304 Law of Cailletet and Mathlas and the Critical Density. 



constants instead o£ in that with two, and if we exclude the 

 alcohols and acetic acid, the variation in a is much smaller 

 than before, the extreme values being '916' and 1*039 as 

 against '882 and 1*090, and the change is especially marked 

 in the case of the hydrocarbons, for which the new constants 

 range from "916 to '968 as against '882 to 1*075. Now « in 

 the formula D c = Do + at + fit 2 differs but little from what it 

 would be in the formula D/ = D +a£ if we were to take only 

 the densities below the boiling-point, and as the variation of 

 a is smaller in this case, it is the more remarkable that this 

 constant should be so very low (*7675) for chlorine. 



In this respect chlorine resembles the alcohols (a = "717, 

 '746, and *844), but the critical densities of the alcohols are 

 abnormally high whilst that of chlorine appears to be very 

 low. It would be of considerable interest if the densities of 

 the saturated vapour of chlorine could be determined at high 

 temperatures so that the values of a, a, and D c could be ascer- 

 tained with certainty, but the experimental difficulties would 

 be very great. 



General Conclusions. 



1. The law of Cailletet and Mathias is very nearly, though 

 in most cases not absolutely, true ; it appears to be only 

 strictly true when the ratio of the actual to the theoretical 



density at the critical point ( jA- 1 has the normal value 3*77. 



2. The curvature of the " diameter " is generally smaller 

 the nearer j~ approaches the normal value, and the nearer 



at =«ty ) approaches the value 0*93. 



3. The curvature is in nearly every case in opposite 

 directions according as -^ is greater or less than 3*77, and as 

 a is greater or less than 0*93, and is such that in the formula 

 D^Do + a^ + ySi 2 j8 is positive when ~ is lower than 3*77 



-L' e 



and negative when it is higher, a being negative in every 

 case. 



4. The curvature is generally so slight that the critical 

 density may be calculated from the mean densities of liquid 

 and saturated vapour at temperatures from about the boiling- 

 point to within a few degrees of the critical point by means 

 of the simpler formula ~D t =D + at with an error rarely 



