Theory of the Equivalent of Refraction. 187 



M. Haagen takes for chlorine a value 1\2 higher, ro'(Cl)=9*79, 

 than corresponds to the observation of the isolated element. 



Haagen, it is true, by means of this higher value for chlorine, 

 gains the power of deriving the retractive equivalents of the ehlor- 

 hydroearbons under the assumption of a small mean error. But 

 the above example of terchloride of phosphorus shows that the em- 

 ployment of mean values may easily lead to mistakes. I myself 

 in my " Studies/ 7 in considering the organic series, could have 

 adopted many more simple derivatives for 2D?, if I had neg- 

 lected the consequent great differences in the equivalent of 

 dispersion 0t If the dispersion be neglected, the mean differ- 

 ences for the refraction between observation and calculation 

 from the elements are certainly small, and in many cases a very 

 simple derivation from the elements is possible. But such a 

 procedure is still one-sided. 



Indeed the numbers for the compounds of chlorine give, as it 

 appears, a very easy proof of the necessity of factors, namely : — 



The difference between the observed values for chlorine and 

 hydrogen (here, and afterwards, D(IT 2 0) = 773) is 



m (CI) -m(H)= 0-01 1-0-002 = 0-009; 

 and this difference (Cl — H) appears on deriving many of the 

 chlorhydrocarbons. 



If we compare such substitution-products (compare my '* Stu- 

 dies"), 



(a) Chloride of ethylene, C 2 H 4 CI 2 , m = 0-0410 A _ ft m , - 

 Bichloride of ethylene, C 2 II 3 CI 3 , 0-0557 - A_U UL *' * 



{b) Chlorobenzol . . . C 6 H 5 C1, m = 006 16. _ . ft ni 10A 

 Trichlorobenzol . . C fi H 3 Cl 3 , 00869^ "^ U1W '» 



the differences A derived from the observations for (Cl — H) differ 

 considerably from the former number, 0*09. In the first case 

 y = 0-0057, in the second v' = 0*0021. If in this calculation 

 i)(ll 2 0) = l, then \7 = 4*40, a deviation which attains almost 10 

 per cent, of the value of the observation itself. 



Similar facts and the necessary consideration of the dispersion 

 have caused me in my " Studies " to retain the theory of simple 

 factors, and to tit this as closely as possible to the molecular 

 processes of chemical substitution. If in this investigation it has 

 appeared that all the atoms of an element which occur in a com- 

 pound are not of equal value, and if, further, the theory of New- 

 ton's equivalents of refraction leads to the assumption of several 

 modifications of the elements, both of these are in accordance 

 with modern chemistry; for chemistry already recognizes four 

 modifications of carbon, distinguished by their atomicity. 



