William John Macquorn Rankine

"The hypothesis of molecular vortices is defined to be that which assumes — that each atom of matter consists of a nucleus or central point enveloped by an elastic atmosphere, which is retained in its position by attractive forces, and that the elasticity due to heat arises from the centrifugal force of those atmospheres revolving or oscillating about their nuclei or central points. According to this hypothesis, quantity of heat is the vis viva of the molecular revolutions or oscillations."

"Discrepancy between theory and practice, which in sound physical and mechanical science is a delusion, has a real existence in the minds of men; and that fallacy, through rejected by their judgments, continues to exert and influence over their acts."

"This law (regarding the theoretical efficiency of heat engines by Mr. Joule), and the law of the maximum efficiency of heat engines, are particular cases of a general law which regulates all transformation of energy, and is the basis of the Science of Energetics."

"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."

"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; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment."

"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."

"The evil influence of the supposed inconsistency of theory and practice upon speculative science, although much less conspicuous than it was in the ancient and middle ages, is still occasionally to be traced. This it is which opposes the mutual communication of ideas between men of science and men of practice, and which leads scientific men sometimes to employ, on problems that can only be regarded as ingenious mathematical exercises, much time and mental exertion that would be better bestowed on questions having some connection with the arts, and sometimes to state the results of really important investigations on practical subjects in a form too abstruse for ordinary use; so that the benefit which might be derived from their application is for years lost to the public; and valuable practical principles which might have been anticipated by reasoning, are left to be discovered by slow and costly experience."

"[O]f that scientifically practical skill which produces the greatest effect with the least possible expenditure of material and work, the instances are comparatively rare. In too many cases we see the strength and the stability which ought to be given by the skilful arrangement of the parts of a structure supplied by means of clumsy massiveness, and of lavish expenditure of material, labour, and money; and the evil is increased by a perversion of the public taste, which causes works to be admired, not in proportion to their fitness for their purposes, or to the skill evinced in attaining that fitness, but in proportion to their size and cost."

"With respect to those works which, from unscientific design, give way during or immediately after their erection, I shall say little; for with all their evils, they add to our experimental knowledge, and convey a lesson, though a costly one."

"But a class of structures fraught with much greater evils exist in great abundance throughout the country—namely, those in which the faults of an unscientific design have been so far counteracted by massive strength, good materials, and careful workmanship, that a temporary stability has been produced, but which contain within themselves sources of weakness, obvious to a scientific examination... that must inevitably cause their destruction within a limited number of years."

"Another evil, and one of the worst which arises from the separation of theoretical and practical knowledge, is the fact that a large number of persons, possessed of an inventive turn of mind and of considerable skill in the manual operations of practical mechanics, are destitute of that knowledge of scientific principles which is requisite to prevent their being misled by their own ingenuity. Such men too often spend their money, waste their lives, and it may be lose their reason in the vain pursuits of visionary inventions, of which a moderate amount of theoretical knowledge would be sufficient to demonstrate the fallacy ; and for want of such knowledge, many a man who might have been a useful and happy member of society, becomes a being than whom it would be hard to find anything more miserable. The number of those unhappy persons — to judge from the patent-lists, and from some of the mechanical journals — must be much greater than is generally believed."

"The most absurd of all their delusions commonly called the , or to speak more accurately, the inexhaustible source of power—is, in various forms, the subject of several patents in each year."

"The ill-success of the projects of misdirected ingenuity has very naturally the effect of driving those men of practical skill, who, though without scientific knowledge, possess prudence and common sense, to the opposite extreme of caution, and of inducing them to avoid all experiments, and to confine themselves to the careful copying of successful existing structures and machines; a course which, although it avoids risk, would, if generally followed, stop the progress of all improvement. A similar course has sometimes... been adopted by men possessed of scientific as well as practical skill: such men having, in certain cases, from deference to popular prejudice, or from a dread of being reputed us theorists, considered it advisable to adopt the worse and customary design for a work in preference to a better but unusual design."

"Some of the evils which are caused by the fallacy of an incompatibility between theory and practice having been described, it must now be admitted, that at the present time those evils show a decided tendency to decline. The extent of intercourse, and of mutual assistance, between men of science and men of practice, the practical knowledge of scientific men, and the scientific knowledge of practical men, have been for some time steadily increasing; and that combination and harmony of theoretical and practical knowledge—that skill in the application of scientific principles to practical purposes, which in former times was confined to a few remarkable individuals, now tends to become more generally diffused."

"Mechanical knowledge may... be distinguished into three kinds; purely scientific knowledge, purely practical knowledge, and that intermediate kind of knowledge which relates to the application of scientific principles to practical purposes, and which arises from understanding the harmony of theory and practice."

"The objects of instruction in purely scientific mechanics and physics are, first, to produce in the student that improvement of the understanding which results from the cultivation of natural knowledge, and that elevation of mind which flows from the contemplation of the order of the universe; and secondly, if possible, to qualify him to become a scientific discoverer."

"In this branch of study exactness is an essential feature; and mathematical difficulties must not be shrunk from when the nature of the subject leads to them."

"The ascertainment and illustration of truth are the objects; and structures and machines are looked upon merely as natural bodies are; namely, as furnishing experimental data for the ascertaining of principles and examples for their application."

"The third and intermediate kind of instruction, which connects the first two... relates to the application of scientific principles to practical purposes. It qualifies the student to plan a structure or a machine for a given purpose, without the necessity of copying some existing example, and to adapt his designs to situations to which no existing example affords a parallel. It enables him to compute the theoretical limit of the strength or stability of a structure, or the efficiency of a machine of a particular kind—to ascertain how far an actual structure or machine fails to attain that limit—to discover the cause of such shortcomings—and to devise improvements for obviating such causes; and it enables him to judge how far an established practical rule is founded on reason, how far on mere custom, and how far on error."

"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."

"Sir John Herschel's "Outlines of Astronomy"—[is] a work in which one of the most profound mathematicians in the world has succeeded admirably in divesting of all mathematical intricacy the explanation of the principles of that natural science which employs higher mathematics most."

"[T]he symbols of algebra, when employed in abstruse and complex theoretical investigations, constitute a sort of thought-saving machine, by whose aid a person skilled in its use can solve problems respecting quantities, and dispense with the mental labour of thinking of the quantities denoted by the symbols, except at the beginning and the end of the operation."

"In treating of the practical application of scientific principles, an algebraical formula should only be employed when its shortness and simplicity are such as to render it a clearer expression of a proposition or rule than common language would be, and when there is no difficulty in keeping the thing represented by each symbol constantly before the mind."

"In theoretical science, the question is—What are we to think? and when a doubtful point arises, for the solution of which either experimental data are wanting, or mathematical methods are not sufficiently advanced, it is the duty of philosophic minds not to dispute about the probability of conflicting suppositions, but to labour for the advancement of experimental inquiry and of mathematics, and await patiently the time when they shall be adequate to solve the question."

"But in practical science, the question is—What are we to do?—a question which involves the necessity for the immediate adoption of some rule of working. In doubtful cases, we cannot allow our machines and our works of improvement to wait for the advancement of science; and if existing data are insufficient to give an exact solution of the question, that approximate solution must be acted upon which the best data attainable show to be the most probable. A prompt and sound judgment in cases of this kind is one of the characteristics of a Practical Man in the right sense of that term."

"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."

"Hypothesis Of Molecular Vortices. In thermodynamics as well as in other branches of molecular physics, the laws of phenomena have to a certain extent been anticipated, and their investigation facilitated, by the aid of hypotheses as to occult molecular structures and motions with which such phenomena are assumed to be connected. The hypothesis which has answered that purpose in the case of thermodynamics, is called that of "molecular vortices," or otherwise, the "centrifugal theory of elasticity. (On this subject, see the Edinburgh Philosophical Journal, 1849; Edinburgh Transactions, vol. xx.; and Philosophical Magazine, passim, especially for December, 1851, and November and December, 1855.)"

"Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena."

"We have... used the word stress to denote the mutual action between two portions of matter. This word was borrowed from common language, and invested with a precise scientific meaning by the late Professor Rankine to whom we are indebted for several other valuable scientific terms."