§ 5 OF ARTS AND SCIENCES. 373 



In all these cases the attraction only of the atoms in 

 direct union with a given atom is taken into account. 



The calculated and observed values of the principal 

 ratio are compared as follows: 



Calculated. Observed. 



Bisulphide of Carbon . . . 0.90 to 0.94 0.89 



Turpentine 0.83 to 0.90 0.93 



Ether 0.84 to 0.91 0.74 



where it will be noticed that the calculated and observed 

 values agree almost within the limit of probable error of 

 the latter, according to a statement already made. 



It was pointed out in the last section that a liquid might 

 in some cases be treated as a mechanical mixture of two of 

 its components, if the properties of these components were 

 known. 



We have for a mechanical mixture of A volumes of a 

 liquid whose properties are designated by a prime ('), and 

 J3 volumes of a liquid designated by two primes ("), the 

 equations, 



J. _ AL' -\-BV 

 A-\-B 



D = 



AD + BD' 



A \- B 



Ae' + Be" 

 A + B 



A + B 



E r= 



~ E ' E" 

 so that, if ^ -|- j^ = I , we have 



A . B 



J LP ^ J {AL' 4- BV) {AD' 4- BD") 

 EeT EE" {A^-{-B^)T '■ 



AE" + BE' 



