CONDENSATION AND CRITICAL PHENOMENA. 265 



thesis. Blumcke demonstrated the reality of the so-called 

 theoretical isothermal for a mixture of carbonic acid and 

 sulphurous acid by slowly expanding the mixture when 

 wholly liquid and lowering the pressure below the pres- 

 sures of the experimental isothermal ; and in the same way 

 by compressing the mixture carefully to a pressure above 

 the pressure at d. The writer of this article has often been 

 able to confirm the former experiment. 



The theoretical isothermal is given in fig i. as a dotted 

 curx'e. It changes gradually into the shape above 4- 

 For single substances we saw the double wave shape dis- 

 appear at the top of the border curve (here at M). At 

 this point the critical isothermal for single substances has a 

 horizontal tangent and the isothermals for higher tempera- 

 tures have no points at which -f >> <?. For mixtures a 



av 



similar transition takes place but now inside the border 

 curve, as may be seen from fig. i. 1 he isothermals 

 for temperatures just below 4) though partly inside the 

 border curve have no unstable part. The critical tempera- 

 ture, as it would be if the mixture remained homogeneous, 

 is below the actual critical temperature. 



It will also be noticed that the law for finding the border 

 curve from the set of complete theoretical isothermals must 

 be different from the same as explained for single sub- 

 stances. In that case the Maxwell-Clausius criterion 

 solved the problem. Here the vapour pressure is a 

 quantity which depends on the volume in consequence 

 of the fact that the composition of the two co-existing 

 phases is as a rule different. As was pointed out by 

 Blumcke the area of the two surfaces inclosed between 

 theoretical and actual isothermal must be again equal in 

 this case. But this condition is evidently altogether in- 

 sufficient for the solution ; the complete solution will be 

 given presently. 



As regards the continuity of the liquid and vapour states 

 the same remark may evidently be made as for single 

 substances. K mixture in the condition of vapour may be 

 changed into a liquid by a continuous set of changes. 



