On Experiments (1850-1859)

"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space." (Charles Davies, "The Logic and Utility of Mathematics", 1850)

"Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'." (Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de Rotation de la Terre", 1851)

"When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena." (Justus von Liebig, "The Study of the Natural Sciences", 1853)

"Mathematics is an experimental science, and definitions do not come first but later on." (Oliver Heaviside, "On Operators in Physical Mathematics", Proceedings of the Royal Society of London, Series A Vol. 54, 1854)

An essential distinction exists between two stages in the process of advancing our knowledge of the laws of physical phenomena; the first stage consists in observing the relations of phenomena, whether of such as occur in the ordinary course of nature, or of such as are artificially produced in experimental investigations, and in expressing the relations so observed by propositions called formal laws. The second stage consists in reducing the formal laws of an entire class of phenomena to the form of a science; that is to say, in discovering the most simple system of principles, from which all the formal laws of the class of phenomena can be deduced as consequences. (William J M Rankine, "Outlines of the Science of Energetics", 1855)

"In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance: - and […] the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth – and […] the better qualified does he become to free the exposition and application of principles from mathematical intricacy." (William J M Rankine, "On the Harmony of Theory and Practice in Mechanics", 1856)

"In the experimental sciences, the epochs of the most brilliant progress are almost always separated by long intervals of almost absolute repose." (François Arago, "Biographies of Distinguished Scientific Men", ['Joseph Fourier'] 1859)

"It is possible to express the laws of thermodynamics in the form of independent principles, deduced by induction from the facts of observation and experiment, without reference to any hypothesis as to the occult molecular operations with which the sensible phenomena may be conceived to be connected; and that course will be followed in the body of the present treatise. But, in giving a brief historical sketch of the progress of thermodynamics, the progress of the hypothesis of thermic molecular motions cannot be wholly separated from that of the purely inductive theory.' (William J M Rankine, "A Manual of the Steam Engine and Other Prime Movers", 1859)

"The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman." (François Arago, "Biographies of Distinguished Scientific Men", [Eulogy on Laplace] 1859)