of Hydrocarbons and their Mixtures, 129 



Illuminating Ratios from Disilluminate Hydrocarbon 

 Point, -138, 0. 



Carbon 

 density. 



Substance. 



Experi- 

 mental 

 number. 



Adjusted 

 number. 



Differences of 



successive 



terms. 



1 

 2 



3 

 4 

 5 



6 



Marsh-gas 



Ethylene 



65 —180 



108 

 180 



228 

 260 

 281-3 

 295-5 



72 

 48 



32 



21-3 



14-2 



•5-138 

 54 -228 



Benzene 



•375- -138 



255 —295-8 



1-.138 



The differences form a geometrical progression, which has 

 the common ratio 2/3, and 108 for the first term. Thus the 

 successive units of carbon density correspond to increments 

 of illuminating ratio in strict geometrical progression, and all 

 the numbers present a continuous law*. 



To find the C.P. of any hydrocarbon, as determined by 

 these numbers, we use the equation 



y — y r =zm(x—x r ), where dj' = '138 and y r = 0. 



m stands for the illuminating ratio. 



Thus to find the value of the C.P. of marsh-gas, as indicated 

 by this scheme, we have 



whenct 



y = 108 0--138) and #='25, 

 y=C.P. = 12-l, 



a somewhat lower value than that (12*4) previously found 

 from the ethylene mixtures. The agreement is remarkable, 

 considering the entire independence of the two methods. 

 For another example take tetrane, C 4 H 10 , 



y = 260(a;--138), and a> = -4, 



C.P. = 68; 



* The difference 48 was taken as fixed, and. the factor found which 

 would bring the benzene number right ; it proved to be just 2 3. This 

 was then applied to form the first term, which fell into its place. 



Phil. Mag. S. 5. Vol. 34. No. 206. July 1892. K 



