132 Dr. M. Wildermami on the 



—■: -distinguishes Loomis's method in a great many points, are 

 affected with greater experimental errors than Mr. Lbomis 

 supposes to be possible. The results which I have obtained 

 with my yJo° thermometer by a method which by far sur- 

 passes Loomis's method in precision, are more or less of the 

 same character (see Table IF.) . At the same time with the 

 observations recorded above and made with a to -q° thermo- 

 meter on cane-sugar, urea, and alcohol, similar observations 

 were made with a t ^q° thermometer. The results obtained 

 are affected by experimental errors of from o, 001-0 o, 002°, 

 and even occasionally greater; and that means that we cannot 

 use the y^o° thermometer for minute readings in very dilute 

 "solutions. For with the yJyo° thermometer we have to deal 

 with experimental errors which cannot easily be removed or 

 eliminated. In the first place it is not easy to avoid errors 

 of from 1 to 2 thousandths degree in making the readings, 

 " even with the use of a microscope and a micrometer-scale, 

 although with the method mentioned above we are able to 

 observe the obtained freezing-point during the 10 to 15 minutes 

 occupied making several readings ; the more must that be 

 the case with other methods, where the obtained freezing- 



- -jpoint can be observed only a short time. Now even in 

 solutions which are only diluted to ^~- or -^ molecule-normal, 

 an experimental error of o, 002 makes a difference of about 

 3 to 5 per cent, (in the case of non-conductors) in the lowering 

 observed, and therefore also in the -calculated molecular 

 lowering of the freezing-point. The j^o° thermometer can 

 therefore in very dilute solutions only give us qualitative data. 



II. Proof of Arrhenius's Generalization. 



We proceed to the generalization of Arrhenius. Van't Hoff 

 showed by four different methods, that a law analogous to that 

 of Avogadro was valid for solutions of non-electrolytes like 

 cane-sugar ; it then became of importance to account for 

 exceptional cases in which the depression of freezing-point 

 was abnormal, and in particular the cases of salts, acids, and 

 bases in aqueous solution. The explanation was given when 

 Arrhenius showed that by two independent quite different 

 methods, the observation of lowering of freezing-point and of 

 the electrical conductivity of a solution, the same value would 

 be obtained for the factor i, which denotes the ratio of the 

 pressure actually exerted by the substance to the pressure 

 which the substance would exert if it consisted entirely of 

 nndissociated molecules. 



Arrhenius made determinations on about 40 bodies in mode- 

 rately dilute solutions of various concentrations and verified 



