[1] Statique expérimentale et théorique des liquids, 1873. See also The Science of Mechanics, p. 384 et seqq., The Open Court Publishing Co., Chicago, 1893.
[2] Compare Mach, Ueber die Molecularwirkung der Flüssigkeiten, Reports of the Vienna Academy, 1862.
[3] In almost all branches of physics that are well worked out such maximal and minimal problems play an important part.
[4] Compare Mach, Vorträge über Psychophysik, Vienna, 1863, page 41; Compendium der Physik für Mediciner, Vienna, 1863, page 234; and also The Science of Mechanics, Chicago, 1893, pp. 84 and 464.
[5] Like reflexions are found in Quételet, Du système sociale.
[6] For the full development of this idea see the essay "On the Economical Nature of Physical Inquiry," p. 186, and the chapter on "The Economy of Science," in my Mechanics (Chicago: The Open Court Publishing Company, 1893), p. 481.
[7] Science may be regarded as a maximum or minimum problem, exactly as the business of the merchant. In fact, the intellectual activity of natural inquiry is not so greatly different from that exercised in ordinary life as is usually supposed.
[8] This experiment, with its associated reflexions, is due to Galileo.
[9] A development of the theory of musical audition differing in many points from the theory of Helmholtz here expounded, will be found in my Contributions to the Analysis of the Sensations (English translation by C. M. Williams), Chicago, The Open Court Publishing Company, 1897.
[10] Sauveur also set out from Leibnitz's idea, but arrived by independent researches at a different theory, which was very near to that of Helmholtz. Compare on this point Sauveur, Mémoires de l'Académie des Sciences, Paris, 1700-1705, and R. Smith, Harmonics, Cambridge, 1749. (See Appendix, p. 346.)