CONDUCTIVITY OF SODIUM HYDROXIDE IN AQUEOUS SOLUTION. 275 



usually the volume was increased to 15 cub. centims. or 25 cub. centims. in order 

 to reduce the errors of adjustment and weighing ; the accuracy of the observations 

 was not very much increased by using larger tubes, and probably the chief source of 

 error arises from fluctuations of temperature. In the case of the concentrated 

 solutions the great viscosity called for the exercise of some degree of patience ; to fill 

 a tube, even with the help of an efficient pump, often required an hour or more, and 

 it was noticed that more than an hour elapsed before a tube of 47 per cent, soda 

 (capacity 25 cub. centims., diameter less than 2 centims.) acquired a steady tempera- 

 ture when cooled in powdered ice. At the lower temperatures the solutions were 

 frequently supersaturated, but we did not experience difficulty on account of 

 crystallisation either in the density tubes or in the conductivity vessels, though 

 occasionally the stock solutions deposited magnificent transparent plates of hydrated 

 soda. From five to ten measurements were made with each solution, the temperature 

 being steadily raised throughout the series ; the error due to the action of the soda 

 on the glass does not appear to be serious, and no change whatever could be detected 

 in the density at 20 C. of a 47-per cent, solution after heating for an hour each at 

 60 C., at 75 C. and at 100 C. 



Form of the Curves. Interpolation Formula. A consideration of the density- 

 temperature curves for a series of percentages beginning with water and ending with 

 50 per cent, soda showed conclusively that all the relationships could be represented 

 with a close approach to accuracy by equations of the form 



p = pt+at+flt'+yfl. 



It was further found that at about 12 per cent. NaOH the coefficient of t 3 vanished, 

 and that thenceforward up to 50 per cent, the relation could be expressed within the 

 limits of experimental error by an equation of the second degree. In order to make 

 these results clear, we append in Table VII. a list of the observed densities for water, 

 decinormal, normal, 26'68 per cent., 34'43 per cent, and 42'54 per cent. NaOH, 

 together with the densities calculated from the cubic or quadratic formulae. Only in 

 exceptional cases did the observed and calculated densities differ by more than 0*0003, 

 but it is necessary to add that a close agreement on a single series of observations did 

 not necessarily afford a measure of the accuracy of the series, since a serious error 

 at 100 C. might well be masked by an alteration in the coefficients which would not 

 seriously disturb the values calculated for the density at lower temperatures, and 

 would not appear until different series were compared with one another. 



For this reason we deemed it very important to check the density-temperature 

 observations by drawing isothermal density-percentage curves for various tempera- 

 tures and by noting the gradual change in the coefficients of expansion with changing 

 concentration. The temperatures chosen for the isothermal curves were C., 18 C., 

 50 C., and 100 C., and, having already plotted an accurate isothermal curve for 18 C., 

 it was only necessary now to plot the differences p Q pw, Popw an d PoPvxr The 



2 N 2 



