188 Heilbron
for engineering, it gave an irresistible push to the quantifi cation of natural
philosophy. Most of the notable French physico- mathematicians active
between 1800 and 1830 taught or studied or did both at the École Poly-
technique. A short list would include François Arago, Biot, Sadi Carnot,
J. B. J. Fourier, L.J. Gay- Lussac, Etienne Malus, and S. D. Poisson. All ex-
cept Sadi Carnot, who died before he could be elected, became members
of the academy in its resurrection after the Terror as the First Class of the
Institut de France. There they could meet with the most successful gradu-
ate of the artillery schools of the ancien régime, the emperor Napoleon,
the patron of Laplace and Volta, who supposed himself a natural philoso-
pher, and had a Casanovan research program to prove it. “Spending the
night between a beautiful woman and a clear sky, and the day reconciling
observations and calculations, seems to me heaven on earth.”^40
The work of the higher technical schools and their graduates stimu-
lated a market for textbooks in applied mathematics and other products
of high technology.^41 The most obvious of these other products were
exact instruments, like Borda’s circle, which P. F. A. Méchain and J. B. J.
Delambre employed in their triangulation of France that defi ned the stan-
dard meter. Meanwhile, Gribeauval perfected his favorite instrument. In
the late 1780s, he and his artisans could make the ingredients of a fi ring
mechanism to such exactitude that they could disassemble one and put it
together again using parts of others selected at random. Earlier methods of
manufacture had required a lengthy adjustment of every part to its neigh-
bors. Gribeauval’s system of interchangeable parts required precision tools
and machinists who could work to tolerances of a hundredth of an inch
or so. Like the standard meter, Gribeauval’s interchangeable parts carried
rationality in the service of society to a point beyond the wildest imagin-
ings of the philosophes.
The English genius did not run to mathematics and centralization. To
be sure, it had an important Military Academy at Woolwich near London,
where, after Hutton became professor in 1773, soldiers could learn more
mathematics than they needed. Like his French counterparts Bézout and
Bossut, Hutton wrote textbooks on all branches of mathematics, pure and
applied. Also like them, he undertook experiments in ballistics and ranked
among the leading exponents of natural knowledge; they belonged to the
Paris Academy, he to the Royal Society. Hutton’s service to his science
extended to the popularizations and entertainments that recommended
it to the wider society. From 1773 to 1818 he edited the Ladies’ diary, an
almanac fi lled with puzzles and problems, mainly in geometry and algebra
but also in the mathematical branches of natural philosophy, on which