( 299 ) 



«=-« + -^ (HI) 



which gave tlie errors given in tho third column of the table. 



3. Laiv of mixtures. "When we wish to apply the corrections 

 for impurities in the gases investigated, we have to assume a law, 

 from which the magnetic rotatory constant of a mixture can be 

 calculated from the constants of its constituents. Tn a former com- 

 munication 1) a simple law has been assumed, without any conside- 

 ration of its theoretical basis. 



We can deduce this law from the supposition that the magnetic 

 rotation is an additive property^ and that the rotatory constant of 

 a mixture is therefore equal to the sum of a number cf terms, to 

 which each molecule contributes one. Let the condition of the mix- 

 ture be determined by the pressure p, by the temperature t and for 

 the rest by assuming that in the unit of volume «iVgrammolecules 

 of one component are mixed with (I — //)iV of the other. Let 

 (Jp.Uv^ ^^ t'le amount which a grammolecule of the first component 

 contributes to the rotatory constant, and ^"/>,f,i_^ the same for the 

 other component and let ^^(Ji>,t,i^ he the rotatory constant of the 

 mixtuie, then we find that 



^V i>j)^ t,i^^ 3' ," (j'p, M^ + A' (1 — a) ()'),^ ,_ i_^ 

 and therefore 



(>P- 1,1^ =^ ft (/'p, (, K + (1 — /') i'"p, 1. 1— c • 



The quantities (Jp,t,^ ■, introduced here, which we might call 

 molecular rotatory power, will depend on the condition of the 

 molecules determined by />, t and fi. The way in which they depend 

 on these variables cannot be deduced from the observations without 

 the aid of a molecular theory, except in the case when u = and 

 we have therefore to deal with simple substances. 



In applying this law we assume these quantities (v to be constants 

 and then we can deduce them from those for the simple gases. Let 

 )•' and r" be the rotatory constants for the two gases at the pressure 

 p and the temperature t. Let further .c and y be the volumes of 

 the two substances which we should have to mix in order to obtain 

 the unit of volume of the mixture, all these volumes being measured 



») Verslag Kon. Akacl. lS9i/95, p. 230. Coram. Pliys. Lub. Leiden \". 15 p. 36. 



