BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 27 



-desired. The next step was to tabulate the volume as a function of 

 pressure over the entire pressure range at 40°, starting from the volume 

 at atmospheric pressure and 40°. These values were then combined 

 with the change of volume for 20° intervals, thus giving the volume 

 for each pressure at 20°, 60° and 80°. To obtain the volume at the 

 intermediate intervals of 10° a device was adopted which at the same 

 time gave the material for determining the thermal dilatation. The 

 change of volume to be expected at 40° and 60° if the change had been 

 linear with temperature over the entire range was calculated from the 

 total change of volume between 20° and 80°. The differences between 

 the actual and the calculated changes of volume were plotted against 

 temperature for each pressure of the table, and smooth curves drawn 

 through these points. From these curves the departure from linearity 

 at the intermediate intervals of 10° was found, and combined with the 

 values computed by the linear relation to give the total change of 

 volume at the desired 10° intervals. This method, as the method for 

 computing the isothermal compressibility, has the advantage of giving 

 smooth curves without smoothing off the second differences. 



Thermal Dilatation. — From the table of volumes the next problem 

 was to compute the more significant quantities of thermodynamic 



interest. The first of these was the thermal dilatation, or f - j . 



-I / 'J \ 



■"Dilatation" is perhaps not generally used in this sense, "It" 



V \otJp 



being more common, but it has the advantage of being the quantity 

 which enters directly into the thermodynamic formulas. The quan- 

 tity of material to which the former differentiation refers is the unit 

 used throughout this paper, namely the quantity which at 0°C. and 

 atmospheric pressure occupies 1 c.c. 



Evidently if the dilatation were uniform over the entire temperature 

 range it could be found from the change of volume between 20° and 80° 

 by dividing by 60. The dilatation is not linear, however, but departs 

 from linearity in a way which can be found from the curves used to 

 -determine the change of volume at 10° intervals. The correction to 

 the linear value is obviously to be found from the slope of the differ- 

 ence curve, which can be found graphically from a large drawing with 

 sufficient accuracy. The dilatation was determined in this way at 

 20° intervals, and was plotted as a function of the pressure for each 

 of the twelve liquids. 



The details of the computations for the volume at 10° intervals 

 and of the dilatation are shown more clearly perhaps in Figures 4 



