[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.'
THOMAS H. HUXLEY'S WORKS.
SCIENCE AND CULTURE, AND OTHER ESSAYS. 12mo. Cloth, $1.50.
THE CRAYFISH: AN INTRODUCTION TO THE STUDY OF ZOÖLOGY. With 82 Illustrations. 12mo. Cloth, $1.75.