Mathias and the Critical Density. 293 



rature and pressure as observed by Knietsch is only 3*03, a 

 very low number. 



Among the other substances examined by M. Mathias is 

 normal decane, for which the densities of liquid have been 

 determined only at low temperatures. In this case the values 

 of a, a, and D e seem to be at variance with those obtained by 

 myself for the lower normal paraffins, as will be seen from 

 the table below : 



Pentane '000460 0*931 "2324 



Hexane '000446 0'967 "2343 



Heptane '000440 1*013 '2344 



Octane '000440 1*075 '2330 



Decane '000380 0*928 *2471 



For the four lower paraffins a and D c show very slight 

 variations, whilst a rises considerably with increase of mole- 

 cular weight, so that the values calculated for decane appear 

 improbable. 



In view of these apparently abnormal results it seemed 

 advisable to undertake a careful examination of the whole of 

 the data which I have obtained for thirty substances. In all 

 cases except the alcohols the critical densities were calculated 

 by the method of (Jailletet and Mathias, the mean densities 

 above the boiling-points only having been used except for one 

 or two substances; and though the deviations from the formula 

 De - D ■+- at differ somewhat considerably, there did not appear 

 to be any definite tendency to curvature except possibly in a 

 few cases. I have, indeed, attributed these deviations to 

 errors of experiment ; and this view was strengthened by the 

 fact that for normal pentane, with which very careful deter- 

 minations were made from 0° to within 0°'05 of the critical 

 temperature, the deviations were exceedingly small and well 

 within the limits of experimental error. 



As will be seen later, however, it turns out that in choosing 

 normal pentane for this special investigation I happen to have 

 hit on the one substance which does not show the slightest 

 deviation from the law of Cailletet and Mathias. 



Since the publication of M. Mathias's paper I have calcu- 

 lated the mean densities of all thirty substances at intervals 

 of ten degrees between 0° and the boiling-point ; and it 

 became evident that for many of them the deviations increased 

 rapidly below the boiling-point. Moreover, on plotting all 

 the differences between the mean densities and those calcu- 

 lated from the formula D^=D -|-a£ against the temperature, 

 distinct curvature was noticeable in many cases. This will be 



