William John Macquorn Rankine

“ 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; ”

“ In fact, a conjecture may be hazarded, that immediate diffusion of the actual energy produced in frictional phenomena, is the circumstance which renders them irreversible ; for, suppose a small part of a substance to have its actual energy increased by the exertion of some kind of work upon it; then, if the increase of actual energy so produced be immediately diffused amongst other parts, so as to restore the uniformity of the metabatic function, the whole process will be irreversible. ”

“ A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them ”

“ This axiom is also equivalent to saying, that energy is transformable and transferable (an allegation which, in the previous paper referred to, was included in the definition of energy) : for, to transform energy, means to employ energy depending on accidents of one kind, in putting a substance into a state of energy depending on accidents of another kind ; and to transfer energy, means to employ the energy of one substance in putting another substance into a state of energy, both of which are kinds of work, and may, according to the axiom, be performed by means of any kind of energy. ”

“ The quantity, even of an absolute accident, can only be expressed by means of a mentally-conceived relation.
The whole condition or state of a substance, so far as it is variable, is a complex accident; the independent quantities which are at once necessary and sufficient to express completely this complex accident, are independent accidents. To express the same complex accident, different systems of independent accidents may be employed; but the number of independent accidents in each system will be the same. ”

“ A mechanical hypothesis is the better, the more extensive the range of phenomena whose laws it serves to deduce from the axioms of mechanics; and the perfection of such a hypothesis would be, if it could, by means of one connected system of suppositions, be made to form a basis for all branches of molecular physics. ”

“ Internal Potential Equilibrium. The internal potential equilibrium of a substance consists in the equilibrium of each of its parts, considered separately ; that is to say, in the nullity of the rate of variation of the potential energy of each part with respect to each of the independent accidents on which the condition of such part depends. ”

“ for in almost every branch of molecular physics it may be held, that a hypothetical theory is necessary as a preliminary step to reduce the expression of the phenomena to simplicity and order, before it is possible to make any progress in framing an abstractive theory. ”

“ Laws respecting the equilibrium of particular kinds of actual energy have been ascertained by experiment, and in some cases anticipated by means of mechanical hypotheses, according to which, all actual energy consists in the vis-viva of motion. ”

“ The neglect of the caution already referred to, however, has caused some hypotheses to assume, in the minds of the public generally, as well as in those of many scientific men, that authority which belongs to facts alone, and a tendency has consequently often evinced itself to explain away, or set aside, facts inconsistent with these hypotheses, which facts, rightly appreciated, would have formed the basis of true theories; thus the fact of the production of heat by friction, the basis of the true theory of heat, was long neglected, because inconsistent with the hypothesis of caloric ”

“ Most kinds of accidents are necessarily relative, but some kinds can only be considered as relative accidents when some hypothesis is adopted as to the occult condition of the substances which they affect, as when heat is ascribed hypothetically to molecular motions ”

“ Let a homogeneous substance possess a quantity Q, of a particular kind of actual energy, uniformly distributed, and let it be required to determine the amount of the effort arising from the actual energy, which tends to perform a particular kind of work W, by the variation of a particular passive accident x. ”

“ The distinction of accidents into absolute and relative is to a certain extent arbitrary; thus, the figure and dimensions of a molecule may be regarded as absolute accidents, when it is considered as a whole, or as relative accidents, when it is considered as made up of parts. ”

“ Equilibrium Of Actual Energy ; Metabatic Function. It is known by experiment, that a state of actual energy is directly transferable; that is to say, the actual energy of a particular kind (such as heat) , in one substance, may be diminished, the sole work performed being an equal augmentation of the same kind of actual energy in another substance. ”

“ It is well known that certain hypothetical theories, such as the wave theory of light, have proved extremely useful, by reducing the laws of a various and complicated class of phenomena to a few simple principles, and by anticipating laws afterwards verified by observation. ”

“ In a paper read to the Philosophical Society of Glasgow on the 5th of January 1853, a first attempt was made to investigate such principles, by defining actual energy and potential energy, and by demonstrating a general law of the mutual transformations of those kinds of energy, of which one particular case is a previously known law of the mechanical action of heat in elastic bodies, and another, a subsequently demonstrated law which forms the basis of Professor William Thomson's Theory of thermo-electricity. ”

“ The Abstractive Method of Forming a Physical Theory, Distinguished from the Hypothetical Method. Two methods of framing a physical theory may be distinguished, characterized chiefly by the manner in which classes of phenomena are defined. ”

“ According to the abstractive method, a class of objects or phenomena is defined by describing, or otherwise making to be understood, and assigning a name or symbol to, that assemblage of properties which is common to all the objects or phenomena composing the class, as perceived by the senses, without introducing anything hypothetical. ”