THERMAL PROPERTIES OF CARBONIC ACID AT LOW TEMPERATURES. 369 



The spacing of the pressure curves on the horizontal 25 C. temperature line is 

 given by the expression 



the values of ( ~ ) were calculated from fig. 1 1 of the former paper. 



\('l6/p 



The spacing of the pressure lines on the 50 C. temperature line was assumed to 

 be uniform, which must be close to the truth as may be seen from fig. 11 of the former 

 paper. 



The pressure curves were then extended from the C. volume line through the points 

 marked at 25 C. and 50C. ; keeping them similar in form to the 700-lb. line which 

 was drawn from experimental data. The lower ends of the high-pressure curves have, 

 however, been omitted from the final chart, because the data for plotting them were 

 considered to be hardly sufficiently accurate. 



Additional constant-temperature curves were interpolated using the above formula 

 to give the initial slope, those above 25 C. being slightly curved to match those at 

 higher temperatures whose form was known. These complete the !</> chart. 



APPENDIX I. 



A Method of Plotting Constant-pressure Curves in tJte Superheated Area of 



the 6<l> Chart. 



Each pressure curve starts from a point on the gas-limit curve whose temperature 

 is given by the pressure-temperature curve for saturated vapour. Above this point 

 it is plotted in 10 C. steps. For each vertical step of 10 C. the horizontal step, d<j>, is 



given by the equation : 



6d(j> 



in which 6 is the mean temperature of the step, dO = 10 C., and a- is the mean specific 

 heat of the gas for the step (see Table B). 



APPENDIX II. 



A Method of Plotting I Lines in the Superheated Area of d<f> Chart. 



The I lines have already been drawn in the saturated area for values differing by 

 5 Th.U., i.e., for I = 0, 5, 10, 15, &c. The last of these is I = 55. It is required to 

 plot the lines I = 60, 65, &c., which fall in the superheated area. The line is plotted 

 by finding the points where it crosses the pressure curves, Let ALP be any 



VOL. ccxv. A. 3 D 



