Part 27
Nature, experience the well-spring of all knowledge of, 181; fashions of, 64; first knowledge of, instinctive, 189; general interconnexion of, 182; has many sides, 217; her forces compared to purposes, 14-15; likened to a good man of business, 15; the economy of her actions, 15; how she appears to other animals, 83 et seq.; inquiry of, viewed as a torture, 48-49; view of, as something designedly concealed from man, 49; like a covetous tailor, 9-10; magic powers of, 189; our view of, modified by binocular vision, 82; the experimental method a questioning of, 48.
Negro hamlet, the science of a, 237.
Neptune, prediction and discovery of the planet, 29.
New views, 296 et seq.
Newton, describes polarisation, 242; expresses his wealth of thought in Latin, 341; his discovery of gravitation, 225 et seq.; his solution of dispersion, 362; his principle of the equality of pressure and counterpressure, 191; his view of light, 227-228; on absolute time, 204; selections from his works for use in instruction, 368; also 270, 274, 279, 285, 289.
Nobility, they displace Latin, 342.
Notation, musical, mathematically illustrated, 103-104.
Numbers, economy of, 195; their connexion with consonance, 32.
Numerical mysticism, 33.
Nursery, the questions of the, 199.
Observation, 310.
Observation, in science, 261.
Ocean-stream, 272.
Oettingen, Von, 103.
Ohm, on electric currents, 249.
Ohm, the word, 343.
Oil, alcohol, water, and, employed in Plateau's experiments, 4; free mass of, assumes the shape of a sphere, 12; geometrical figures of, 5 et seq.
One-eyed people, vision of, 98.
Ophthalmoscope, 18.
Optic nerves, 96.
Optimism and pessimism, 234.
Order of physics, 197.
Organ, bellows of an, 135.
Organic nature, results of Darwin's studies of, 215 et seq. See _Adaptation_ and _Heredity_.
Oriental world of fables, 273.
Orientation, sensations of, 282 et seq.
Oscillation, centre of, 147 et seq.
Ostwald, 172.
Otoliths, 301 et seq.
Overtones, 28, 40, 349.
Ozone, Schöbein's discovery of, 271.
Painted things, the difference between real and, 68.
Palestrina, 44.
Parameter, 257.
Partial tones, 390.
Particles, smallest, 104.
Pascheles, Dr. W., 285.
Paulsen, 338, 340, 373.
Pearls of life, strung on the individual as on a thread, 234-235.
Pencil surpasses the mathematician in intelligence, 196.
Pendulum, motion of a, 144 et seq., increased motion of, due to slight impulses, 21; electrical, 110.
Percepts, of like form, 390.
Periodical, changes, 181; series, 256.
Permanent, changes, 181, 199; elements of the world, 194.
Perpetual motion, a, 181; defined, 139; impossibility of, 139 et seq.; the principle of the, excluded, 140 et seq.; excluded from general physics, 162.
Personality, its nature, 234-235.
Perspective, 76 et seq.; contraction of, 74 et seq.; distortion of, 77.
Pessimism and optimism, 234.
Pharaohs, 85.
Phenomenology, a universal physical, 250.
Philistine, modes of thought of, 223.
Philology, comparison in, 239.
Philosopher, an ancient, on the moral and physical sciences, 89.
Philosophy, its character at all times, 186; mechanical, 155 et seq., 188, 207, 259 et seq.
Phonetic alphabets, their economy, 192.
Photography, by the electric spark, 318 et seq.
Photography of projectiles, 309-337.
Photography, stupendous advances of, 74.
Physical, concepts, fetishism in our, 187; ideas and principles, their nature, 204; inquiry, the economical nature of, 186; research, object of 207, 209.
Physical phenomena, as mechanical phenomena, 182; relations between, 205.
Physico-mechanical view of the world, 155, 187, 188, 207 et seq.
Physics, compared to a well-kept household, 197; economical experience, 197; the principles of, descriptive, 199; the methods of, 209; its method characterised, 211; comparison in, 239; the facts of, qualitatively homogeneous, 255; how it began, 37; helped by psychology, 104; study of its own character, 189; the goal of, 207, 209.
Physiological psychology, its methods, 211 et seq.
Physiology, its scope, 212.
Piano, its mirrored counterpart, 100 et seq.; used to illustrate the facts of sympathetic vibration, 25 et seq.
Piano-player, a speaker compared to, 192.
Picture, physical, a, 110.
Pike, learns by experience, 267.
Pillars of Corti, 19.
Places, heavy bodies seek their, 224 et seq.
Planetary system, origin of, illustrated, 5.
Plasticity of organic nature, 216.
Plateau, his law of free liquid equilibrium, 9; his method of getting rid of the effects of gravity, 4.
Plates of oil, thin, 6.
Plato, 347, 371.
Plautus, 347.
Playfair, 138.
Pleasant effects, cause of, 94 et seq.
Pliny, 349.
Poetry and science, 30, 31, 351.
Poinsot, on the foundations of mechanics, 152 et seq.
Polarisation, 91; abstractly described by Newton, 242.
Politics, Chinese speak with unwillingness of, 374.
Pollak, 299.
Polyp plant, humanity likened to a, 235.
Pompeii, 234; art in, 80.
Popper J., 172, 216.
Potential, social, 15; electrical, 121 et seq.; measurement of, 126; fall of, 177; swarm of notions in the idea of, 197; its wide scope, 250.
Pottery, invention of, 263.
Prediction, 221 et seq.
Prejudice, the function, power, and dangers of, 232-233.
Preparatory schools, the defects of the German, 346-347; what they should teach, 364 et seq.
Pressure of a stone or of a magnet, will compared to, 14; also 157.
Primitive acts of knowledge the foundation of scientific thought, 190.
Problem, nature of a, 223.
Problems which are wrongly formulated, 308.
Process, Carnot's, 161 et seq.
Projectiles, the effects of the impact of, 310, 327-328; seen with the naked eye, 311, 317; measuring the velocity of, 332; photography of, 309-337.
Prony's brake, 132.
Proof, nature of, 284.
Prophesying events, 220 et seq.
Psalms, quotation from the, 89.
Pseudoscope, Wheatstone's, 96.
Psychology, preceded by astronomy, 90; how reached, 91 et seq.; helps physical science, 104; its method the same as that of physics, 207 et seq.
Pully arrangement, illustrating principle of least superficial area, 12-13.
Purkinje, 284, 285, 291, 299.
Purposes, the acts of nature compared to, 14-15; nature pursues no, 66.
Puzzle-lock, a, 26.
Puzzles, 277.
Pyramid of oil, 6.
Pythagoras, his discovery of the laws of harmony, 32, 259.
Quality of tones, 36.
Quantitative investigation, the goal of, 180.
Quantity of electricity, 111, 118, 119, 167-170, 173; of heat, 166, 167-171, 174, 177, 244; of motion, 184.
Quests made of the inquirer, not by him, 30.
Quételet, 15, footnote.
Rabelais, 283.
Raindrop, form of, 3.
Rameau, 34.
Reaction and action, principle of, 191.
Reactions, disclosure of the connexion of, 270 et seq.
Realgymnasien, 365.
Realschulen, 365, 373.
Reason, stands above the senses, 105.
Reflex action, 210.
Reflexion, produces symmetrical reversion of objects, 93 et seq.
Refraction, 29, 193, 194, 208, 230, 231.
Reger, 328.
Reliefs, photographs of, 68.
Repetition, its rôle in æsthetics, 89, footnote, 91 et seq., 97, 98 et seq., 390.
Reproduction of facts in thought, 189, 193, 198, 253.
Repulsion, electric, 109 et seq., 168.
Research, function of experimental 181; the aim of, 205.
Resemblances between facts, 255.
Resin, solution of, 7.
Resistance, laws of, for bodies travelling in air and fluids, 333 et seq.
Resonance, corporeal, 392.
Response of sonorous bodies, 25.
Retina, the corresponding spots of 98; nerves of compared to fingers of a hand, 96 et seq.
Reversible processes, 161 et seq., 175, 176, 181, 182.
Rhine, the, 94.
Richard the Third, 77.
Riddles, 277.
Riders, 379.
Riegler, 319.
Riess, experiment with the thermo-electrometer, 133 et seq., 169.
Rigid connexions, 142.
Rind of a fruit, 190.
Rings of oil, illustrating formation of rings of Saturn, 5.
Ritter, 291, 299.
Rods of Corti, 19.
Rolph, W. H., 216.
Roman Church, Latin introduced with the, 340 et seq.
Romans, their provinciality and narrow-mindedness, 270.
Romeo and Juliet, 87.
Römer, Olaf, 51 et seq.
Roots, the nature of, in language, 252.
Rosetti, his experiment on the work required to develop electricity, 131.
Rotating bodies, 285.
Rotation, apparatus of, in physics, 59 et seq.; sensations of, 288 et seq.
Rousseau, 336.
Rubber pyramid, illustrating the principle of least superficial area, 10-11.
Ruysdael, 279.
Sachs, Hans, 106.
Salcher, Prof. 319.
Salviati, 144.
Saturn, rings of, their formation illustrated, 5.
Saurians, 257.
Sauveur, on acoustics, 34, 375 et seq.
Savage, modes of conception and interpretation of a, 218 et seq.
Schäfer, K., 298.
_Schlierenmethode_, 317.
Schönbein's discovery of ozone, 271.
School-boy, copy-book of, 92.
Schoolmen, 214.
Schools, State-control of, 372 et seq.
Schopenhauer, 190.
Schultze, Max, 19.
Science, a miserly mercantile principle at its basis, 15; compared to a business, 16; viewed as a maximum or minimum problem, 16, footnote; its process not greatly different from the intellectual activity of ordinary life, 16, footnote; economy of its task, 16; relation of, to poetry, 30, 31, 351; the church of, 67; beginnings of, 189, 191; belief in the magical power of, 189; can dispense with mystery, 189; lavish extravagance of, 189; economy of the terminology of, 192; partly made up of the intelligence of others, 196; stripped of mystery, 197; its true power, 197; the economical schematism of, 206; the object of, 206; the tools of, 207; does not create facts, 211; of the future, 213; revolution in, dating from Galileo, 214 et seq.; the natural foe of the marvellous, 224; characterised, 227; growth of, 237; dramatic element in, 243; described, 251; its function, 253; classification in, 255, 259 et seq.; the way of discovery in, 316. See also _Physics_.
Sciences, partition of the, 86; the barriers and relations between the 257-258; on instruction in the, 338-374.
Scientific, criticism, Socrates the father of, 1, 16; discoveries, their fate, 138; knowledge, involves description, 193; thought, transformation and adaptation in, 214-235; thought, advanced by new experiences, 223 et seq.; thought, the difficulty of, 366; terms, 342-343; founded on primitive acts of knowledge, 190.
Scientists, stories about their ignorance, 342.
Screw, the, 62.
Sea-sickness, 284.
Secret computation, Leibnitz's, 33.
Seek their places, bodies, 226.
Self-induction, coefficient of, 250, 252.
Self-observation, 211.
Self-preservation, our first knowledge derived from the economy of, 197; struggle for, among ideas, 228.
Semi-circular canals, 290 et seq.
Sensation of rounding a railway curve, 286.
Sensations, analysed, 251; when similar, produce agreeable effects, 96; their character, 200; defined, 209; of orientation, 282 et seq.
Sense-elements, 179.
Senses, theory of, 104; the source of our knowledge of facts, 237.
Seventh, the troublesome, 46.
Shadow method, 313 et seq., 317 footnote.
Shadows, rôle of, in vision, 81.
Shakespeare, 278.
Sharps, reversed into flats, 101.
Shell, spherical, law of attraction for a, 124, footnote.
Shoemaker, inquirer compared to, 105-106.
Shooting, 309.
Shots, double report of, 229 et seq.
Similarity, 249.
Simony, 280.
Simplicity, a varying element in description, 254.
Sines, law of the, 193.
Sinking of heavy bodies, 222.
Sixth sense, 297.
Smith, R., on acoustics, 34, 381, 383.
Soap-films, Van der Mensbrugghe's experiment with, 11-12.
Soapsuds, films and figures of, 7.
Social potential, 15.
Socrates, the father of scientific criticism, 1, 16.
Sodium, 202.
Sodium-light, vibrations of, as a measure of time, 205.
Solidity, conception of, by the eye, 71 et seq.; spatial, photographs of, 73.
Solids, and liquids, their difference merely one of degree, 2.
Sonorous bodies, 24 et seq.
Soret, J. P., 89.
Sounds, symmetry of, 99 et seq.; generally, 22-47, 212.
Sound-waves rendered visible, 315 et seq.
Sources of the principle of energy, 179 et seq.
Space, 205; sensation of, 210.
Spark, electric, 117, 127, 132, 133, 190.
Spatial vision, 386.
Species, stability of, a theory, 216.
Specific energies, 291.
Specific heat, 166, 244.
Specific inductive capacity, 117.
Spectral analysis of sound, 27.
Spectrum, mental associations of the, 190.
Speech, the instinct of, cultivated by languages, 354.
Spencer, 218, 222.
Sphere, a soft rotating, 2; the figure of least surface, 12; electrical capacity of, 123 et seq.
Spherical shell, law of attraction for 124, footnote.
Spiders, the eyes of, 67.
Spirits, as explanation of the world 186, 243.
Spiritualism, modern, 187.
Spooks, metaphysical, 222.
Squinting, 72.
Stability of our environment, 206.
Stallo, 336.
Stars, the fixed, 90.
State, benefits and evils of its control of the schools, 372 et seq.; the Church and, 88.
Statical electricity, 134.
Stationary currents, 249.
Statoliths, 303.
Steam-engine, 160, 265.
Steeple-jacks, 75.
Stereoscope, Wheatstone and Brewster's, 73.
Stevinus, on the inclined plane, 140; on hydrostatics, 141; on the equilibrium of systems, 142; discovers the principle of virtual velocities, 150; characterisation of his thought, 142; also 182, 187, 191.
Stone Age, 46, 321.
Störensen, 306.
Stove, primitive, 263.
Straight line, a, its symmetry, 98.
Straight, meaning of the word, 240.
Street, vista into a, 75.
Striae, in glass, 313.
Striate method, for detecting optical imperfections, 317.
Striking distance, 115, 127.
Strings, vibrations of, 249.
Struggle for existence among ideas, 217.
Substance, heat conceived as a, 177, 243 et seq.; electricity as a, 170; the source of our notion of, 199; rôle of the notion of, 203, 244 et seq.; energy conceived as a, 164, 185, 244 et seq.
Substitution-value of heat, 178, footnote.
Suetonius, 348.
Sulphur, specific inductive capacity of, 117.
Sun, human beings could not exist on, 3.
Swift, 84, 280.
Swimmer, Ampère's, 207.
Symmetry, definition of, 92; figures of, 92 et seq.; plane of, 94; vertical and horizontal, 94; in music, 99 et seq.
Sympathetic vibration, 22 et seq., 379.
Tailor, nature like a covetous, 9-10.
Tangent, the word, 263.
Taste, doubtful cultivation of, by the classics, 352-353; of the ancients, 353.
Taylor, on the vibration of strings, 249.
Teaching, its nature, 366 et seq.
Telegraph, the word, 263.
Telescope, 262.
Telestereoscope, the, 84.
Temperament, even, in tuning, 47.
Temperature, absolute, 162; differences of, 205; differences of, viewed as level surfaces, 161; heights of, 174; scale of, derived from tensions of gases, 174.
Terence, 347.
Terms, scientific, 342-343.
Thales, 259.
Theories, their scope, function, and power, 241-242; must be replaced by direct description, 248.
Thermal, energy, 174, 177; capacity, 123, footnote.
Thermodynamics, 160 et seq.
Thermoelectrometer, Riess's, 133, 169.
Thing-in-itself, the, 200.
Things, mental symbols for groups of sensations, 200-201.
Thomson, James, on the lowering of the freezing-point of water by pressure, 162.
Thomson, W., his absolute electrometer, 127, footnote; on thermodynamics, 162; on the conservation of energy, 165; on the mechanical measures of temperature, 174, footnote; on waste of mechanical energy, 175; also 108, 173, footnote.
Thought, habitudes of, 199, 224, 227, 232; relationship between language and, 329; incongruence between experience and, 206; luxuriance of a fully developed, 58; transformation in scientific, 214-235.
Thoughts, their development and the struggle for existence among them, 63; importance of erroneous, 65; as reproductions of facts, 107.
Thread, the individual a, on which pearls are strung, 234-235.
Tides, 283.
Timbre, 37, 38, 39.
Time, 178, 204, 205, footnote.
Toepler and Foucault, method of, for detecting optical faults, 313 et seq., 320.
Tone-figures, 91.
Tones, 22-47, 99 et seq., 212.
Torsion, moment of, 132.
Torsion-balance, Coulomb's, 109, 168.
Torricelli, on virtual velocities, 150; his law of liquid efflux, 150; on the atmosphere, 273.
Tourist, journey of, work of the inquirer compared to, 17, 29, 30.
Transatlantic cable, 108.
Transformation and adaptation in scientific thought, 214-235.
Transformation of ideas, 63.
Transformative law of the energies, 172.
Translation, difficulties of, 354.
Tree, conceptual life compared to a, 231.
Triangle, mutual dependence of the sides and angles of a, 179.
Triple accord, 46.
Truth, wooed by the inquirer, 45; difficulty of its acquisition, 46.
Tumblers, resounding, 23.
Tuning-forks, explanation of their motion, 22 et seq.
Tylor, 186.
Tympanum, 18.
Type, natural laws likened to, 193; words compared to, 191.
Ulysses, 347.
Understanding, what it means, 211.
Uniforms, do not fit heads, 369.
Unique determination, 181-182.
Unison, 43.
Unit, electrostatic, 111. See _Force_ and _Work_.
United States, 336.
Universal Real Character, a, 192.
Utility of physical science, 351.
Variation, the method of, in science, 230; in biology, 216.
Velocity, of light, 48 et seq.; of the descent of bodies, 143 et seq.; meaning of, 204; virtual, 149-155.
_Verstandesbegriffe_, 199.
Vertical, perception of the, 272, 286 et seq.; symmetry, 389.
Vertigo, 285, 290.
Vestibule of the ear, 300.
Vibration, 22 et seq.
Vibration-figures, 91.
Vinci, Leonardo da, 278, 283.
Violent motions, 225.
Virtual velocities, 149-155.
Visibility, general conditions of, 312.
Vision, symmetry of our apparatus of, 96. See _Eye_.
Visual nerves, 96.
Visualisation, mental, 250.
Volt, the word, 343.
Volta, 127, footnote, 134.
Voltaire, 260.
Voltaire's ingènu, 219.
Vowels, composed of simple musical notes, 26.
Wagner, Richard, 279.
Wald, F., 178, footnote.
Wallace, 216.
War, and peace, reflexions upon, 309, 335 et seq.
Waste of mechanical energy, W. Thomson on, 175.
Watches, experiment with, 41; in a mirror, 93.
Water, jet of, resolved into drops, 60; free, solid figures of, 8; objects reflected in, 94, 191; possible modes of measurement of, 170.
Watt, 266.
Wealth, the foundation of, 198.
Weapons, modern, 335.
Weber, 108, 306.
Weight of bodies, varies with their distance from the centre of the earth, 112.
Weismann, 216.
Wheatstone, his stereoscope, 73; his pseudoscope, 96; also 59.
Wheel, history and importance of, 61 et seq.
Whewell, on the formation of science, 231.
Whole, the, 204, footnote.
Why, the question, 199, 223.
Will, Schopenhauer on the, 190; man's most familiar source of power, 243; used to explain the world, 186; forces compared to, 254; compared to pressure, 14.
Windmill, a rotating, 53.
Wire frames and nets, for constructing liquid figures of equilibrium, 4 et seq.
Witchcraft, 187.
Wollaston, 284, 285.
Wonderful, science the natural foe of the, 224.
Woods, the relative distance of trees in, 68.
Wooer, inquirer compared to a, 45.
Words and sounds, 343.
Words, compared to type, 191.
Work, of liquid forces of attraction, 14; in electricity, 173; measure of, 119 et seq., 130, 223; relation of, with heat, 162, 245 et seq.; amount required to develop electricity, 131 et seq.; produces various physical changes, 139; substantial conception of, 183-184. See _Energy_.
World, the, what it consists of, 208.
World-particles, 203.
Wronsky, 172.
Wundt, on causality and the axioms of physics, 157-159; 359 footnote.
Xenophon, 49, footnote.
Young, Thomas, on energy, 173.
Zelter, 35.
Zeuner, 171.
Zoölogy, comparison in, 239.
THE WORKS OF ERNST MACH.
THE SCIENCE OF MECHANICS.
A CRITICAL AND HISTORICAL EXPOSITION OF ITS PRINCIPLES.
By DR. ERNST MACH.
PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE UNIVERSITY OF VIENNA.
Translated from the Second German Edition By THOMAS J. McCORMACK.
250 Cuts. 534 Pages. Half Morocco, Gilt Top, Marginal Analyses.
Exhaustive Index. Price $2.50.
TABLE OF CONTENTS.
STATICS.
The Lever.
The Inclined Plane.
The Composition of Forces.
Virtual Velocities.
Statics in Their Application to Fluids.
Statics in Their Application to Gases.
DYNAMICS.
Galileo's Achievements.
Achievements of Huygens.
Achievements of Newton.
Principle of Reaction.
Criticism of the Principle of Reaction and of the Concept of Mass.
Newton's Views of Time, Space, and Motion.
Critique of the Newtonian Enunciations.
Retrospect of the Development of Dynamics.
THE EXTENSION OF THE PRINCIPLES OF MECHANICS.
Scope of the Newtonian Principles.
Formulæ and Units of Mechanics.
Conservation of Momentum, Conservation of the Centre of Gravity, and Conservation of Areas.
Laws of Impact.
D'Alembert's Principle.
Principle of _Vis Viva_.
Principle of Least Constraint.
Principle of Least Action.
Hamilton's Principle.
Hydrostatic and Hydrodynamic Questions.
FORMAL DEVELOPMENT OF MECHANICS.
The Isoperimetrical Problems.
Theological, Animistic, and Mystical Points of View in Mechanics.
Analytical Mechanics.
The Economy of Science.
THE RELATION OF MECHANICS TO OTHER DEPARTMENTS OF KNOWLEDGE.
Relations of Mechanics to Physics.
Relations of Mechanics to Physiology.
PRESS NOTICES.
"The appearance of a translation into English of this remarkable book should serve to revivify in this country [England] the somewhat stagnating treatment of its subject, and should call up the thoughts which puzzle us when we think of them, and that is not sufficiently often.... Professor Mach is a striking instance of the combination of great mathematical knowledge with experimental skill, as exemplified not only by the elegant illustrations of mechanical principles which abound in this treatise, but also from his brilliant experiments on the photography of bullets.... A careful study of Professor Mach's work, and a treatment with more experimental illustration, on the lines laid down in the interesting diagrams of his _Science of Mechanics_, will do much to revivify theoretical mechanical science, as developed from the elements by rigorous logical treatment."--Prof. A. G. Greenhill, in _Nature_, London.
"Those who are curious to learn how the principles of mechanics have been evolved, from what source they take their origin, and how far they can be deemed of positive and permanent value, will find Dr. Mach's able treatise entrancingly interesting.... The book is a remarkable one in many respects, while the mixture of history with the latest scientific principles and absolute mathematical deductions makes it exceedingly attractive."--_Mechanical World_, Manchester and London, England.
"Mach's Mechanics is unique. It is not a text-book, but forms a useful supplement to the ordinary text-book. The latter is usually a skeleton outline, full of mathematical symbols and other abstractions. Mach's book has 'muscle and clothing,' and being written from the historical standpoint, introduces the leading contributors in succession, tells what they did and how they did it, and often what manner of men they were. Thus it is that the pages glow, as it were, with a certain humanism, quite delightful in a scientific book.... The book is handsomely printed, and deserves a warm reception from all interested in the progress of science."--_The Physical Review_, New York and London.