It would have been anachronistic for Lavoisier to use Berzelius-style formulae to record atom ratios, but he had to record mass balance for his chemical or biochemical transformations. His expertise with financial balance sheets had a profound influence on his approach to chemistry.
Here is an example of his mass balance sheet for fermentation of sugar. In Table I he records the amounts (pounds, ounces, gros, and grains; 1 lib = 16 oz ; 1 oz = 8 gros ; 1 gros = 72 grs) of water, sugar, and yeast paste before fermentation. In Table II he breaks this down into the amounts of the constituent elements.
In Table III he collects the elements from the constituents to show what C, H, O, N he started with:
Below is the balance sheet of his analysis after fermentation. Notice that his analysis was not what used to be called "ultimate", that is, he did not measure the elements themselves as by combustion. Instead this is "proximate" analysis, that is, he measured the amounts of the various compounds present after fermentation and translates these results into the amount of the elements each component represents by computation.
and in Table V he reworks these results:
Note that everything came out just right, just as a balance sheet should!
Lavoisier, an experienced accountant, comments as follows on the agreement:
I shall finish what I have to say upon vinous fermentation, by observing, that it furnishes us with the means of analysing sugar and every vegetable fermentable matter. We may consider the substances submitted to fermentation, and the products resulting from that operation as forming an algebraic equation; and, by successively supposing each of the elements in this equation unknown, we can calculate their values in succession, and thus verify our experiments by calculation, and our calculation by experiments reciprocally. I have often successfully employed this method for correcting the first results of my experiments, and to direct me in the proper road for repeating them to advantage. I have explained myself at large upon this subject, in a Memoir upon vinous fermentation already presented to the Academy, and which will speedily be published.
He also says:
In these results, I have been exact, even to grains; not that it is possible, in experiments of this nature, to carry our accuracy so far, but as the experiments were made only with a few pounds of sugar, and as, for the sake of comparison, I reduced the results of the actual experiments to the quintal* or imaginary hundred pounds, I thought it necessary to leave the fractional parts precisely as produced by calculation.
*) According to the OED, "quintal" comes from the Arabic "kantar", which comes from the Latin "centenarium". All of them mean 100 pounds, but what was understood as 100 pounds varied from place to place around the Mediterranean.
(1) What do you think about the accuracy of Lavoisier's experiments and balance sheets?
(2) How does his comment on the possibility of correcting his results relate to his accuracy?
(3) Do you think Lavoisier was an honest scientist?
(4) To what precision do you think
calculations using such experimental results should be made and
(N.B. this is a particularly relevant question when, with no effort, one can read 10-12 digits from an electronic calculator.)