( 765 
as an ion-reaction as shown from the data on pg. 766 ; then the end 
concentration of the ions is in the one case 0.000701 and the 
initial-concentration 0.002690 and in the second case the end-concen- 
tration of the ions is 0.000501 and the initial-eoncentration 0.001885. 
The following tables derived from a series of determinations by 
Paunt Henry show that the above reaction-equation is a correct one 
For the spontaneous transformation of y-hydroxybutyric-acid we 
find: (see table p. 766). 
5. It has been shown by the writer, that, if so much of a foreign 
acid (HCI, H,SO,) is added that the concentration of the H-ions during 
the whole progress of the reaction may be taken as constant, the 
usual reaction-equation applies; therefore in this case that of the 
unimolecular reaction in which an equilibrium is formed. 
If we consider these reactions as ion-reactions it may be easily 
proved, that in the supposed case that equation appears. 
If the concentration of the hydroxy-acid at a definite period is C, that 
of the added H-ions C and p the part of the hydroxy-acid which has 
split up into ions, then Chydroxy-acid — (1 — p) C; Coios =p C+ C'; 
Oner: ions — P C. 
This acid is in equilibrium with its ions, consequently, 
a) all 
p(pC+C) _ 
1l—p 
If so many H-ions have been added that this concentration may 
be regarded as constant, pC + C' is a constant and the above 
equation becomes : 
D 
BEES i, 
1--p 
that is to say, whatever value the concentration of the hydroxy-acid (C) 
attains, p remains constant and during the whole of the progress of 
the reaction, the concentration of the negative ions will amount to the 
same part of the hydroxy-acid present. In this case we therefore, have: 
negative ions + positive ions = lactone + water. 
Suppose the concentration of the negative ions = y, and that of 
the positive ions = Cy, then if the concentration of the lactone 
= Cr and that of the water = Cy we have: 
CRE k Ale (Ô! ' ! ' al 
— =k, GHY —k,CwCr= Ty ke Chr=k,y—k,(C,—C); 
then Cy and Cyr may be taken as constant. 
It has been shown above that during the progress of the action 
