Mathias and the Critical Density. 301 



the table, and it will be seen that the improvement effected 

 by introducing the third constant is very much smaller than 

 for the whole range of temperature. Thus the mean value of 



— falls only from 2*46 to 1*71, as against 5*40 to 1*51 for the 

 n £, 



whole temperature range, and for — the fall is only from 



0-fi4 to 0*30 as against 3*43 to 0*14. 



There is therefore for this range of temperature, except in 

 the more extreme cases (near the top and bottom of the table), 

 not very much to choose between the two formulae. ■ 



A' 

 On the other hand a comparison of the values of — for the 



n 



two formulae below the boiling-point brings out the difference 

 between them in a most striking manner. For the formulae 

 with two constants the first eight values are negative, and the 

 rest with one exception (ether, for which the experimental 

 errors are large and the temperature range small) are positive, 

 and, omitting the alcohols, they range from — 31*62 to + 22*36, 

 or, including the alcohols, to + 94*00. For the formula with 

 three constants the 4- and — signs are fairly evenly dis- 

 tributed, and, excluding the alcohols and acetic acid, the 

 extreme values are —0*90 and +1*00. Again, for the 



A' 

 simpler formula, the mean value of — , excluding the alcohols 

 1 n 



and acetic acid, is + 10*54, but for the formula with three 

 constants it is only +0*43. It is quite clear from this that 

 the constants for the formula D t = D + at calculated ex- 

 clusively from the densities at temperatures below the boiling- 

 point would in many cases differ very considerably from 

 those calculated from the densities at temperatures above the 

 boiling-point ; and that the differences between the calculated 

 critical densities \D c =D + a(T c — 273)} and also between the 

 values of a in the two cases might also be considerable. 

 Thus for normal octane the numbers would be 



D . a. D e . a. 



Below the boiling-point... '3592 -000409 '2381 0*978 

 Above the boiling-point... *3634 *000440 *2330 1*075 



The constants calculated from the densities below ihe boiling- 

 point approach fairly close to those obtained by M. Mathias 

 for normal decane from the densities between 0° and 100° 

 (p. 293) though, as might be expected from the higher mole- 

 cular weight of decane and from the fact that the densities 



Phil. Mag. S. 5. Vol. 50. No. 304. Sept. 1900. Y 



