﻿Critical Temperatures of Homologous Compounds. 601 



6 per unit change in n, and (iii.) may therefore be written 



dd c__ v 



if we treat n as a continuous variable. This equation can — 

 theoretically — be integrated, yielding a relation between 6 

 and n which could then be compared with those of Bamuge 

 and of Walker. Unfortunately the resulting integral, 

 though apparently simple in form, does not integrate in 

 terms of any of the simple functions, and the series-form 

 into which it does integrate is somewhat unwieldy to 

 handle *. 



It will be seen that in Walker's formula 6 is assumed to 

 be proportional to a definite power of M; in the formula 

 now to be proposed a similar relation is assumed to exist 

 between the logarithms of 6 and of M — that is 



log<9=£(logM)% (v.) 



or, what amounts to the same thing, 



= M*(l°gM)*-i (vi.) 



When 6 is measured on the absolute scale, and logarithms 

 are taken to the base 10, we obtain for the normal paraffins 

 £• = 1-929 and * = -4134. These values for the constants I 

 and s hold with considerable accuracy over the range n = 4 

 to >i= 17, and were obtained by treating the observed boiling- 

 points over this range by the method of least squares. The 

 last two columns in Table I. f show the boiling-points as 











Table I. 













Boiling- 



Walker. 



Bainage. 



Young. 



Ferguson. 



Paraffin. 



Point 

 (Obs.). 











Calc. 



Diff. 



Calc. 



Diff. 



Calc. 



Diff. 



Calc, 



Diff. 





o 







« 



o 





o 







: 

 o 



C 4 H 10 ... 



274-0 





... 



275-6 



4-16 



2726 



-1-4 



2747 



4-0-7 



C 5 H 12 .. 



309-3 







312-2 



4-2-9 



309-4 



4-0-1 



3102 



4-0-9 



C 6 H 14 ... 



342-0 







343-9 



-1-1-9 



3420 



4-00 



341-9 



-01 1 



C 7 H 1G ... 



371-4 



373-8 



+2-4 



372-3 



4-0-9 | 371-3 



-01 



370-7 



-0-7 



C 8 H 18 „. 



398-0 



399-1 



4-0-5 



398-3 



-0-3 



398-1 



-0-5 | 397-2 - 1*4 1 



C,H,o- 



422-5 



422-9 



+0-4 



422-5 



4-00 



422-9 



4-0-4 ! 421-8 -0-7 i 



O 10 H 22 . 



446-0 



445-5 



-0-5 



445-2 



-0-8 



4459 



-01 I 444-8 | - 1-2 



C U H., 4 . 



407-0 



466-8 



-0-2 



4668 



-0-2 



467-4 



4-0-4 



466-5 I - 0*5 



C 1 . ) H. 1( . . 



487-5 



487-2 



-0-3 



487-3 



-0-2 



487-7 



4-02 



487-0 ' -0-5 



C 13 H 28 . 



5070 



507-3 



4-0-3 



507-0 



4-0-0 



506-8 



-0-2 



5064 -0-6 



°V1 H 30 • 



525-5 



5260 



4-0-5 



5260 



4-05 



5250 | 



-0-5 



525-1 -0-4 



G 15 H 32 . 



5435 



544-1 



4-0-6 



544-2 



4-0-7 



5423 



-1-2 



542-9! -0-6 



C IU H 34 • 



560-5 



561-9 



4-1-4 



5619 



4-1-4 



558-9 



-1-6 



560-2 -0-3 



C 17H 3C . 



576-0 







5790 



+3-0 



574-7 



-1-3 



576-4 4-0-4 



* For assistance in elucidating the properties of this integral I am 

 indebted to the friendly counsel of Mr. G. B. Mathews, 

 t The observed boiling-points are those given by Young, Phil. Mag. /. c. 



