282 
Proceedings of Royal Society of Edinburgh. [sess. 
densities of water at the various temperatures those given by 
Landolt and Bornstein.* 
Other solutions were made from those prepared directly by 
mixing measured volumes of the solutions and distilled water at 
15° C. The percentage concentration was then got from the 
formula, p = 
GY x 100 
VD + WA 
, where G is the number of grams of salt 
per c.c. of original solution at 15° C., Y the volume of the solution, 
D the density of the solution at 15° C., W the volume of water, 
and A the density of the water at 15° C. The volumes were 
measured out by pipettes and burettes which had been certified 
correct by the Physikalisch-technisclie Reichsanstalt, Berlin. 
The accuracy aimed at in the estimation of the chemical com- 
position of the solutions was the greatest attainable, and in the 
estimation of the solutions of barium, and, to a lesser degree, of 
strontium, the errors were greater than in the case of the solutions 
of sodium. The so-called “ probable errors ” in the estimation of 
concentrations were found in no case to exceed ‘00003 per gram of 
solution. 
Determination of Density. 
The density determinations were made primarily to measure 
expansion on solution, and I found that the error introduced into 
the measurement of expansion by the error in the concentration 
set a limit to the density accuracy necessary. It was found 
unnecessary to measure densities to any greater degree of accuracy 
than 5 in the fifth decimal place. Accordingly, the pyknometer 
method of determining density was adopted. 
My attention was drawn to a method devised by Mr Manley f 
of eliminating the error in a density determination by the 
pyknometer, due to a difference in the amount of moisture con- 
densed on the glass of the pyknometer in different weighings. 
The method consists in using as a counterpoise a similar, sealed, 
pyknometer, which is treated as regards heating, handling, etc. in 
exactly the same way as the pyknometer containing the liquid 
whose density is to be measured. Mr Manley finds that “ when 
* Pliysilcalisch-Chemische Tabellen , 1894. 
t Proc. E.S.K, 24, 357, 1902-3. 
