Stiles and J argensen. — Studies in Permeability. IV. 73 
Hence 
dm 
It 
ccf (M —m) 0 (C), 
where / ( M — m) is a function of the mass of substance left in the membrane 
unchanged and (p (C) is a function of the concentration of the external 
solution, a being a constant. 
If this concentration is so high that only a small quantity is used 
up throughout the experiment, <£ (C) is a constant for any particular concen- 
tration. Also it may be assumed that the rate of change of the substance 
in the membrane is directly proportional to the amount of it left, when the 
equation therefore becomes 
dm 
dt 
— A ( M—m ), A being a constant, 
or 
dm 
M—m 
— Adi; 
whence, integrating between limits, 
. M—m 
l0 s~i 7- 
= -At 
or 
M—m 
~~M~ 
— e 
-At 
and m — M (1 —e At ). 
Now the rate of exosmosis will be proportional to the amount of 
the membrane substance destroyed, and also to the difference in concentra- 
tion of electrolytes inside and outside the tissue. 
If at the time t the concentration of the electrolytes in the outer 
solution is s , and inside the cell s\ the rate of exosmosis is 
d £ = (3m(s’-s), 
where /3 is a constant. 
If N is the concentration of electrolytes inside the cell at the beginning 
of the experiment, and if u and v are the respective volumes of the tissue 
and external solution 
whence 
and 
zt(S-s') = vs 
or s — S — — 
It 
ds 
u + v 
= J pM{i-e- A ‘)dt, 
u 
