286 Proceedings of Royal Society of Edinburgh. [sess. 
Expansion on Solution. 
The volume of unit mass of the various solutions examined 
was calculated, and also the volume which the solvent water 
contained in unit mass would occupy if its temperature were the 
same as that of the solution. The amount by which the volume 
of unit mass of the solution is greater or less than that of the 
solvent water employed in its preparation is the difference of these 
quantities. Knowing the density, p (gms. per c.c.), of a solution 
at t° C., we can find the volume, — , of 1 gm. of the solution at 
P 
that temperature ; and knowing the concentration of a solution (c), 
and the density of water at t°, A, we can find the volume that 
the water in 1 gm. of solution would occupy if it were free, viz., 
\ — ; hence the excess of the one volume over the other 
A 
is — — — . This may he called the expansion on solution. 
P ^ 
The “ probable error ” in the determination of the expansion was 
found to be '00004, the values of the expansion varying from 
•00957 to *00001. 
The following tables give the results found. The headings are 
self-explanatory. 
Sodium Hydroxide. 
Grams of 
substance in 
100 grams 
Solution. 
Temp. 
t° C. 
Density 
grams per c.c. 
Volume of 
1 gram of 
Solution at 
t° 0. (V c.c.). 
Volume at t° 
C. of water in 
1 gram Solu- 
tion (V' c.c.). 
Expansion 
V-V' c.c. 
16'3329 
15 
1*18463 
*84415 
•83740 
+ *00675 
20 
1*18208 
*84596 
•83815 
+ *00781 
26 
1*17891 
*84823 
•83935 
+ *00888 
30 
1-17676 
*84988 
•84031 
+ -00957 
6-0785 
15 
1*06884 
•93559 
•94003 
- *00444 
20 
1*06699 
•93721 
•94087 
- -00366 
26 
1*06452 
•93938 
•94222 
- -00284 
30 
1*06294 
•94078 
•94329 
- -00251 
3-1305 
15 
1-03532 
•96589 
•96954 
- -00365 
20 
1-03373 
•96737 
•97041 
- *00304 
26 
1-03180 
•96918 
•97179 
- -00261 
” 
30 
1 *03074 
•97045 
•97290 
- -00245 
