6 McBAIN 



in special cases will equal volumes of solutions of different con- 

 centrations contain the same amount of solvent. Hittorf^ 

 picked out particular cases measured by Wiedemann and 

 showed that the error thus introduced amounted to as much as 

 20 percent of the migration value ; in other cases it was neg- 

 ligible. In very dilute solutions this error vanishes. Another 

 method bases the calculation upon constant weight of solution ; 

 as is evident, this is always wrong. Here, again, the error is 

 worst in concentrated solutions, and becomes negligible when 

 the solutions are very dilute. In general, I have had to leave 

 it to the reader to calculate whether the error introduced by 

 wrong methods of calculation is large or not ; in a few cases, 

 however, I have made the calculation myself, and when the 

 error was vanishingly small, I have stated that the results were 

 correctly calculated. 



Possibly the following consideration of the effect on the trans- 

 port number caused by neglecting the loss of gases at the elec- 

 trodes may be of use. During the passage of 96,540 coulombs 

 8 grams of oxygen escape, hence the amount of the constituents 

 of the solvent at the anode appears to be 8 grams less than 

 really was, and so the apparent migration value of the anion is 

 increased by the number of g-mols of electrolyte contained in 

 8 grams of water. This holds for all electrolytes where oxygen 

 is evolved at the anode. Similarly, the migration value of the 

 cation obtained at the cathode where hydrogen is escaping is 

 increased by the number of g-mols of electrolyte in one gram of 

 water; this is generally negligible. The correction to be sub- 

 tracted from the migration value of the anion found b}- analysis 

 at the anode is therefore 0.008 for normal solutions and 0.0008 

 for decinormal solutions ; similarly for the cathode analysis, one 

 eighth as much has to be added to the migration number of the 

 anion. These corrections are mostly negligible, but the calcu- 

 lation is useful as showing the absolute value of the errors intro- 

 duced by the chemical processes at the electrodes. It is easy to 

 extend it to other cases ; for instance, the correction at the 

 cathode where a metal is precipitated and not weighed, is equal 

 to its gram-equivalent weight multiplied by the correction de- 



iPog. Ann., 103, 8 (185S). 



