380 Boiling-Points of Homologous Compounds. 



8. It may be noticed that the logarithmic form of f(n) is 

 capable of a considerable range of adaptability. Thus when 

 b is small in comparison with c the differences become nearly 

 constant, and the linear formula is practically reproduced. 

 Again, it satisfies the halogen compounds, as shown in 

 Table IX., and in another form it represents the fragmentary 

 series of iso-paraffins, as shown in Table I. The corresponding 

 difference equation is 



AT = <KT)=alog(l + &.10- T/a ). 



If AT is strictly a function of T only, a and b must be 

 absolute constants. But in practice the merely approximate 

 truth of this law is probably consistent with a certain range 

 of variation in these numbers. The values used for the 

 halogen groups were a = 1000°, 6 = 0*155. It is more 

 difficult to compare the logarithmic with the hyperbolic 

 difference equation for the normal paraffins. But the values 

 a = 815, 6 = 0-223 make the two nearly coincide from 400° 

 to 600°, and below 400° they diverge more and more. 



Hence it is impossible to represent the normal paraffin 

 series as a whole by the logarithmic formula. And yet the 

 relation is worth examination. Experience suggests that it 

 is more important to represent the higher members than to 

 imitate the whole series by an indifferent compromise, for the 

 greatest difficulties are always met with in the lower terms. 

 When this is done the lower members show marked residuals 

 which can, however, be easily represented by an empirical 

 correcting term. The result is to give the formula : 



T = 800° log (0-2323 n 4- 1-290) - 70°/2", 



which is compared with experiment in Table X. The 

 formula is certainly artificial, but its type is suggested by 



Table X. 

 Normal Paraffins : C 7l H 2n -}-2. 



n. T. Calc. O-C. 



o o o 



0. 204 18-5 +19 



1. 1083 111-0 -2-7 



2. 180-0 177-8 +2-2 



3. 229-0 229-7 -0'7 



4. 272-8 272-6 +0-2 



5. 309-2 309-3 -01 



6. 3420 341-9 4-0-1 



7. 371-4 371-2 4-0-2 



8. 398-6 398-1 4-05 



9. 423-5 4231 4-04 



n. T. Calc. O-C. 



10. 416°0 4462 -0°2 



11. 467-0 467-9 -09 



12. 487-5 488-3 -0'8 



13. 507-0 507-6 -06 



14. 525-5 525-8 -03 



15. 543-5 543-1 4-0-4 



16. 560-5 559-6 +0-9 



17. 5760 575-4 +0-6 



18. 590-0 5905 -0-5 



19. 6030 604-9 -19 



