THERMAL PROPERTIES OF CARBONIC ACID AT LOW TEMPERATURES. 77 



be calculated from the temperature coefficient of the liquid. This coefficient* does 

 not appear to have been determined below C., so the experiments called Series V. 

 were undertaken to measure it. AMAGAT'S (5) results give a few values above C. 



Fig. 10. 



Series V. The general arrangement of the apparatus is shown in fig. 10. A 

 capillary glass tube, closed at the bottom, was partly filled with liquid CO a ; on the 

 top rested a mercury indicator. The upper end of the tube was connected through a 

 valve to a flask of C0 a gas at high pressure. A release valve was also connected. 

 By adjusting these two valves any desired pressure could be obtained in the glass 

 tube. The glass tube was placed upright in the calorimeter, so that it could be kept 

 at any desired temperature, while the volume of the liquid CO 3 was read directly 

 by noting its length in the glass tube as shown by the position of the mercury 

 indicator. 



A series of measurements of volume were made at different temperatures and 

 pressures. The results are plotted in fig. 11, with pressure and volume as co-ordinates. 

 The slope of the curves is the elasticity (dr/dp) t , and the distance between the curves 

 divided by the temperature difference is the dilatation (dr/dS) p . 



To calculate $<f>, however, it is not necessary to evaluate these functions, for the 

 area between any two adjacent curves at temperatures Q l and 6 y is 



* The specific volume of the liquid at low temperatures for points on the limit curve is known. This 

 enables the rate of change of volume with temperature, along the limit curve, to be calculated, but what is 



required is (dv/dtyp, which is equal to 



dv/dO + (dvjdp)t <lp/d9, 



where dvjdO and dp/dO are taken along the limit curve. 



