THERMAL PROPERTIES OF CARBONIC ACID AT LOW TEMPERATURES. 365 



the rest of the area we have assumed a value for the specific heat at constant volume, 

 viz., C v = 0'214. This assumption is probably close to the truth, since this value, 

 found by JOLY for the line J 4 is exactly equal to the value deduced from our own 

 experiments for the line A. MOLLIEK assumed that C v was constant and equal to 

 0'182 for the whole of the area outside the limit curve. 



It would appear at first sight that most of the 10 chart might be constructed by 

 simply replotting the 0<p chart on the new co-ordinates, and our first chart was plotted 

 in this way, but when it was checked it was found to be inaccurate. Investigation 

 showed that the errors were due to three causes ; the difficulty of reading the I values 

 accurately enough from the $</> chart; the insufficient accuracy of MOLLIER'S (5) 

 table of AMAGAT'S results which we had used ; and lastly a small error in the limit 

 curve which was greatly magnified when transferred to the new co-ordinates, where 

 the (/> scale is about five times as large as in the 6</> chart. MOLLIER'S table gives 

 AMAGAT'S results in a very convenient form ; it is accurate enough for most purposes, 

 but not for plotting the volume lines of the !</> chart, particularly near the critical 

 point. We found it necessary to plot AMAGAT'S results and interpolate graphically 

 to obtain the required data with sufficient accuracy. The errors in the first chart led 

 us to devise a number of ways of checking it, many of which turned out to be most 

 useful in reconstructing it. For this purpose the following equations connecting the 

 total heat I with the other variables, p, v, 6 and <j> are useful. 



(l) The slope of any constant-pressure curve in an !</> chart is equal to the 

 temperature, or 



(2) The slope of any constant-temperature curve in an !</> chart is equal to the 



absolute temperature minus - : , or 



the dilatation 



'dl\ fde\ 



= Q V [ (ll) 



df/t \dvlp 



\ 



Cor. 1. At the critical point the limit curve, the constant- temperature curve, and 

 the constant-pressure curve are mutually tangent to one another, and their slope is 

 equal to the critical temperature. There is a point of inflexion in the constant- 

 temperature curve, and the curvature of the constant-pressure curve is zero at this 

 point. 



Cor. 2. Constant-pressure curves do not change their direction on crossing either 

 limit curve. 



Cor. 3. There is no point of inflexion in any constant-pressure curve ; curves of 

 the shape shown by MOLLIER (7) for the 80 and 90 kg. curves in the CO 2 chart are 

 therefore impossible. 



