Mathias and the Critical Density. 299 



A comparison of the results by the two formulae is given in 



A 

 Table III. Under — are given the mean differences mul- 



tiplied by 10 4 between the observed and calculated densities 



A' 

 without regard to sign ; under — . the algebraical sum of the 



differences multiplied by 10 4 and divided by the number of 

 observations. 



The numbers under I. refer to the formula with two con- 

 stants, those under II. to the formula with three constants 

 (four for the alcohols). 



Taking the whole range of temperature for each substance 

 it will be seen that the agreement when the three constants 

 formula is used is very much better than when the simpler 

 one is employed. Excluding the alcohols and acetic acid, the 

 molecules of which are almost certainly of different complexity 



in the gaseous and liquid states, the mean value of - for the 



26 substances is 5*40 for the formula with two constants as 



A' . 

 against 1*51 for that with three. That — is very small in 



each case for the formula with three constants, not only for 

 the whole range of [temperature but also for the temperatures 

 above and below the boiling-point taken separately, may be 

 regarded as evidence that the curves represent the results 



with satisfactory accuracy ; and, if that is so, the values of — 



for the same formula may be taken as a measure of the 

 experimental errors which, it will be seen, differ considerably 

 for different substances. The large errors in the case of 

 stannic chloride may be explained by the fact that this com- 

 pound attacks mercury at all temperatures whilst carbon 

 tetrachloride does so at high temperatures, so that special 

 experimental methods had to be devised. Again, the observa- 

 tions with iodobenzene had to be made by artificial light as 

 the substance becomes rapidly coloured on exposure to day- 

 light. Acetic acid gave a good deal of trouble at the highest 

 temperatures, owing to repeated bursting of the tubes, but the 

 comparatively large errors with ether and ethyl and propyl 

 alcohol are not easily accounted for. 



It remains to be seen whether the simpler formula D<=D 

 + at is sufficiently accurate to be employed for temperatures 

 between the boiling-point and the critical-point. The values 



A A' 



of — and — above the boiling-point are therefore given in 



