526 PROFESSOR DITTMAR AND MR C. A. FAWSITT ON 



From 20 per cent., or rather somewhere between 20 and 30 per cent, 

 downwards, the value a as we see becomes ^constant. Retaining the second 

 term in the formula S — $ t = at + bf, we found the following values for this a 

 and for b : — 



Percentage of CH 4 0. 



100 to 80 



a. 



b. 



Some small 



value 



70 



74-03 



+ 0158 



60 



7243 



-0-018 



50 



64-94 



+ 0-022 



40 



54-63 



+ 0107 



30 



43-59 



+ 0-055 



20 



21-30 



+ 0-408 



10 



3-06 



+ 0-535 



5 



-4-05 



+ 0-672 



0* 



-5-65 



+ 0-685 



Seeing that the equation S — S 4 = at affords a sufficient approximation for 

 all alcohols from 30 per cent, to 100 per cent., we tried to calculate an inter- 

 polation formula for the relation between the per-unitage p of CH 4 and the 

 value of a which should cover the whole of this interval, but found that an 

 equation of the second degree did not establish sufficient agreement between 

 experiment and calculation. We ultimately divided the interval into sections 

 as follows : — 



I. From£>=l to^> = 0*6 {i.e., from 100 per cent, to 60 per cent.). Adopted 

 formula 



a = a + bp + cp 2 ; 



the constants were calculated from the six experimental values by the method 

 of the least squares, and found to be 



« = 35-018; log a = 1-544 29 

 b = 68-379; log b =1-834 92 

 c = -11-718; logc =1-068 84 



Contrasting the calculated with the experimentally determined values of a, 

 we have 



p- 



a. 



By Formula. 



a. 

 15y Direct Det. 



1- 



91-68 



91-75 



0-95 



8940 



89-40 



090 



87-07 



86-81 



0-80 



82-22 



82-86 



0-70 



77-14 



76-35 



0-60 



71-83 



7217 



* By Rosetti's Table for the specific gravities of water. Our constants give +4°-l as (be 

 temperature of maximum density. 



