Index of Refraction of Liquefied Gases. 359 



perfect concordance between the theoretical relation and the experi- 

 mental values is necessary, yet the w 2 -expression can be adapted in 

 much higher degree to the observations than the empirically estab- 

 lished ^-expression ; and the difference between the calculated and 

 observed quantity is in most cases no more than that existing also in 

 the very accurate experiments of Lorenz, given in the table on p. 358. 

 With the latter expression the value of the proportion is generally 

 decreasing when the substance becomes gaseous ; with the former it is 

 increasing ; yet there are some exceptions.* Especially with nitrous 

 oxide, there is a greater difference than with others, and I know of 

 no peculiar cause for it, as I repeatedly examined the index. I must 

 observe that also among the substances given in the paper of Lorenz, 

 some of them may be remarked (for instance, the acetate of ethyl) as 

 presenting a far greater difference than others. The ethylene, also, is 

 distinguished among the other substances by a far less concordance, but 

 I may perhaps account for it by the very conditions of the experiment, 

 as this had to be conducted very near to the critical temperature of 

 the liquefied substance. I must add, however, that if, with the value 

 of the proportion given in the table for the liquid ethylene, the equi- 

 valent of refraction is calculated, the result is most satisfactory, 

 corresponding to that deduced from refraction equivalents of the 

 composing elements, added together.f Accordingly we have 



Refr. equiv. C 2 H 4 =0'321 x 28=8'99, 

 Eefr. equiv. 2C + Refr. equiv. 4H=4- 



Of course such verifications may be made also for the other sub- 

 stances of the former table, and calculated for their liquid condition, 

 but as these may be deduced as well from the gaseous state, and 

 generally with more accuracy, I think there is no peculiar interest in 

 adding the results. 



* In the experiments of Lorenz this value is for the examined compounds always 

 increasing when they become gaseous ; in those of Prytz it is for some increaeing, 

 for others decreasing. 



f I employed in this calculation the expression M( z l)/( 2 + 2)rf, in which M 

 represents the molecular weight of the compound, and the refraction equivalents of 

 C( = 2'43), and of H( = 1'02) were taken from the paper of Landolt (" Sitzungsber. 

 Preuss. Acad. v. Wissensch.," 1882, I, p. 43). If the other expression, M( l)/rf, 

 and the corresponding values, C = 4'86 and H= 1/29, are admitted, the concordance 

 is much less, as we obtain 13'94 (observed) and 14'88 (calculated). Professor 

 Gladstone remarks that as the carbon atoms in this compound, according to current 

 theories of chemical constitution, are to be considered as double-linked, the 

 calculated value is much higher (10'53 or 16'88) ; the difference from the experi- 

 mental value is too great to be accounted for by errors of ob-ervation. 



J Landolt, in the paper alluded to above, made such verifications with both 

 expressions applied on nearly fifty organic compounds, and concluded that the 2 

 formula gives more accurate results than the other when applied to the index of a 



