The Cylinder. Helmut Müller-Sievers

that governed, and bedeviled, Newton’s mechanics gave way to processes that were conceived as contiguous or, as historians later would call it, analog.² Insofar as it translated every physical change into a fully measurable effect, the steam engine was, on a very fundamental level, nothing but a mechanism to transmit the “motive power of heat” present in the universe. Kinematicists, who conceptualized and facilitated this transmission, could therefore claim to be concerned with the very essence of machines.

      What engineers had tacitly presupposed since the middle of the eighteenth century found its basic expression in the first law of thermodynamics: not only are forces convertible into one another, but such conversions also happen without absolute loss. The accounts of all transactions in nature are always balanced, nothing is added to and nothing lost from the overall sum. The law of the conservation of force confirmed that machines were calculable and therefore scientific objects and that the input in energy equaled the output in work minus the inevitable price paid to the environment in terms of evaporation, cooling, friction, and so on.³ Their calculability as material systems in interaction with their environment distinguished nineteenth-century machines from the automata of the eighteenth century, which needed to be insulated against their environment, had an input consisting in some form of kinetic energy, and had an output that was not measurable—or, in the case of pendulums, clocks, and other instruments, was measurement itself.⁴

      The interconversion and the conservation of force—as well as the interconversion of the knowledge of engineers, physicists, and physiologists—provided a finite frame in which translatability was a much more concrete and immediate concern than originality.⁵ Of course, the question of the origin of force was not “solved” by this approach, but, in a fashion not untypical of the epoch’s concentration on practicability, it was pushed toward the margins of metaphysics and religion. Under the auspices of the laws of thermodynamics, the earth, fueled by the heat of the sun, became part of a vast cosmic heat engine; the individual machines built on earth did nothing but intercept and utilize the stream of energy flowing through them. Cosmic heat, stored in subterranean coalfields, needed only to be reignited to provide energy for untold machines independently of their location.

      Unfortunately, physicists also discovered that while forces could be translated into one another, the overall flow of energy was unidirectional and irreversible, from hot to cold. This second law of thermodynamics marked the beginning of ecological thinking; remarkably early, physicists and philosophers realized that human beings were, in the words of a French observer, “nothing but concessionaires” of the earth’s finite resources.⁶ Physicists, many of them devout Christians, scrambled to reconcile this inglorious dissipation with the biblical apocalypse, but the fact remains that ecological thinking is characterized by a renunciation of transcendence and divine intervention: while in Newton’s universe God still had to intervene to correct potentially catastrophic irregularities of planetary motion, the fully analog and slowly stalling universe of the nineteenth century no longer had an opening for such correction. Not the origin of forces but their end became a major preoccupation for the epoch; entropy, the inevitable descent of all organization into undifferentiated matter and meaningless noise, was the flipside of the fully calculable universe.⁷

      In this situation, kinematics as the science of mechanical energy exchange and transmission rose quietly to prominence, not only because under the first law of thermodynamics every machine is a transmission mechanism anyway, but because under the second law the transmission is that part of a machine that can minimize entropy—by finding the best paths, by reducing stress on materials, and by avoiding as much as possible leakage through friction.⁸ This is not its stated goal, and the first great theorist of the field, the German Franz Reuleaux, explicitly excluded all material considerations; but in the end he too dreamt of a totally negentropic machine, one that would run in perfect silence with the least amount of energy loss.

      Modern kinematics owes its theoretical formulation and its formation as a discipline to the emergence of new schools and curricula, particularly in Napoleonic and post-Napoleonic France.⁹ While France—to say nothing of Germany—lagged behind in the development and industrial deployment of steam engines, the Grands Écoles, founded in the wake of the French Revolution, were among the first institutions to reward engineers with academic positions and to urge mathematicians to think about the practical implications of mechanisms. Already in 1794, Gaspard Monge proposed courses on the theory of machines that would focus on the elementary mechanisms of force transmission: “By these elements are to be understood the means by which the directions of motion are changed; those by which progressive motion in a right line, rotative motion and reciprocating motion, are made each to reproduce the others. The most complicated machines being merely the result of a combination of some of these elements, it is necessary that a complete enumeration of them should be drawn up.”¹⁰ The mathematician Monge here identifies machine transmissions as instantiations of Leonard Euler’s earlier observation that the motion of all rigid bodies may be broken down into translation along a straight line and rotation around an axis.¹¹ To transfer motion to act at any point in space and to act as translational, reciprocal, or rotational motion, the machine designer has to devise a chain of joints and linkages that best embodies and combines motions. Franz Reuleaux will later summarily call these chains cylinder chains.

      The recognition of rotation as an irreducible and entirely technical form of motion meant that the moving object under investigation and construction could no longer be conceived as a mathematical point; points, lacking extension, cannot rotate. As Kleist’s choreographic criticism had implied, the coherence and predictive success of Newton’s mass point mechanics were in large part predicated on the fact that celestial objects in motion could be reduced to geometrical points because they were so far away and their orbits were so large; at close range and in rapid repetition, however, otherwise negligible imperfections (in the axial symmetry of an object, for example) were magnified and could quickly lead to the breakdown of a system of linkages. This is why standardization and precision tool making would take the place of mathematical solutions in nineteenth-century engineering.

      Newton’s celestial objects were moving along straight-line paths, or on paths that could be analyzed as the result of forces jointly impacting an imaginary center where all mass was concentrated. Rotary motion, by contrast, had to be conceived as the impact of two forces at separate points of an extended body. To reiterate, it makes no sense to speak of the rotation of a point, but neither does it make sense to speak of a single rotating force.¹² Louis Poinsot, also a product of the new French education system, argued that rotation should be viewed as the result of a “couple” of forces, acting equally from opposite directions on a line drawn through the center of a rotating body. Thus rotation can be quantified as the product of the forces times the length of the line on which they act: this is the measure of torque—a quantity unknown to the eighteenth century—which even today is the true measure of the output of machines, most prominently the automobile engine.¹³ (A good example is turning a car’s steering wheel: one hand pulls downward, the other pushes upward, and both are at an equal distance from the center of the wheel. Before the introduction of power steering, the diameter of steering wheels in heavy trucks was particularly large to help the driver expend less force in turning the vehicle.)

      Kinematics relies on a still more restricted description of motion than that outlined by Newton and amplified by Poinsot. It is defined as a view of motion independent from the forces causing it. Since machines are, from one point of view, manifest attempts to eliminate random, or, as Franz Reuleaux would say, “cosmic,” forces, kinematics is always “kinematics of machinery.”¹⁴ The text that is most often mentioned as the declaration of independence of kinematics, André-Marie Ampère’s Essai sur la philosophie des sciences (1834), clearly recognizes this interdependence of machinery and geometric description:

      It [i.e., the new science of kinematics] should treat in the first place of spaces passed over, and of times employed in different motions, and of the determination of velocities according to the different relations which may exist between those spaces and times. Furthermore it should study the various instruments by means of which one motion can be changed into another; so that if one conceives of these instruments as machines (as is usually the case) one must define a machine not, as one customarily