niMtrrTIVlTY OF SODIUM HYDROXIDE IN AQUEOUS SOLUTION. 277 



The observed values for water are taken from WATT'S ' Dictionary of Chemistry,' 

 where the values deduced by VOLKMANN from the determinations of HAGEN, 

 MATTHIBBEN, PIERRE, KOPP and JOLLY are given to five places of decimals. The 

 differences shown in the table indicate that an additional term must be introduced 

 into the equation p = p n +at-\-/3t*+yt? in order to express the influence of temperature 

 on the density of water correctly to the fourth decimal place. 



The values which we have set out for the densities of caustic soda solutions at 

 different temperatures are all based upon the measurements at 18 C. described in 

 Part II. of the paper. The values for C. are deduced from those at 18 C. with the 

 help of the difference curve for p pi, and as the maximum deviation of any individual 

 experimental values from this curve, as shown in Diagram II., is only 0*0002, we 

 believe that the values for p are accurate within O'OOOl. This close agreement 

 is of considerable value, as p n is an important constant in the equation 

 p, = p n +ait+/3t*+yt* used in deducing the densities at 10 C., 20 C., 30 C., &c. 



The values for 50 C. are deduced from those at C. by means of the difference curve 

 for pupio ', in this case the maximum difference between the experimental values 

 and the curve was 0*0003, and we consider that the values for p^ t are probably 

 accurate within 0*0002. 



The values for 100 C. were deduced from those at C. by means of the difference 

 curve for p p\no ' m this series the experimental values differ in two cases from 

 those deduced from the curve by as much as O'OOl, and the average error amounts 

 to 0*0003, but we consider that the values for 100 C. are probably accurate within 

 0-0005. 



Table VIII. gives the values of p p, 8 , p p M , p p }no , which were used for the 

 above purpose ; and also the temperature coefficients a, ft and y. 



A remarkable confirmation of the substantial accuracy of the values for /J 100 , at 

 which temperature the experimental error reaches a maximum, was afforded by 

 the discovery that the values for p ~/ ) ioo could be represented by the simple 

 logarithmic law 



Po-Pm = A lgio 



where P = percentage of soda in solution. 



This formula was not in any way used to fix the final values for p l(X) . and indeed 

 was not discovered until after these had been tabulated, but the substantial agree- 

 ment between the two series of values, shown in Table VIII., which do not differ in 

 any case by more than 0*0004, appears to indicate that we have not over-estimated 

 the accuracy of our observations by placing the probable error in p 100 within 0*0005. 



