178 Heilbron
self claimed and was accorded the title of physicien, an apt usage for the
time that caused distress two hundred years later among historians of
chemistry who fretted that a “physicist” might have reconstructed their
science. Lavoisier meant that he was a natural philosopher.^12
The second direction of expansion of physics after 1770 took place
across its boundary with mathematics. Mixed mathematics, or, as the En-
cyclopédie and its echo Hutton had it, “physico- mathematics,” included
quantifi ed portions of astronomy, optics, acoustics, and mechanics.^13 As
it pushed quantifi cation in the subsciences of heat, electricity, and mag-
netism, natural philosophy began to acquire parts of mixed mathematics
and some of the arrogant rhetoric of the mathematician. “Everyone now
agrees that a physics lacking all connections with mathematics... would
only be an historical amusement, fi tter for entertaining the idle than for
occupying the mind of a philosopher.” Thus Franz Karl Achard, a promi-
nent member of the Berlin Academy of Sciences who pretended to read
his electroscope to six places, addressed his colleagues in 1773. “Having
thus learnt to distinguish knowledge from what has only the appearance
of it,” added J. A. Deluc, a man as exact and exacting as his barometer,
“we shall be led to seek for exactness in everything.”^14 More and better
instruments made possible the measurement of newly devised quantities,
like electrical force and tension, and increased the precision of the deter-
mination of familiar ones, like temperature and pressure. The result was
exact natural philosophy, to use an historian’s rather than an actor’s term.
The neologism is meant to emphasize that most of the measurements
done around 1800 did not serve as checks on theory, indeed could not
have been predicted by any theory then available. “Mathematical phys-
ics,” that is, quantitative theories predictive of the phenomena, was more
the goal than the content of Biot’s Traité. “The law of a phenomenon can
only be established experimentally... To make it absolutely certain and
rigorous, it must be related to the general laws of mechanics... When
such a reduction can be effected completely, it necessarily makes clear the
FORCES that produce the phenomena, which is as far as human science
can go.”^15
Natural experimental philosophy was thus richer around 1800 than it
had been during the dominance of experimental philosophy in the mid-
dle decades of the eighteenth century. It had acquired some lost ground
by sharing progress in chemistry and it had begun to fi ll out its mechan-
ics, optics, acoustics, and so on by capture from mixed mathematics. In
another aspect also it experienced a partial return to its umbrella status of- Rohault’s Physique had the unity of Cartesian qualitative corpuscu-
larism. The natural philosophers around 1800 had two unifying schemes.