 being plotted on the same sheet. The cjuantities of liquid used in 

 the two series were usually so nearly the same that the mean of the 

 piston displacements could be assumed without error to be the piston 

 displacement of the mean quantity of liquid. The mean of the two 

 independent series of readings was found graphically from the dia- 

 gram by drawing a smooth curve through the two sets of points. 

 From this value of the piston displacement, after corrections had been 

 applied for the kerosene, mercury, and steel, the change of volume 

 per unit quantity for intervals of 20° was computed in a way analogous 

 to the similar computations for the compressibility. Here again the 

 values for the low pressures are most likely to be in error. The change 

 of volume at 20° intervals at atmospheric pressure was taken directly 

 from the tables of Landolt and Bornstein. Finally, the experimental 

 points and the points at atmospheric pressure were plotted together 

 on a single diagram, smooth curves drawn through them, and from 

 these curves the changes of volume for intervals of 20° were obtained 

 which were used in the construction of the tables of volume. 



In plotting as above on a single diagram AV for 20° intervals, two 

 independent series of measurements, namely those of this paper and 

 those on which the formulas of Landolt and Bornstein are based were 

 therefore brought together. The two sets of data should of course, 

 if consistent, lie on a smooth curve, so that the amount of discrepancy 

 might be expected to afford an indication of the order of accuracy at 

 low pressures. The change in the dilatation is, however, so rapid at 

 the low pressures that it was possible in nearly every instance to make 

 smooth connection between the two sets of points, without departing 

 from either of them. Furthermore, it would be possible in most cases 

 to make just as smooth connection if somewhat different values were 

 used at atmospheric pressure. Slight discrepancies between the 

 smooth curves and the individual points do nbt therefore, give a 

 reliable indication of the accuracy. 



The thermal dilatation is probably not so accurate as are the changes 

 of volume with pressure, because the dilatation is much smaller. The 

 dilatation can be measured with no greater accuracy than the changes 

 of pressure accompanying the changes of temperature at constant 



