TIIKKMAL PROPERTIES OF CARBONIC ACID AT LOW TEMPERATURES. 101 



The starting points of the 700-lh. and 900-lb. constant-pressure curves (0 = 273 C., 

 ^ = '0024 and '0049), found on p. 80, were first marked, and the two constant- 

 pressure curves were then drawn in segments of 10 degrees each. 



The liquid-limit curve was then set off from these pressure curves at the distances 

 fy given in Table VIII. 



The gas-limit curve was then set off from the liquid-limit curve at the distances 

 fy = L/tf (Table VI). 



A constant I line was then drawn through the origin, at a slope determined by the 

 Joule-Thomson effect. Thus the value of I at the origin (calculated on p. 80) 

 was transferred to the two constant-pressure curves. The points 1 = 0, +5, +10, 

 + 15, and 5, 10, 15, 20, 25 were then marked on these curves and trans- 

 ferred back to the limit curve by drawing I lines as before. Thus the starting points 

 of the I lines on the limit curve were determined. Measuring from these, a number 

 of points were then marked off at distances $<f> = 5/6, 10/6, 15/6, &c., and I lines 

 drawn through these points. The space between the limit curves was then divided 

 into quarters, thus determining a few dryness lines. The constant-pressure curves in 

 the superheated area were then drawn, starting at the corresponding saturation 

 temperatures at slopes 



= 



where the values of Q l 6 a were the actual temperature ranges in the experiments, 

 Series III., and a- was the corresponding specific heat of the gas at constant pressure, 

 given in fig. 6. 



The maximum probable error in the liquid limit curve is <ty> = '0008 at 30 C. 

 and '0032 at 50 0. At higher temperatures the error is probably not more than 

 '0005. 



MOLLIER'S ti<f> diagram was constructed in a very different manner. He assumed 

 that the characteristic equation of the gas might l>e expressed in VAN DER WAAL'S 

 form 



K0 



V-a. ( 



and determined the constants by means of AMAOAT'S observations. He also assumed 



li-} 



that f(6) was of the form f(6) = e* '', and by means of these equations obtained a 



general expression for the entropy of the gas, which would hold down to the limit 

 curve. With this he plotted the gas limit curve on the 6<f> diagram. 



He then found an empirical mathematical formula for the slope of the pressure- 

 temperature curve, dp/d6, which, on integration, corresponded well with the pressure- 

 temperature curve constructed from AMAGAT'S and REGNAULT'S observations. With 

 this and AMAGAT'S values for the vapour and liquid densities (extrapolated) he 

 calculated the values of L, and set off the liquid limit curve to the left of the gas limit 

 curve at distances $<f> = L/0. 



