Franz Reuleaux

“ In the school of Galileo,—where his experiments on falling bodies first threw a ray of light through the scholastic cloud which had veiled all knowledge,—there began early in the seventeenth century those experiments in physical science with the growth of which the invention of the steam-engine is inseparably bound up. It is no mere chance that the place is distinguished also as the centre of great artistic development;—art and science nourish together on a rich soil. ”

“ From such a summary review we might almost be led to believe in the entirely spontaneous unfolding of ideas, were it not that each separate energetic step forward shows us the grasp of more distinguished endowments, and convinces us afresh of the importance of genius in the further growth of the race. Throughout the whole, however, we can discern the one idea developing itself out of the other, like the leaf from the bud or the fruit from the blossom; just as throughout nature everywhere each new creation is developed from those which have preceded it. ”

“ The whole process of thought and conclusion seldom lies on the surface,—seldom takes, that is, the form of a chain of reasoning clearly thought out, although we may endeavour to attain this in order to be able to give ourselves and others an account of what has occurred: commonly, however, the rumination by which the material received from without is converted into thoughts, occurs as it were in darkness,—taking place almost as unconsciously as the change of the nourishment into the fluid and substance of the body. ”

“ While in appearance a machine differs greatly from any of the force- or motion-distributors of nature, yet for the theoretical or pure mechanician no such difference exists,—or rather it completely disappears on analysis, so that to him the problems of machinery fall into the same class as those of the mechanical phenomena of nature. He sees in both forces and motions existing, and subject to the same great laws which, developed in their most general form, govern and must govern every single case. In pure Mechanics machines are now treated only as illustrations ”

“ If the processes of thought by which the existing mechanisms have been built up are known, it must be possible to continue the use of these processes for the same purpose;—they must furnish the means for arriving at new mechanisms—must, that is to say, take up the position hitherto assigned to invention. I hope not to fall under the suspicion of saying anything so absurd as that the new method will make it possible for the commonplace head to become oracularly inventive like that of the genius. ”

“ We shall then note that in the kosmical system the mutual motions of the bodies, both as to their paths and their velocities, are entirely dependent on the influence of sensible forces, while in the machine system the paths of motion are absolutely determined, and at the same time no point can alter its velocity without the velocities of all other points being correspondingly altered; that in the latter case, therefore, disturbing sensible forces are without influence,—they are everywhere balanced by the latent forces. Not less is it these last which carry the moving forces from body to body. ”

“ In other words, the invention of a mechanism will be to the scientific kinematist a synthetic problem,—which he can solve by the use of systematic, if also difficult, methods. The clever man, supplied with such powerful instruments, will leave the less clever behind in future as hitherto,—just as the mathematical genius leaves behind the mere algebraist who works only with operations learnt by rote.
The thorough understanding of old mechanisms, however, is even more important than the creation of new ones. ”

“ For the understanding of the nature of machines the last-named science is evidently as important as the three first; indeed in many respects it must stand first and prepare the way for them, and on this account single sections of Kinematics are often included in all three. The union of the three last sciences is necessary that the machine may be completely understood, the first having pointed out its existence and treated it teleologically. All four interact continually; only as a whole do they furnish the practical mechanist with complete solutions to all the problems of his work. ”

“ For the scientific theory of mechanisms, if it give a complete mastery over analysis, sweeps entirely away a great portion of the difficulties, and entirely alters the nature of those which remain. While the empirical method is only a groping in the dark in the hope that by good luck we may lay hold of the solution, we come here to the application of an inductive method, based upon a well-understood analysis. The difficulties now consist only in the increased demands upon the capacity for induction. In this itself, however, Kinematics follows its own strict laws, like all other sciences. ”

“ Then came Watt (circa 1763) , whose far-reaching genius furnished a whole series of mechanical and kinematic inventions, and brought the machine in a short time to a high degree of completeness, enriching at the same time all the kindred realms of knowledge. From that time onward the rapidly extending employment of the machine and its continual development, improvements from a thousand heads and a thousand hands, have brought it to its present perfection, and made it absolutely the common property of all. ”

“ With the growth of clear ideas in physical science it became possible to separate the ideas of force, time and motion, and to consider the latter merely for its own sake without reference to the other two. ”

“ The real cause of the insufficiency of the system is not, however, the classification itself; it must be looked for deeper. It lies, as I have already pointed out, in the circumstance that the investigations have never been carried back far enough,—back to the rise of the ideas; that classification has been attempted without any real comprehension being obtained of the objects to be classified. The formation of a science cannot be entered upon in medias res; it requires that we should start, as in mathematics, from the very simplest elements, the axiomatic beginnings. ”

“ As I have here to do chiefly with theoretical questions, it might seem that I could hardly expect to interest others than those concerned only with the theoretical side of this special study. But Theory and Practice are not antagonistic, as is so often tacitly assumed. Theory is not necessarily unpractical, nor Practice unscientific, although both of these things may occur. Indeed in any department thoroughly elucidated by Science the truly practical coincides with the theoretical, if the theory be right. The popular antithesis should rather be between Theory and Empiricism. ”

“ The prevention of disturbing motions by latent forces is then a principle in the machine. Its application is connected with various objects. When a machine is constructed it is meant to be an arrangement for carrying on some definite mechanical work—it may be the moving of some body, or the alteration of its form, or both together. For such a purpose we require that so soon as motion is caused by any effort in any part of the machine that motion shall be of an absolutely defined nature. ”

“ It must not, however, be considered that theory has only and always to limp behind practice, as is too often the case; it may rather be said to comprehend in itself all the mutual relations of the laws which in their application constitute this practice; it raises a clear flame out of each spark of truth, and so renders possible new and various roads to its higher development. The attitude of Theory and Practice to each other, in connection with the Machine, must be one of mutual respect. ”

“ This study we shall begin in the following section.
It can be readily understood that such an investigation is neither simple nor easy, to me at least it does not appear possible to pass quickly over such wide-reaching questions. Whoever attentively examines the nature of the machine, discovers in it so many phenomena having mutual relations difficult to understand that he cannot penetrate to the deep under-lying laws which connect them, and he comprehends how it has often taken the whole power of single men to carry forward even one step some of the problems which present themselves. ”

“ I believe I have shown in the preceding paragraphs that a more or less logical process of thought is included in every invention. The less visible this is from outside, the higher stands our admiration of the inventor,—who earns also the more recognition the less the aiding and connecting links of thought have been worked out ready to his hand. To-day, when scientific aids are so abundant in every branch of technical work, progressions of the greatest importance are frequently made without receiving any such high recognition as in former times. ”

“ Terms have been made with this inconsistency, which would not readily be submitted to in any other of the exact sciences, by considering Invention either avowedly or tacitly as a kind of revelation, as the consequence of some higher inspiration. It forms the foundation of the kind of special respect with which any man has been regarded of whom it could be said that he had invented this or that machine. To become acquainted with the thing invented we leap over the train of thought in which it originated, and plunge at once, designedly, in medias res. ”

“ Nothing is to be seen of the inner force so long as it is not awakened by an outer one. It is as it were concealed in the interior of the body. We shall not be carrying the analogy with Thermal Physics too far if we call these molecular forces, which in their hiding-places guard the stability of the material world, latent forces, as opposed to the directly measurable sensible forces which externally influence bodies through gravitation and other causes. ”

“ In proceeding to examine these properties more closely, we shall assume in the first instance that the bodies possess complete rigidity, and shall pay no attention to their size,—in other words we take all questions belonging to what we have called the special study of machinery and the study of machine-design as solved, so that only geometrical properties remain for us to consider. ”

“ It is unquestionably true that by the aid of mathematics this treatment of mechanisms has given us many most valuable results, but it is equally true that the method itself is defective, and was only used for want of a better. This better method Prof. Reuleaux has attempted, and I think with great success, to indicate. Starting with the idea of motion as change of position only—and limiting himself to cases where such changes are absolutely determinate at every instant,—as always in the machine—he points out that they are conditioned simply by the geometric form of the moving bodies. ”

“ The fundamental notions of force and motion themselves are subject to uncertain interpretation. In the attempt to define ideas standing on the boundary line between Physics and Metaphysics an uncertainty which demands the closest mathematical and philosophical investigation makes itself felt. This uncertainty or indistinctness, by holding open a perspective of ideas entirely beyond all purpose of the study concerned, exercises a disturbing influence on it. It affects every definition, every explanation intended to be exhaustive ”

“ As many systems as authors, no resting point reached, always new trying and seeking,—and as a conclusion we have Ampère's well-defined science split into two, indeed into four sciences, as if it were one of those Infusoria which are propagated by division. On the other hand, we may make the consolatory remark that the observations have grown more and more in exactness and delicacy, as also that both the methods of examination and the mechanisms examined have by degrees greatly increased in number. ”

“ For a long time no satisfactory results were obtained, but at last, in 1696, Papin at Marburg discovered the true solution—the condensation of steam in a cylinder fitted with a piston. The steam-engine was invented. Papin, an experimenter really worthy of respect, who attempted to solve the problem in the most various ways, and who has made a whole series of other remarkable inventions, is its true inventor. ”

“ Every time, however, that we have to choose between the useful and the useless, we are compelled to return from the abstract to the concrete. In the school, therefore, kine- matic science must frequently be connected with its practical applications it has not only to show what theoretical solution applies to problems already solved empirically, but in. most cases to construct the theory as well as to find it. It is remarkable that there is scarcely any kinematic problem, scarcely any turning, however bold, in the theoretical propositions, for which we cannot find an example in practice. ”

“ On the contrary, if the new theory is to lay claim to general interest, it must be capable of producing something new; it must make problems solvable which before could not be solved in any systematic way. This may certainly be said to be the case if it succeeds in making Machine-Kinematics, down to its simplest problems, truly scientific. ”

“ Every turning of relatively to must necessarily be accompanied by alterations in the positions of and of —the chain is therefore closed. In itself a closed chain does not postulate any definite absolute motion. In order to obtain this a similar method must be adopted to the one employed above with pairs of elements,—namely, to hold fast or fix in position one linkof the chain relatively to the portion of surrounding space assumed to be stationary. The relative motions of the links then become absolute. A closed kinematic chain, of which one link is thus made stationary, is called a mechanism. ”

“ The balancing of sensible by latent forces is therefore not solely a distinctive mark of the machine but we have in it a principal characteristic of the machine-like or machinal as distinguished from the kosmical, and it must be kept distinctly in view in endeavouring to understand the exact idea conveyed by the word machine. ”

“ In his system of sciences Ampère ranked the study created by Monge and Carnot as one of the third order, and attempted to lay down its exact limits. He considered in connection with it Lanz's treatise, and said, among other things—"It (this science) must therefore not define a machine, as has usually been done, as an instrument by the help of which the direction and intensity of a given force can be altered, but as an instrument by the help of which the direction and velocity of a given motion can be altered." ”

“ The whole study of the constitution of machines—the Kinematics of Machinery—naturally divides itself into two parts, the one comprehending the theoretical, and the other the applied or practical side of the subject; of these the former alone forms the subject of this work. It deals chiefly with the establishment of those ideas which form the foundation of the applied part of the science, and in its treatment of these its method differs in great part essentially from those hitherto employed. ”

“ The remodelling which has become necessary requires undisturbed adherence to clear, simple, logical principles. What, however, is to be drawn from our criticism of the system hitherto used,—what I have endeavoured to illustrate and develope by single instances,—what the philosophical sentences I have quoted bring before us in a condensed form,—we may contract into one word. So far as our special problem is concerned, the question is to make the science of machinery deductive. The study must be so formed that it rests upon a few fundamental truths peculiar to itself. ”

“ The peculiar condition consequently presents itself throughout the whole region of investigation into the nature of the machine that the most perfect means have been employed to work upon the results of human invention—that is of human thought without anything being known of the processes of thought which have furnished these results. ”

“ If new ideas therefore are to be substituted for the common ones, it can only be by a wrench sufficiently powerful to overcome the cohesion of established notions and prejudices. There are the traditional courses of instruction in the schools,—the widely extended and important technical literature,—the force of habit, acquired with difficulty, and on that very account firmly rooted; there is also the real difficulty that the new study requires to be grasped as a whole, and not taken up partially and occasionally,—all these pile up mighty hindrances. ”