378 Prof. H. C. Plummer on the 



approximate, is good and useful in its own sphere. A 

 residual of 10 per cent, in a difference is often innocuous 

 and smaller than the effect of experimental error. But a 

 residual of 1 per cent, in the absolute temperature is 

 generally unsatisfactory. Hence the determination of f(n) 

 and </>(T) are in practice quite different problems, and the 

 former is the more exacting. 



Thus we have been led to treat differently three classes of 

 compounds. The first, typified by the alcohols, with marked 

 chemical association, is represented by a linear formula. 

 The second, an intermediate type containing the ethers and 

 esters, has slight molecular association and the boiling-points 

 show a slight degree of curvature which is fairly represented 

 by a parabolic formula. Finally, the very complete series 

 of normal paraffins has been taken as the type of compounds 

 free from association, and the well-developed curve formed 

 by their boiling-points has also been represented by a 

 parabolic formula of another kind. In one or another of 

 these three classes probably all series of boiling-points can 

 be more or less well represented. Thus to the first class 

 may be attributed : 



Cyanides (Cja 2?l+1 -ON) : T = 19°-14 (ii + 17'5), 

 Nitro-compounds (O n Ha» + i-NO s ) : T = 16°'9 (n + 21), 

 Ketones (CH 8 - 00-0^^0 : T = 23°'52 (n+13), 



and to the second class : 



Acids (C n H 2>l+1 -CO()H) : T = 368°-83 + 23 o -34rc-0°-6437i 2 . 



The comparison, which suggests some irregularities in the 

 experimental data, need not be given. 



So far as the parabolic formula found to represent the 

 normal paraffins can be regarded as strictly typical, it applies 

 to series of hydrocarbons which are for the most part very 

 fragmentary. Two examples are given in Table VIII. In 

 the first series the constant additive to n in the formula is 0, 

 and the calculated values are taken without change from the 

 third column of Table VII. In the second case the constant 

 added to n in the formula is 6*1. 





Table VIII. 









HC»H2»C 



= CHC n H2 ?l . 





C 6 H 5 w H2 ra -j-i. 





n. T. 



Oalc. O-C. 



n. 



T. 



Calc. 



O-O. 



4. 2740 



272°-7 +1-3 



1. 



383°6 



382-4 



o 

 + 1-2 



5. 309-5 



309-4 +0-1 



2. 



409-0 



408-4 



4-0-6 



6. 341-0 



342-0 -1-0 



3. 



4315 



432-4 



-0-9 



7. 371-0 



3713 -0-3 



4. 



453-0 



454-9 



-1-9 







5. 



4745 



476-0 



-IS 



