﻿Critical Temperatures of Homologous Compounds. 603 



values of these constants, as 

 between log R and log n, are 

 closeness with which equation (vii.) fit 

 is exhibited in Table IT. below. 



determined from the graph 

 £=•120 and A = 1-841. The 



the observed values 



Table II, 



V. 



R (observed). 



R (calculated). 



Per cent, error. 



1 



1764 



[1-841] 





2 



1-694 



1-693 



-0 06 



3 



1-623 



1-614 



- 0-56 



4 





1-559 



-0-38 



5 



1-520 



1-517 



-0-20 



6 



1-485 



1-481 



-0-27 



7 



1-454 



1-457 



+0-21 



8 



1-427 



1-434 



+0-50 



9 





1-415 



+0-14 



10 



1-402 



1-396 



-0-43 



Average percentage difference neglecting sign =0'33 per cent. 



It seems therefore that, apart from the first member of 

 the series, which, as usual, is anomalous, equation (vii.) fits 

 the observed values very exactly. It can easily be deduced 

 from (vii.) that if R» and R, l+ i be two successive values of 

 R for two paraffins having n and n + 1 carbon atoms in the 

 molecule, then 



R » (-, ] Y , «.\ 



iw = l 1+ »)' • • • • (viI1 -> 



bringing out quite clearly the observed facts that the value 

 of R decreases as n increases, but at a decreasing rate. In 

 fact, if (vii.) can be assumed to hold over any wide range, 

 (viii.) shows that for large values of n the corresponding- 

 values of R tend to become equal. 

 Writing (vii.) in the form 



c n*=h0, (ix.) 



it is clear that 9 can be eliminated between (ix.) and any of 

 the various formulae [(i.), (ii.), (iii.), and (v.)] proposed to 

 represent the relation between boiling-point and constitution. 

 We thus obtain empirical formulae for C which will vary 

 in form according to the particular boiling-point relation 

 chosen. 



Thus, eliminating 6 between (ix.) and AValker's equation (i.) 



* The observed values of R are given by Young, ' Stoichiometrv, 5 

 p. 183. ' e 



