150 -R. B. Drew and E. I. Rosenblum : 



The following results are of a preliminary natui'e, and are 

 concerned with the simpler cases of sueh an inquiry. 



Exveri men till. 



The method followed in the measurements hei-e recorded was to 

 make mixtures of various concentrations from materials prepared 

 as freshly as possible. The density, refractive index, and rotation 

 of these were taken at 25° C, with such methods and precautions 

 as accurate physicochemical Avork suggests. 



The pyknometer held about 6 c.c's., and the temperature adjust- 

 ment was correct to .Olo. The rotations were taken in a 100 mm. 

 *ube in a Schmidt and Haensch polarimeter. and the refractivia 

 indices in a Zeiss refractometer, and for eacli of these the diver- 

 gence in temperature did not exceed .1°. 



The mixtures themselves were made up by successive additions of 

 one constituent to a definite amount of the other — a method 

 economical of material — and the results have shown it to be justi- 

 fied, for any systematic error arising from this cause would in- 

 crease with each addition, and such increases have not appeared. 



Cnlculafion of Restdfs. 



We may comment here on the methods emphiyed for calculating 

 the theoretical value of any physical property of a liquid mixture'. 

 If the property under consideration is additive, and no anomaly 

 is present, Ave have — - 



P ^ m,V, + urj", 



(calc.) ^ yn^n,'^ 



where P,, P.j, are the Values of tlie pi-operty considered, fur the 

 individual substances, and m^ and u/.^ are the masses of these sub- 

 stances in the mixture. If the additive relationshiji does not hold, 

 however, we must modify the formula to express the effects of the 

 molecules, atoms oi- ions, wliich are the disturbing factor. Thus, 

 if the molecules are the reacting entities to be considered, we have 

 [Ml, M2 1)eing the molecular weights] — 



m,Pi ^/..Po 



P _ M7 M., 



(calc.) rn.2 m,^ 



Ml M, 



Since many factors in liquid mixtures are influencing a par- 

 ticular property, it is necessary to introduce more and more terms 

 before we can attain concordance. But since tlie diflficultv of in- 



