1400 
the shortening reflex and the paradoxal contraction. I am inclined 
to suppose that the latter is the pathological form of the first. 
The curves I have given as physiological were those taken in a 
patient with a severe trigeminus-neuralgia caused by periostitis alveo- 
laris, who is now cured. His reflexes were not altered in the least. 
The curves 3 and + were taken from the healthy side of a hemi- 
plegic patient and are perhaps not to be considered as purely physio- 
logical. There is some reason to suppose, that hemiplegia may cause 
a heightening of the shortening reflex of the healthy extremity. 
Amongst the pathological forms of the reflex we might perhaps 
include some forms of hysterical contraciure and also some cases of 
crampi. But I intended to consider onty the physiological aspects of 
the reflex. 
Physics. — “On the thermodynamical functions for mixtures of 
reacting components.” By Dr. L. S. ORNsTriN. (Communicated 
by Prof. H. A. Lorentz). 
(Communicated in the meeting of November 30, 1912). 
In his dissertation Dr. P. J. H. Hornen has developed a theory 
of the thermodynamical functions for mixtures of reacting components *). 
Considerations closely connected to those of this dissertation are 
obtained if the statistical method of Gipss is applied to the study 
of the equilibrium in chemical systems. I will show this in the 
following communication, and will restrict myself to the case that 
only one kind of reactions is possible in the mixture, the extension 
to other cases being possible without any diltficulty. 
In the following considerations I shall use a canonical ensemble 
of the modulus 0(=57) (R is the constant of Avogrado for the 
grammolecule, V the number of molecules present in this quantity 
of matter. We might as well use the micro-canonical ensembles, 
but for the calculations then being somewhat more complicated. 
The molecules participating in the reaction are indicated by u, ux. uk 
Then the reaction will be characterised by the stoechiometrical formula 
k 
DP os Se =o! ee ee 
1 
the numbers v, indicating the smallest numbers of molecules that 
1) Dissertation Leiden 1912, comp. also these proceedings XV p. 614. 
