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Re: <none>

again me:
note that df1+df2   C-system
        df3       borate 

       df5+df6+df11  phosphorus
         df7      silica

al are negative
the small error has, of course, no effect at all
on the solution.
As the second derivative d2 Alk/dx**2 is positive
it could be that the small error causes a slightly
improve of convergence, at least when approaching
from small x-values.