518 Proceedings of the Royal Society of Edinburgh. [Sess. 
determined at two temperatures, viz. 2° C. and 13° C. The liquids used 
were bromonaphthalene and toluene. A mixture of these liquids was 
placed in a small test-tube and a few small crystals of tetra-propyl- 
ammonium chloride were introduced. The density of the liquid was 
adjusted by adding a few drops of bromonaphthalene or toluene until the 
crystals remained suspended in the liquid. The density of the mixture 
was then determined at 13° C. : this was found by means of the Westphal 
Balance, while at 2° C. the density of the liquid was determined by means 
of a pyknometer. 
The following- results were obtained : — 
3° C. 
13° C. 
1-0329 
1-0290 
1-0330 
1-0295 
1-0344 
1-0300 
Average 1 *0334 
1-0296 
The values 1*0341 and 1*0255 were taken as the density of the solid at 
0° C. and 25° C. respectively, these values being obtained by extrapolation. 
In order to determine the expansion on solution, it was necessary to 
determine the volume of unit mass of the various solutions, the volumes 
which the water in that unit mass would occupy at the same temperature, 
and also the volume of the solid in unit mass of each solution. 
If d be the density of the solution at t° C., = volume 1 gm. solution 
at f C. Suppose now that c is the concentration in gms. of solid per 100 
gms. solution, and that A is the density of water at t° C., then - — 
is the volume that the water in 1 gm. of solution would occupy if it were 
free. 
JL c 
If S be the density of the solid, then - x ^7— is the volume of solid in 
o 100 
1 gm. of solution. 
The expansion on solution will be given by the formula 
1 j 1 - c/100 , c/100 l 
d I A + 8 J ' 
The following table gives the results calculated for five of the foregoing 
solutions 
