376 



Prof. H. C. Plummer on the 



5. But by far the most important single series is presented 

 by the normal paraffins, both on account of the number of 

 consecutive members and the special care with which the 

 boiling-points have been determined. It has also received 

 the greatest amount of discussion. Table VII. conveys the 

 results of considering this series from more than one point 

 of view. In the first place, the boiling-points in the third 

 column are calculated bj- the formula 



T= -69-0 + 184-65v/n- 6'89 n. 



The comparison given in the next column shows that this 

 formula successfully represents T as a function of n. In 









Table VII. 













Normal Paraffins : C n H 2w +2. 





n. 



T. 



Calc. 



o-c. 



AT. 



Calc. 



O — C. Cum. sum. 



(Young. 



1. 



108-3 



1087 



o 



-0-4 



o 

 71-7 



o 

 70-5 



o 



4-1-2 



o 



-0-2 



o 



4-1-2 



2. 



180-0 



178-3 



+ 1-7 



490 



51-4 



-2-4 



4-1-0 



4-1-9 



3. 



229-0 



230-1 



-1-1 



43-8 



42-7 



4-11 



-1-4 



-1-2 



4. 



272-8 



272-7 



+o-i 



36-4 



36-4 



00 



-0-3 



-0-2 



5. 



309-2 



309-4 



-0-2 



328 



32-5 



4-0-3 



-0-3 



-0-6 



6. 



341-95 342-0 



o-o 



29-4 



293 



4-0-1 



o-o 



-0-4 



7. 



371-4 



371-3 



+0-1 



27-2 



26-8 



4-0-4 



4-0-1 



-0-3 



8. 



398-6 



398-2 



+0-4 



24-9 



24-8 



+0-1 



4-0-5 



4-0-1 



9. 



4235 



423-0 



+0-5 



22-5 



230 



-0-5 



4-0-6 



4-0-2 



10. 



446-0 



446-0 



o-o 



21-0 



21-6 



-0-6 



+0-1 



-0-2 



11. 



467-0 



467-6 



-0-6 



20-5 



20-4 



4-0-1 



-0-5 



-0-8 



12. 



487-5 



487 9 



-0-4 



19-5 



19-3 



+0-2 



-0-4 



-0-6 



13. 



507-0 



507-2 



-0-2 



18-5 



18-3 



4-0-2 



-0-2 



-02 



14. 



525-5 



525-6 



-01 



18-0 



17-3 



4-0-7 



00 



+0-1 



15. 



543-5 



542-8 



+ 0-7 



170 



16-5 



4-0-5 



4-0-7 



4-0-8 



16. 



560-5 



559-4 



4-11 



15-5 



15-8 



-0-3 



4-1-2 



4-1-2 



17. 



576-0 



575-2 



4-0-8 



14-0 



15-2 



-1-2 



40-9 



4-09 



18. 



590-0 



590-4 



-0 4 



130 



14-6 



-1-6 



-0-3 



-0-3 



19. 



603 



605-0 



-.20 









-1-9 



-1-9 



the second place, the observed boiling-points have been 

 differenced, following the ideas of Prof. Young, and 

 represented by the formula 



20648 



AT. 



13-82. 



T 4- 136-6 



The numbers calculated in the sixth column by this formula 

 are based on the observed values of T in the second column. 

 The residuals are shown in the seventh column, and the 

 cumulative sum of these in the eighth column, the first term 

 being chosen so that the sum of the column is. nearly zero. 

 This column fairly shows the result of building up the series 

 by successive differences and should be comparable with the 



