Properties of Aqueous Solutions to their State of Ionization, 49 



Bender's determinations of thermal expansion are for the 

 interval between 15° and 20° 0. ; and will therefore be suffi- 

 ciently nearly proportional to the coefficients of expansion at 

 18° for my purpose. He considers that they may be in error 

 by ± 2 in* the sixth place of decimals. On plotting his obser- 

 vations, however, it becomes obvious that they do not all 

 attain this degree of accuracy. The expansion of water was 

 taken, according to his observations, to be O0 3 878 for the 

 same interval. 



Bruckner's observations of viscosity were made at 15° C. ; 

 but he gives an interpolation formula, applicable between 15° 

 and 20°, by means of which at least approximate values for 

 18° were obtained. His values for water at 15° and 20° do 

 not agree well with those given by Landolt and Bornstein. 

 1 have therefore taken 0"010613 as the viscosity at 18° of the 

 water used by him, a value which has to his value at 15° the 

 same ratio as Landolt and Bornstein's for the same tempe- 

 ratures. The actual concentrations of Bruckner's solutions 

 differed from those given in the tables below by about 0*1 

 per cent. ; but so small a difference could produce no appre- 

 ciable error in the result. He gives as his " mean probable 

 error of observation," +2*4 in the fifth place of decimals for 

 sodium- chloride solutions, and +1*8 for those of potassium 

 chloride. 



Rother's observations of surface-tension were made at 15°, 

 and are therefore not precisely comparable with calculated 

 values based on the values of ionization-coefficients for 18°. 

 From Kohlrausch's data*, however, it would appear that 

 between 15° and 18° in the case of potassium-chloride solu- 

 tions containing 0'5 and 3 gramme-molecules per litre, the 

 ionization-coefficient changes only by about 0*13 and 1*3 per 

 cent, respectively ; and in the case of sodium-chloride solu- 

 tions of the same concentrations only by about 04 and 0*6 

 per cent, respectively. For the more dilute solutions, there- 

 fore, my calculations will be practically comparable with 

 Rother's observations. He seems to regard his determina- 

 tions as possibly in error by + 5 to 8 in the third place of 

 decimals. The surface-tension of the water he used he found 

 to be 7-357. 



Bender's observations of refractive index were made at 

 15° 0., but were reduced to 18° by means of data provided 

 in his paper, based on observations made by Fouqucf. The 

 refractive index of the water he used he found to be 1-33310 



* Wied. Ann. xxvi. (1885) p. 2L>3. 

 t Compt. Rend. lxiv. (1867) p. 121. 



Phil Mag. S. 5. Yol. 43. No. 260. Jan, 1897. E 



