Chapter 64
Mechanics and motion of bodies; force, weight, machines and the laws of motion.
100 passages · 47 principal · Covers the 49 volumes of primary texts
Mechanics, in the books gathered here, is the science of bodies in motion and of the forces that set them moving, hold them in balance, or bring them to rest. It includes weight and gravitation, the laws by which motion persists and passes from one body to another, and the machines by which human beings lift stones, haul sails and drive clocks. It is a great idea for these volumes for two reasons. It is the one science whose method seemed, to the moderns who founded it, fit to become the method of all natural knowledge. It also prompted the sharpest doubt about such ambitions, the question whether a living or choosing being can be understood as a machine at all.
Pascal states the simplest premise: motion is the object of mechanics, and motion requires something that moves1. Newton gives the classic definition. Mechanics is the science of motions that result from forces, and of the forces required to produce given motions. It has a rational part, which proceeds by demonstration, and a practical part, the work of artificers. Geometry itself, he argues, is founded in mechanical practice2. Voltaire adds a historical judgment: the ancients made great use of mechanics, yet they did not know the laws of motion3. The contrast between using machines and understanding them runs through every later stage of the discussion.
The question of scope arises at once. Newton hopes that the rest of nature’s phenomena might be derived from mechanical principles by the same kind of reasoning he applied to the heavens, and he extends his treatment to motions in resisting mediums4. Pascal agrees that nature is in general explained by figure and motion, but he thinks it ridiculous to claim to say which figures and motions, or to compose the machine in detail5. Later writers carried the mechanical model well beyond physics. Emerson imagines a single initial shove that produces the harmony of centrifugal and centripetal forces and passes through every atom6. Mill takes the composition of forces in dynamics as the pattern for a logical process7. Taine treats the effects of race, surroundings and epoch in history and morals as a mechanical problem of forces and their directions8. Whether these are true extensions or only analogies is a question the texts leave open.
At the centre of rational mechanics stand the laws of motion. Hobbes states the law of inertia as a principle of reason: a body at rest stays at rest, and a body in motion stays in motion, unless something else hinders it, because nothing can change itself9. Kelvin, two centuries later, shows what Newton made of this. Equal forces produce equal motions in equal quantities of matter, so inertia gives a test of quantity of matter10. Weight is gravitation toward the earth and mass is inertia, and Newton’s achievement was to show that bodies of equal heaviness have equal inertia11. Voltaire reports the Newtonian demonstration that bodies moving through fluid vortices meet resistance and lose motion, which tells against the Cartesian picture12.
How such laws are known is a philosopher’s question, and Hume puts it most pointedly. When one billiard ball strikes another, no one could foresee a priori that motion would pass to the second ball. The connection is learned from experience13. Even the law that a body’s force is proportional to its quantity of matter and its velocity, and the use of machines to increase velocity, are discoveries of experience, though mathematics then applies them14. In a note Hume takes up the dispute over whether a moving body’s force varies with its velocity or with the square of its velocity. He holds that we measure the power only by its effect15. Berkeley approaches from another direction. He states swiftness as the reciprocal proportion of time to space traversed, and then argues that motion so measured is relative to the perceiver16. Later his Hylas defends the doctrine that quantity of motion is proportional to velocity and quantity of matter, and that bodies fall with equal velocity17. Burke is more modest, though not entirely unlike Hume. Falling bodies and percussion show that we can explain how things happen without knowing why18.
Weight is the most familiar force, and Faraday’s lectures make it tangible. Weight is a downward pressure, as air resisting the fall of a bladder shows, and a pendulum swings because its bob is always trying to reach its lowest point19. Bodies of equal weight may differ enormously in bulk, from a gas to platinum20. Gravity, which holds the worlds together, keeps the melted wax level in a candle’s cup21. Hydrogen’s lightness makes bubbles and balloons rise22,23. Gases can be weighed, compressed air on a balance24, and the pressure of the atmosphere is pictured as cubes resting one upon another25.
Falling bodies are where ancient opinion and modern demonstration part most visibly. Faraday shows that all bodies, light or heavy, fall by gravity at the same rate26. Gold leaf and a lump of gold fall differently in open air only because of the air’s resistance. Sealed in a bottle they fall alike27, and coin and paper fall together once the resistance is removed28. Voltaire sets out Galileo’s law of accelerated fall, and Newton’s finding that gravity weakens as the inverse square of the distance29,30.
Universal gravitation then joins the falling stone to the planets. Descartes had already held that the parts of the earth tend toward its centre and that the moon causes the tides31, though he explained these effects by motion and impulsion. Voltaire describes how Newton calculated from inverse-square attraction how far a body falls in a second and a minute32. Inverse-square gravitation together with equal action and reaction accounts for planetary motion33, and attraction reaches comets and every part of every body in proportion to its quantity of matter34. It is a central force acting throughout the universe by invariable laws35. Faraday teaches the same doctrine to children. Gravitation is a mutual attraction among all bodies, and things fall to the earth because it is so much larger. Even a mountain draws a ball toward itself36,37. Attraction grows with size, and it keeps people upright on every side of the globe38. It diminishes as the square of the distance, which Faraday illustrates with a lamp and shadows39. It never fails40. Kelvin draws the most striking consequence. The earth and moon fall toward each other while revolving about a common centre of gravity41. The moon is always falling yet never comes down, like a stone thrown hard enough42. Because the moon’s pull differs from one side of the earth to the other, it raises the tidal protuberances43.
The centre of gravity links attraction to balance. Faraday defines it as the point where a mass’s gravitating power is centred44. He finds it in a piece of pasteboard where two plumb-lines cross, and relates it to standing on one leg45. A lowered centre of gravity explains the self-righting toy and the balancing figure46.
Machines bring the question back to practice, and here Helmholtz supplies the governing principle. Machines produce endlessly varied movements, but every one needs a moving force, as human works need muscles47. The amount of work a machine does means the force it spends, not the variety of what it does48. Pasteur uses the labour of raising a ton to a house-top to show that work does not depend on the time taken49. Emerson had stated the moral form of the rule: what we gain in power with mechanical forces we lose in time50. Dana watches it in use, as tackle laid upon tackle multiplies the force that drives hides into a ship’s hold51. Helmholtz proves it. Pulleys, levers and cranes raise loads, but do they yield motive power52? A small weight falling four times as far raises one four times larger, so nothing is gained53. Levers, toothed wheels and winches confirm that greater power means less velocity, and that total work never increases54. Hume’s remark that machines increase velocity14 thus finds its exact accounting.
The doctrine widens when Helmholtz shows that motive force can be stored and can change its form. A weight-driven clock runs only as its weight sinks, and winding restores its capacity55. Work grows with the weight and with the height of its fall56. Falling water turns the overshot wheel and must be raised again before it can work again57. Undershot wheels, windmills, bullets and hammers show that the velocity of a moving mass is itself a motive force, called vis viva58. A pendulum’s velocity carries the weight back up to its original height59, and vis viva, measured in foot-pounds, passes between motion and the tension of springs without being lost or increased60. Crossbow and clock release the work of the arm at different rates, but never more than was put in61. Burke, by contrast, uses the pendulum’s continued swinging only as an analogy for repeated vibrations in the senses62.
Friction seems at first to break the rule. Friction and inelastic impact bring every terrestrial motion to rest, yet the work destroyed reappears as heat63. The motion passes into the smallest particles of bodies and can be transferred again to a piston64. A falling weight is comparable to chemical attraction, since both convert potential into motion and heat65. Turning a handle can even produce work that separates chemical elements66. In this way mechanics becomes the doorway to the conservation of force across nature.
The actual engines in these books cover the whole history of the subject. Herodotus describes Nile boats kept swift and straight by a crate drawn by the current and a stone dragging behind67, and pyramid stones raised stage by stage with machines of short timbers68. These are the ancients using mechanics without its laws, as Voltaire said. Bacon’s New Atlantis imagines engines that multiply winds69 and engine-houses with swifter, stronger motions and even “perpetual motions”70. Helmholtz’s proof that no work is ever gained54 rules out exactly that last dream. Adam Smith uses a boy’s improvement of the fire-engine valve to illustrate a machine’s mechanism71. Helmholtz shows how piston, valve, crank and flywheel turn the expansion of steam into work72. Dana, asked how steam drives a vessel, cannot explain it and falls back on the facts of speed73. He does see the windlass overcome a sail that strong sailors could not haul in by hand74. Kelvin’s tide machine, with its gearing, integrators, cranks, disks and a heavy flywheel, does mathematics mechanically75,76,77. Emerson replies that no number of inventions adds weight to the spiritual fact of life78.
Mechanical explanation of natural bodies flourishes in the nineteenth-century texts. Darwin explains the click-beetle’s leap by an elastic spine bending like a spring, not by simple muscular contraction79. He explains the condor’s soaring by an inclined wing pressing against the air, which counterbalances gravity with little force80, and the form of volcanic bombs by rotation, centrifugal force and cooling81. Helmholtz measures how glacier speed varies with season and position, and stresses the ice’s irresistible force82. He derives crevasses from unequal velocities83 and moraines from the parallel motion of the ice’s layers84. Kelvin reasons that the force needed to vibrate a mass grows as the square of the frequency, so the vibrations of light would demand enormous force85. He pictures transverse vibration with a whirled rope86, and explains Dover’s great tidal range by inertia and resonance in a channel87.
The hardest case is the living body. Harvey compares the heart’s tension to the contraction of muscle fibres88,89. Its successive motions, like the wheels of a machine or the parts of a gunlock, appear as a single motion90. He follows the action of the valves that prevent backflow91,92, and he finds the origin of local motion in contraction, with the auricles striking the blood into the ventricles like a ball-player hitting on the rebound93. Descartes goes further. The heart’s motion follows necessarily from the arrangement of its parts, as a clock’s does from weights and wheels94. Animal spirits move the body by the rules of mechanics, so that the body is a machine like the automata95. Hobbes traces visible action back to small insensible motions within96.
Rousseau draws the limit. Natural philosophy may explain the mechanism of the senses, but not the power of choosing, which no law of mechanics accounts for97. Motion communicated, like that of a watch driven by its spring, must be distinguished from spontaneous motion98. That disagreement, between Descartes’s automaton and Rousseau’s free agent, is the question these books leave open. Newton’s hope4 and Pascal’s warning5 still stand side by side. The great conservation law shows how far mechanics can reach, and whether it reaches the will remains in dispute.
Introductory essay written by Claude Opus 5.5 from the outline and the notes on every passage below; quotations are checked against this edition.
See also: Quantity 4a
See also: Astronomy and Cosmology 4b · Mathematics 4a · Cause 8b
See also: Cause 8b
See also: Cause, Physics, Quantity, Astronomy and Cosmology, Mathematics, Experience