Jude,
So-called isotope mass balance solves your problem. With all del << 1000,
then 

del =  del1 * f1 + del2 * f2 + del3 * f3
1 = f1 + f2 + f3

With all three mass fractions unknown then you would have three unknowns, but
you say you know one of them so you have two linear equations in two
unknowns! In practice you will output a best fit to a number of replicates,
and I expect that you do not calculate the true amount of carbonate in each
and every sample: I think your third "known" is a stochastic variable which
will provide the bounds for the parameters of your fit.
John

John Furey
Physical Scientist
US Army ERDC EP-P
3909 Halls Ferry Rd
Vicksburg, MS 39180
(601)-634-2778
(601)-634-4002 fax
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-----Original Message-----
From: Stable Isotope Geochemistry [mailto:[log in to unmask]] On Behalf
Of judemaul
Sent: Wednesday, July 26, 2006 5:58 PM
To: [log in to unmask]
Subject: [ISOGEOCHEM] Three source mixing model

Folks,

I am characterizing particulate plant derived organic matter input to 
the soil.  The approach I have taken is planting C3 plants into a 
soil with a long C4 history.  The particulate organic matter in the 
soil at the start of the experiment had a del vPDB signature of 
-14.000 and the new C3 input has a del vPDB of -28.000.  My problem 
is that the protocol for isolating the organic matter requires that I 
co-collect the organic matter with the sand fraction of the soil, 
which contains about 18% carbonate with a del vPDB of 0. I'm 
wondering if anybody can help me with a three source mixing model 
that can be run using only one isotope?  Using a separate analysis of 
the soil I can calculate the amount of carbonate in each sample but I 
need to determine the proportion of each plant source (C3 or C4) in 
the remaining organic carbon.
Ideally I would have removed the carbonate prior to isotopic analysis 
but at the time of sample prep I didn't realize how much of an issue 
the carbonate would be.

Thanks
jude

-- 
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Jude Maul
Department of Horticulture
Cornell University
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(607)255-0883 (office)
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