I've made a little progress figuring out what Woehler and Liebig are
talking about. First of all, they do a combustion analysis of two samples
of oil of bitter almonds, namely

I. 0.386 gramme = 1.109 carbonic acid, and 0.200 water.
II. 0.341 " = 0.982 " " " 0.175 "

From that, they claim to have computed the following weight percentages,
which are fairly close to what I get from their data:
I II
Carbon ........... 79.438 .......... 79.603
Hydrogen ......... 5.756 .......... 5.734
Oxygen ......... 14.808 .......... 14.663

From these, one easily gets the ratio 7:6:1 for the numbers of atoms of
carbon, hydrogen and oxygen or, what is the same, the ratio 14:12:2, as
Woehler and Liebig do. How exactly they decided on 14 instead of 7 isn't
clear to me, but given that they did, the next table:

becomes perfectly clear. For example, if one uses Berzelius' scale,
wherein the weight of oxygen is taken to be 100, the weight of carbon
is about 76.44 and that is close to what one gets by dividing 1070.118
by 14. So, the column on the left is simply their calculation of the
weights of 14 carbon atoms, of 12 hydrogen atoms and of 2 oxygen atoms.
Throughout the rest of the paper, they use their own scale in which the
weight of oxygen is taken to be 10, and whenever they have 14 carbons
after an analysis, they give the weight as 107.0118, except for one place
that is probably a typo. So, that explains the column on the left.

As for the column on the right, of one expresses these weights as percentages
of the total weight 1344.995, one gets the column on the right, more or less.

So, now I have an overview of the kind of computations they are presenting.
What I'm still confused about are their conventions for working with their
numbers and for dealing with questions of precision, etc. Note that they
take all their numbers to three decimal places, even after successive
computations. Some of their results suggest that they simply truncated
their numbers, no matter what came afterwards (I think MF's lab instructor
would be pleased). But I don't have it all nailed down.

If, instead of 1.109 for the weight of carbon dioxide, the value was really
1.10891, and they used that instead of the rounded value 1.109 in their
actual computations, and if the weight of the oil of bitter almonds was
exactly 0.386, and if one used their value (according to Benfey's footnote)
of 7.644 for the atomic weight of carbon and 10 for that of oxygen, then one
would get their value of 79.438 for carbon in the first column of the
combustion analysis. I haven't tried to find out all possible modifications
but note also that 1.1089 and 1.10892 won't work to do that. So, if that is
what they did, it would imply that they had a method of weighing that
had a precision of 5 decimal places. Did they?

So, after all this math, I have a question about the chemical laboratory
of Woehler and Liebig: how exactly did they weigh things and what precision
could they achieve with their apparatus?

I am cross posting this to sci.math, since someone there might know something
about the history of numerical methods in the time of Woehler and Liebig
and have some idea of what conventions they might have used in dealing
with numbers. If someone can explain how to get EXACTLY the numbers
Woehler and Liebig claim to have derived from their initial combustion
measurements that would be very helpful.

Ignorantly,
Allan Adler [Only registered users see links. ]

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Allan Adler <[Only registered users see links. ].mit.edu> wrote in message news:<[Only registered users see links. ].mit.edu>...

Dr. Adler
You have noticed that molecular formula is a multiple of empirical
formula. Note that combustion analysis can give you only and only the
simplest ratios of atoms in a compound. When the molecular weight is
known, which can be determined by Dumas method (1826), Victor-Meyer
density method (1870's), and I stronlgy suspect Wohler and Liebeig
used one of these methods to determine the molecular weight of
benzaldehyde, we can easily detrmine the molecular formula which in
this case is C14H12O4. They should have mentioned the method they used
to determine its molecular weight.
There is a simple relationship : Molecular formula = (empirical
formula)*n
where n = molecular weight / empirical formula weight.
Accurate determination of molecular weight can give you the correct
molecular formula.

I think I mentioned Yale University website on combustion analysis,
did you get the time to read it? As a spare time experiment: Find out
the good old log tables from a library, and try doing the calculations
"without" a calculator, carry out division and multiplication with
logarithms and see whether your results EXACTLY match with their
results or not.
As with the concept of significant figures, I doubt if this concept
was used in Wohler or Liebig's time.

In article <[Only registered users see links. ]> , Mohammed
Farooq <[Only registered users see links. ]> writes

The subject is well explored in "Liebig's Alkaloid Analyses: the
Uncertain Route from Elemental Content to Molecular Formulae" by Melvyn
C. Usselman, Ambix, vol 50 part 1, March 2003, pp. 71-89.