1906-7.] On the Application of a Differential Densimeter. 227 
Accepting the density of the natural water, K 3 , as a standard, and 
taking the differences between it and those of the other four waters, we 
can show what possible changes may be produced in the value for the 
relative density of an abnormal water, when the temperature is allowed 
to fluctuate within somewhat exceptionally large limits. By adopting this 
plan, and denoting the density of the water K 3 at any temperature by p, 
and the density of any of the others at the same temperature by A, the 
results given in Table IX. are obtained. 
Table IX. — Showing Effects Produced upon the Relative Densities of 
Abnormal Waters by Extreme Variations in Temperature. 
Water. 
Differences between 
Deviations from A 20 . 1 
Pio and Aw- 
P 2 0 and A 20 - 
P 30 and Ago- 
At 10° C. 
At 30° C. 
- -0135 
- *0132 
-•0130 
+ -0003 
- -0002 
k 2 
- -0076 
- -0075 
- -0074 
+ 1 
1 
k 4 
+ *0066 
+ •0064 
+ -0063 
+ 2 
1 
k 5 
+ •0132 
+ •0129 
+ •0126 
+ 3 
3 
This table brings out very clearly the somewhat singular but important 
fact that, notwithstanding the considerable variations both in the tempera- 
ture and chlorine values of the several waters, the error introduced by 
determining a relative density by means of the differential densimeter 
would, even in the most extreme cases, have amounted to no more than 
dz '0003 for a range of 10° C. on either side of the standard temperature 
of 20° C. 
By referring to the temperature coefficients in Table VIII., we may 
discern that the reason for the insignificance of these deviations, except 
in the case of the waters K x and K 5 , is that the temperature coefficients 
are not greatly dissimilar ; hence any increase or decrease in the volume 
of the waters, consequent upon a change in temperature, will be nearly 
identical for all. 
The close similarity between the coefficients of expansion for the five 
waters is well shown by the curves given in fig. 3. The various 
volumes of the several waters are taken as ordinates and plotted against 
the corresponding temperatures as abscissae, the unit volume being in all 
cases taken at 10° C. For the sake of comparison, a similar curve for 
pure water has also been drawn. 
