[A] There are excellent remarks to the same effect in
Zeller's _Philosophie der Griechen_, Theil II. Abth. ii p.
407, and in Eucken's _Die Methode der Aristotelischen,
Forschung_, pp. 136 _et seq_.
[B] Fresnel, after a brilliant career of discovery in some
of the most difficult regions of physico-mathematical
science, died at thirty-nine years of age. The following
passage of a letter from him to Young (written in November
1824), quoted by Whewell, so aptly illustrates the spirit
which animates the scientific inquirer that I may cite it:
'For a long time that sensibility, or that vanity,
which people call love of glory is munch blunted
in me. I labor much less to catch the suffrages of
the public than to obtain an inward approval which
has always been the mental reward of my efforts.
Without doubt I have often wanted the spur of
vanity to excite me to pursue my researches in
moments of disgust and discouragement. But all the
compliments which I have received from M.M. Arago,
De Laplace, or Biot, never gave me so much
pleasure as the discovery of a theoretical truth
or the confirmation of a calculation by
experiment.'
[C] 'Mémorable exemple de l'impuissance des recherches
collectives appliquées à la découverte des vérités
nouvelles!' says one of the most distinguished of living
French _savants_ of the corporate chemical work of the old
Académie des Sciences. (See Berthelot, _Science et
Philosophie_, p. 201.)
[D] I am particularly indebted to my friend and colleague
Professor Rücker, F.R.S., for the many acute criticisms and
suggestions on my remarks respecting the ultimate problems
of physics, with which he has favored me, and by which I
have greatly profited.
[E] I am aware that this proposition may be challenged. It
may be said, for example, that, on the hypothesis of
Boscovich, matter has no extension, being reduced to
mathematical points serving as centres of 'forces.' But as
the 'forces' of the various centres are conceived to limit
one another's action in such a manner that an area around
each centre has an individuality of its own extension comes
back in the form of that area. Again, a very eminent
mathematician and physicist--the late Clerk Maxwell--has
declared that impenetrability is not essential to our
notions of matter, and that two atoms may conceivably occupy
the same space. I am loth to dispute any dictum of a
philosopher as remarkable for the subtlety of his intellect
as for his vast knowledge; but the assertion that one and
the same point or area of space can have different
(conceivably opposite) attributes appears to me to violate
the principle of contradiction, which is the foundation not
only of physical science, but of logic in general. It means
that A can be not-A.
[F] 'Molecule' would be the more appropriate name for such a
particle. Unfortunately, chemists employ this term in a
special sense, as a name for an aggregation of their
smallest particles, for which they retain the designation of
'atoms.'
[G] 'At present more organic analyses are made in a single
day than were accomplished before Liebig's time in a whole
year.'--Hofmann, _Faraday Lecture_, p. 46.
[H] In the preface to his _Mécanique Chimique_ M. Berthelot
declares his object to be 'ramener la chimie tout entirère
... aux mêmes principes mécaniques qui régissent déjà les
diverses branches de la physique.'
[I] This is the more curious, as Ampère's hypothesis that
vibrations of molecules, causing and caused by vibrations of
the ether, constitute heat, is discussed. See vol. ii. p.
587, 2nd ed. In the _Philosophy of the Inductive Sciences_,
2nd ed., 1847, p. 239, Whewell remarks, _à propos_ of
Bacon's definition of heat, 'that it is an expansive,
restrained motion, modified in certain ways, and exerted in
the smaller particles of the body;' that 'although the exact
nature of heat is still an obscure and controverted matter,
the science of heat now consists of many important truths;
and that to none of these truths is there any approximation
in Bacon's essay.' In point of fact, Bacon's statement,
however much open to criticism, does contain a distinct
approximation to the most important of all the truths
respecting heat which had been discovered when Whewell
wrote.
[J] Perhaps I ought rather to say Button's axiom. For that
great naturalist and writer embodied the principles of sound
geology in a pithy phrase of the _Théoris de la Terre_:
'Pour juger de ce qui est arrivé, et même de ce qui
arrivera, nous n'avons qu'à examiner ce qui arrive.'