THERMAL PROPERTIES OF CARBONIC ACID AT LOW TEMPERATURES. 367 



Cor. 3. The horizontal distance S<f> between two constant-temperature lines in the 

 saturated area of the 10 chart which differ in temperature by is 



The distance may be found for any value of <j> by using the corresponding value of 

 V (depending on the dryness). 



This expression was used in plotting the 10 chart to find the distance of the 30 C. 

 line from the 23 '2 C. line (900 Ib.) and the distance of the critical point from the 

 30 C. line. 



Using the above equations as checks a second 10 chart was drawn, plotting from 

 the original data as far as possible instead of copying from the 9<j> chart. During 

 construction it was constantly checked by the above formulae and small corrections 

 made ; in this way we finally arrived at a result which represents all the experimental 

 data and also complies with the above general theorems. The only part of the 

 diagram which does not fit in quite satisfactorily is the short piece of the liquid-limit 

 curve between-f 10 C. and + 23 C. 



In order to make sure of the remarkable form of the temperature curves on the 

 left of the diagram, these curves were extended some distance further than they are 

 shown. There was no difficulty in doing this, since AMAGAT'S results go to much 

 higher pressures, but as the pressures increased we found it impossible to make the 

 slopes of the pressure curves comply with equation (i). This discrepancy appears to 

 point to some variation in the specific heat at constant volume in this region. As 

 there are no data available we have omitted the curves beyond 1800 lb.,up to which 

 pressure the discrepancy, is very slight. 



If the chart be examined it will be seen that JOLY'S experiments and ours overlap 

 and may therefore be compared. JOLY measured C^ and we measured C p ; to compare 

 the results it is necessary to obtain an equation connecting the two. The most 

 convenient equation is 



a form which may be derived directly from the fundamental thermodynamic relations, 

 and is quite general. 



The familiar relation for a perfect gas - 



>- c - =>*>, 



does not give even approximate results. Comparing JOLY'S results with ours by 

 equation (i) and using AMAGAT'S figures to obtain the differential coefficients, we found 

 that they agreed within the limits of accuracy of JOLY'S experiments. 



The first lines drawn on the 10 chart were the 700-lb. line from zero down to 



