Part II. On Aqueous Solutions. 71 
Now 8, is a fraction, and as p—o the R.H.S.— 0, on the 
assumptions made above, because v > b, Ab, < 0. 
Therefore 8, > 1 as p— «, for all values of S. 
| Hence for p > 2 the curves lie between the curve for p= 2 and 
the asymptote 8,=1. They have each one minimum value, viz. 
that given by the relation (7). The portions of the curves which 
lie between the ordinates corresponding to 0° C. and 100°C. are 
very approximately linear. The exact positions of the minima for 
the curves of higher values of p do not matter, at least so far as 
the first approximation only is desired, since we have proved 
that the curvature of such curves is very small. On the other 
hand the principle of continuity demands that for the lower values 
of p the positions of the minima of @, shall approximate with 
decreasing p to the position of the minimum for p= 2. 
The curves must be of the form shown in fig. 2. 
Onz 1, Simple molecules. 
(a =0, p-fold molecules. 
Fig. 2. 
For all groups, the rate at which dissociation takes place over 
the region 0° C. to 140° C. is very approximately uniform. It is to 
be noted here that if we were to supercool or to superheat the 
solution to a sufficient degree, this step, in taking the curves as 
approximately linear, would no longer be justifiable, and the 
following reasoning holds only for solutions between the tempe- 
ratures 273° and 400° absolute. It is conceivable that outside 
this range of temperature the formulae which will hereafter be 
deduced may require to be considerably modified. 
We may therefore write 
1 (SS igs Weel pen bneceosvescpesuoue (8) 
* Note added. M. M. Garver, Journ. Phys. Chem. Nov. 1912, p. 669. The 
experimental relation between polymerization and temperature is shown to be 
approximately linear. 
