270 MR. W. R. BOUSFIELD AND DR. T. M. LOWRY ON THE ELECTRICAL 



At the lower concentrations the density measurements are less tedious and more 

 exact, and the strength of the solution is known with sufficient accuracy to justify 

 the inclusion of the fifth place of decimals in the table of density. Within the 

 range from 20 per cent, to per cent., 28 measurements of density were made. 

 Usually two determinations were made with each solution, and the densities deduced 

 from the weighings of the two pyknometers did not differ in any case by more than 

 0-00002. Within the whole range, from 20 per cent, to per cent., the relative 

 values for the densities are probably exact within '00002, but the absolute values 

 are subject to a possible error of about 0-00005 in the range from 25 per cent, to 

 20 per cent. NaOH, 0'00004 from 20 per cent, to 15 per cent., and 0-00003 from 

 15 per cent, to 10 per cent. 



Interpolation Formulae. The curve connecting density and concentration is 

 approximately linear in character, curvature being most marked from 5 per cent, 

 to per cent., and less so in the range from 30 per cent, upwards, but apart from 

 this it does not exhibit special peculiarities. The curve is therefore of little use 

 either for indicating the constitution of the solution or for interpolation. For the 

 latter purpose we have made use of three kinds of sensitive curves. 



I. A very convenient means of interpolation consists in recording the extent to 

 which the ordiuates of the density curve differ from those of the diagonal line y = x 

 shown in Diagram I. (p. 310). This sensitive curve is obtained by plotting p (1 -j-0'01 P) 

 against P, and has the form shown hi the diagram. In using it we have set out the 

 percentage as abscissae on such a scale that O'l per cent, was represented by 

 1 millim.,and the ordinates on such a scale that 1 millim. corresponded to a difference 

 of O'OOOl in the density ; when using this scale, it was easy to read off the density to 

 four places of decimals, and the calculation required was reduced to a minimum. 

 Thus, in reading the density from the curve we have for 49*98 per cent. 

 p (1 + 0-01 P) = 0-0268, and p = 0'0268 + 1 + 0'4998 = T5266. 



II. The second sensitive curve represents the deviation of the density curve from 

 a straight line by means of the variations in the tangent of the angle between 

 the radius vector and the axis of concentration. It is obtained by plotting 

 (p 0'99866)/0'01 P against P, and has the form shown in Diagram I. This curve 

 has the advantage that its sensitiveness increases with the dilution, and it has proved 

 especially useful for interpolation at concentrations at which it was desired to record 

 the fifth place of decimals in the density. 



III. Over the range from 5 per cent, to 18 per cent. NaOH the density-percentage 

 curve is a straight line. This is shown by the first sensitive curve, but is entirely 

 masked in the second. The accuracy of the observations may therefore be tested 

 by comparing the values calculated from the linear formula p = /c> 6 +0-01105 (P 5) 

 with those which were obtained by interpolation from our experimental values by 

 means of the second sensitive curve. 



The result is shown in Table III. 



