Part 26
Differential coefficients, their relation to symmetry, 98.
Differential laws, 204.
Differential method, for detecting optical imperfections, 317.
Diffraction, 91, 194.
Diffusion, Fick's theory of, 249.
Discharge of Leyden jars, 114 et seq.
Discoveries, the gist of, 270, 375.
Discovery and invention, distinction between, 269.
Dissonance, explanation of, 42; definition of, 33, 44. See _Consonance_.
Distances, estimation of, by the eye, 68 et seq.
Dogs, like tuning-forks, 23; their mentality, 190.
Domenech, Abbé, 92.
Dramatic element in science, 243.
Drop of water, on a greased plate, 8; on the end of a stick, 8; in free descent, 8.
Dubois, 218.
Dubois-Reymond, 370, footnote.
Dufay, 271.
Dynamics, foundations of, 153 et seq.
Ear, researches in the theory of, 17 et seq.; diagram of, 18; its analysis of sounds, 20 et seq.; a puzzle-lock, 28; reflected in a mirror, 93; no symmetry in its sensation, 103.
Earth, its oblateness not due to its original fluid condition, 2; rotation of, 204; internal disturbances of, 285.
Economical, nature of physical inquiry, 186; procedure of the human mind, 186; order of physics, 197; schematism of science, 206; tools of science, 207; coefficient of dynamos, 133.
Economy, of the actions of nature, 15; the purpose of science, 16; of language, 191 et seq.; of the industrial arts, 192; of mathematics, 195-196; of machinery, 196; of self-preservation, our first knowledge derived from, 197; generally, 186 et seq., 269.
Education, higher, 86; liberal, 341 et seq., 371.
Efflux, liquid, 150.
Ego, its nature, 234-235.
Egypt, 234.
Egyptians, art of, 78 et seq., 201.
Eighteenth century, the scientific achievements of, 187, 188.
Eleatics, on motion, 158.
Electrical, attraction and repulsion, 109 et seq., 168; capacity, 116 et seq.; force, 110, 119, 168; spark, 117, 127, 132, 133, 190; energy, measurement of, 128 et seq., 169; currents, conceptions of, 118, 132, 135-136, 226-227, 249, 250; fluids, 112 et seq., 228; pendulums, 110; levels, 173; potential, 121 et seq.; quantity, 111, 118, 119.
Electricity, as a substance and as a motion, 170; difference between the conceptions of heat and, 168 et seq., rôle of work in, 120 et seq.; galvanic, 134. See _Electrical_.
Electrometer, W. Thomson's absolute, 127, footnote.
Electrometers, 122, 127.
Electrostatic unit, 111.
Electrostatics, concepts of, 107 et seq.
Elements, interdependence of the sensuous, 179; of bodies, 202; of phenomena, equations between, 205; of sensations, 200; used instead of sensations, 208-209.
Ellipse, equation of, 205; the word, 342.
Embryology, possible future state of, 257.
Energies, conformity in the deportment of, 171-175; differences of, 175.
Energy, a metrical notion, 178; conservation of, 137 et seq.; defined, 139; metaphysical establishment of the doctrine of, 183; kinetic, 177; potential, 128 et seq.; substantial conception of, 164, 185, 244 et seq.; conservation of, in electrical phenomena, 131 et seq.; limits of principle of, 175; principle of, in physics, 160-166; sources of principle of, 179, 181; thermal, 177; Thomas Young on, 173.
Energy-value of heat, 178, footnote.
Enlightenment, the, 188.
Entropy, a metrical notion, 178.
Environment, stability of our, 206.
Equations for obtaining facts, 180; between the elements of phenomena, 205.
Equilibrium, conditions of, in simple machines, 151; figures of liquid, 4 et seq.; general condition of, 15; in the State, 15.
Etymology, the word, misused for entomology, 316.
Euclid, on consonance and dissonance, 33; his geometry, 364.
Euler, on the causes of harmony, 34; impression of the mathematical processes on, 196; on the vibrations of strings, 249, 285, 376.
Euler and Hermann's principle, 149.
Euthyphron, questioned by Socrates, 1.
Evolute, the word, 342.
Evolution, theory of, as applied to ideas, 216 et seq.
Ewald, 298, 304.
Excluded perpetual motion, logical root of the principle of, 182.
Exner, S., 302, 305.
Experience, communication of, 191; our ready, 199; the principle of energy derived from, 179; the wellspring of all knowledge of nature, 181; incongruence between thought and, 206.
Experimental research, function of, 181.
Explanation, nature of, 194, 237, 362.
Eye, cannot analyse colors, 20; researches in the theory of the, 18 et seq.; loss of, as affecting vision, 98.
Eyes, purpose of, 66 et seq.; their structure symmetrical not identical, 96.
Face, human, inverted, 95.
Facts and ideas, necessary to science, 231.
Facts, description of, 108; agreement of, 180; relations of, 180; how represented, 206; reflected in imagination, 220 et seq.; the result of constructions, 253; a continuum of, 256 et seq.; equations for obtaining, 180.
Falling bodies, 204, 215; Galileo on the law of, 143 et seq., 284.
Falling, cats, 303, footnote.
Falstaff, 309.
Familiar intermediate links of thought, 198.
Faraday, 191, 217, 237; his conception of electricity, 114, 271.
Fechner, theory of Corti's fibres, 19 et seq.
Feeling, cannot be explained by motions of atoms, 208 et seq.
Fetishism, 186, 243, 254; in our physical concepts, 187.
Fibres of Corti, 17 et seq.
Fick, his theory of diffusion, 249.
Figures, symmetry of, 92 et seq.
Figures of liquid equilibrium, 4 et seq.
Fire, use of, 264.
Fishes, 306.
Fixed note, determining of a, 377.
Fizeau, his determination of the velocity of light, 55 et seq.
Flats, reversed into sharps, 101.
Flouren's experiments, 272, 290.
Flower-girl, the baskets of a, 95.
Fluids, electrical, 112 et seq.
Force, electric, 110, 119, 168; unit of 111; living, 137, 149, 184; generally 253. See the related headings.
Forces, will compared to, 254.
Foreseeing events, 220 et seq.
Formal conceptions, rôle of, 183.
Formal need of a clear view of facts, 183, 246; how far it corresponds to nature, 184.
Formative forces of liquids, 4.
Forms of liquids, 3 et seq.
Forward movement, sensation of, 300.
Forwards, prophesying, 253.
Foucault, 57, 70, 296.
Foucault and Toepler, method of, for detecting optical faults, 313 et seq., 320.
Foundation of scientific thought, primitive acts of knowledge, the, 190.
Fourier, on processes of heat, 249, 278.
Fox, a, 234.
Franklin's pane, 116.
Frary, 338, footnote.
Fraunhofer, 271.
Freezing-point, lowered by pressure, 162.
Fresnel, 271.
Fritsch, 321.
Frogs, larvæ of, not subject to vertigo, 298.
Froude, 333.
Frustra, misuse of the word, 345.
Future, science of the, 213.
Galileo, on the motion of pendulums, 21; his attempted measurement of the velocity of light, 50 et seq.; his exclusion of a perpetual motion, 143; on velocities acquired in free descent, 143-147; on the law of inertia, 146-147; on virtual velocities, 150; on work, 172; his laws of descent, 193; on falling bodies, 225; great results of his study of nature, 214 et seq.; his rude scientific implements, 215; selections from his works for use in instruction, 368; also 105, 182, 187, 237, 272, 274, 283.
Galle, observes the planet Neptune, 29.
Galvanic, electricity, 134; current, 132; dizziness, 291; vertigo, 298.
Galvanoscope, 135.
Galvanotropism, 291.
Garda, Lake, 239.
Gas, the word, 264; mass of, enclosed in a cylinder, 179.
Gases, tensions of, for scales of temperature, 174.
Gauss, on the foundations of dynamics, 154; his principle, 154; also, 108, 274.
Genius, 279, 280.
Geography, comparison in, 239.
Geometers, in our eyes, 72.
Geotropism, 289.
German schools and gymnasiums, 372, 373, 338, footnote.
Ghosts, photographic, 73.
Glass, invisible in a mixture of the same refrangibility, 312; powdered, visible in a mixture of the same refrangibility, 312.
Glove, in a mirror, 93.
Goethe, quotations from, 9, 31, 49, 88; on the cause of harmony, 35.
Goltz, 282, 291.
Gossot, 332.
Gothic cathedral, 94.
Gravitation, discovery of, 225 et seq.
Gravity, how to get rid of the effects of, in liquids, 4; also 228.
Gray, Elisha, his telautograph, 26.
Greased plate, drop of water on a, 8.
Great minds, idiosyncrasies of, 247.
Greek language, scientific terms derivedfrom, 342-343; common words derived from, 343, footnote; still necessary for some professions, 346; its literary wealth, 347-348; narrowness and one-sidedness of its literature, 348-349; its excessive study useless, 349-350; its study sharpens the judgment, 357-358; a knowledge of it not necessary to a liberal education, 371.
Greeks, their provinciality and narrow-mindedness, 349; now only objects of historical research, 350.
Griesinger, 184.
Grimaldi, 270.
Grimm, 344, footnote.
Grunting fishes, 306.
Habitudes of thought, 199, 224, 227, 232.
Haeckel, 222, 235.
Hamilton, deduction of the conical refraction of light, 29.
Hankel, 364.
Harmonics, 38, 40.
Harmony, on the causes of, 32 et seq.; laws of the theory of, explained, 30; the investigation of the ancients concerning, 32; generally, 103. See _Consonance_.
Harris, electrical balance of, 127, footnote.
Hartwich, Judge, 343, 353, footnote.
Hat, a high silk, 24.
Hats, ladies', development of, 64.
Head-wave of a projectile, 323 et seq.
Hearing and orientation, relation between, 304 et seq.
Heat, a material substance, 177; difference between the conceptions of electricity and, 168 et seq.; substantial conception of, 243 et seq.; Carnot on, 156, 160 et seq.; Fourier on the conduction of, 249; not necessarily a motion, 167, 170, 171; mechanical equivalent of, 164, 167; of liquefaction, 178; quantity of, 166; latent, 167, 178, 244; specific, 166, 244; the conceptions of, 160-171; machine, 160; a measure of electrical energy, 133 et seq.; mechanical theory of, 133; where does it come from? 200.
Heavy bodies, sinking of, 222.
Heights of ascent, 143-151.
Helm, 172.
Helmholtz, applies the principle of energy to electricity, 184; his telestereoscope, 84; his theory of Corti's fibres, 19 et seq.; on harmony, 35, 99; on the conservation of energy, 165, 247; his method of thought, 247; also 138, 305, 307, 375, 383.
Hensen, V., on the auditory function of the filaments of Crustacea, 29, 302.
Herbart, 386 et seq.
Herbartians, on motion, 158.
Herculaneum, art in, 80.
Heredity, in organic and inorganic matter, 216, footnote.
Hering, on development, 222; on vision, 210.
Hermann, E., on the economy of the industrial arts, 192.
Hermann, L., 291.
Herodotus, 26, 234, 347, 350.
Hertz, his waves, 242; his use of the phrase "prophesy," 253.
Herzen, 361, footnote.
Hindu mathematicians, their beautiful problems, 30.
Holtz's electric machine, 132.
Horse, 63.
Household, physics compared to a well-kept, 197.
Housekeeping in science and civil life, 198.
Hudson, the, 94.
Human beings, puzzle-locks, 27.
Human body, our knowledge of, 90.
Human mind, must proceed economically, 186.
Humanity, likened to a polyp-plant, 235.
Huygens, his mechanical view of physics, 155; on the nature of light and heat, 155-156; his principle of the heights of ascent, 149; on the law of inertia and the motion of a compound pendulum, 147-149; on the impossible perpetual motion, 147-148; on work, 173; selections from his works for use in instruction, 368; his view of light, 227-228, 262.
Huygens, optical method for detecting imperfections in optical glasses 313.
Hydrogen balloon, 199.
Hydrostatics, Stevinus's principle of, 141.
Hypotheses, their rôle in explanation, 228 et seq.
Ichthyornis, 257.
Ichthyosaurus, 63.
Idea? what is a theoretical, 241.
Idealism, 209.
Ideas, a product of organic nature, 217 et seq.; and facts, necessary to science, 231; not all of life, 233; their growth and importance, 233; a product of universal evolution, 235; the history of, 227 et seq.; in great minds, 228; the rich contents of, 197; their unsettled character in common life, their clarification in science, 1-2.
Ideography, the Chinese, 192.
Imagery, mental, 253.
Imagination, facts reflected in, 220 et seq.
Inclined plane, law of, 140-141.
Incomprehensible, the, 186.
Indian, his modes of conception and interpretation, 218 et seq.
Individual, a thread on which pearls are strung, 234-235.
Industrial arts, economy of the, E. Hermann on, 192.
Inertia, law of, 143 et seq., 146 et seq., 216, footnote, 283 et seq.
Innate concepts of the understanding, Kant on, 199.
Innervation, visual, 99.
Inquirer, his division of labor, 105; compared to a shoemaker, 105-106; what constitutes the great, 191; the true, seeks the truth everywhere, 63 et seq.; the, compared to a wooer, 45.
Instinctive knowledge, 189, 190.
Instruction, aim of, the saving of experience, 191; in the classics, mathematics, and sciences, 338-374; limitation of matter of, 365 et seq.
Insulators, 130.
Integrals, 195.
Intellectual development, conditions of, 286 et seq.
Intentions, acts of nature compared to, 14-15.
Interconnexion of nature, 182.
Interdependence, of properties, 361; of the sensuous elements of the world, 179.
Interference experiments with the head-wave of moving projectiles, 327-328.
International intercourse, established by Latin, 341.
International measures, 108.
Invention, discovery and, distinction between, 269.
Inventions, requisites for the development of, 266, 268 et seq.
Iron-filings, 220, 243.
Italian art, 234.
Jacobi, C. G. J., on mathematics, 280.
James, W., 275, 299.
Java, 163.
Jews and Christians, monotheism of the, 187.
Jolly, Professor von, 112, 274.
Joule, J. P., on the conservation of energy, 163-165, 167, 183; his conception of energy, 245; his metaphysics, 183, 246; his method of thought, 247; also 137, 138.
Journée, 317.
Judge, criminal, the natural philosopher compared to a, 48.
Judgment, essentially economy of thought, 201-202; sharpened by languages and sciences, 357-358; also 232-233, 238.
Juliet, Romeo and, 87.
Jupiter, its satellites employed in the determination of the velocity of light, 51 et seq.
Jurisprudence, Latin and Greek unnecessary for the study of, 346, footnote.
Kant, his hypothesis of the origin of the planetary system, 5; his _Critique of Pure Reason_, 188; on innate concepts of the understanding, 199; on time, 204; also footnote, 93.
Kepler, 187, 270.
Kinetic energy, 177.
Kirchhoff, his epistemological ideas, 257-258; his definition of mechanics, 236, 258, 271, 273.
Knight, 289.
Knowledge, a product of organic nature, 217 et seq., 235; instinctive, 190; made possible by economy of thought, 198; our first, derived from the economy of self-preservation, 197; the theory of, 203; our primitive acts of the foundation of science, 190.
Kocher, 328.
Koenig, measurement of the velocity of sound, 57 et seq.
Kölliker, 19.
Kopisch, 61.
Kreidl, 299, 302, 306; his experiments, 272.
Krupp, 319.
Labels, the value of, 201.
Labor, the accumulation of, the foundation of wealth and power, 198; inquirer's division of, 105, 258.
Labyrinth, of the ear, 18, 291, 305.
Lactantius, on the study of moral and physical science, 89.
Ladder of our abstraction, the, 208.
Ladies, their eyes, 71; like tuning-forks, 23-24.
Lagrange, on Huygens's principle, 149; on the principle of virtual velocities, 150-155; character of the intellectual activity of a, 195, 278.
Lake-dwellers, 46, 271.
Lamp-shade, 70.
Lane's unit jar, 115.
Language, knowledge of the nature of, demanded by a liberal education, 356; relationship between, and thought, 358; communication by 237; economy of, 191 et seq.; human its character, 238; of animals, 238; instruction in, 338 et seq.; its methods, 192.
Laplace, on the atoms of the brain, 188; on the scientific achievements of the eighteenth century, 188; his hypothesis of the origin of the planetary system, 5.
Latent heat, 167, 178, 244.
Latin city of Maupertuis, 339.
Latin, instruction in, 311 et seq.; introduced with the Christian Church, 340; the language of scholars, the medium of international intercourse, its power, utility, and final abandonment, 341-347; the wealth of its literature, 348; the excessive study of, 346, 349, 354, 355; its power to sharpen the judgment, 357-358.
Lavish extravagance of science, 189.
Law, a, defined, 256; a natural, not contained in the conformity of the energies, 175.
Law-maker, motives of not always discernible, 9.
Layard, 79.
Learning, its nature, 366 et seq.
Least superficial area, principle of, accounted for by the mutual attractions of liquid particles, 13-14; illustrated by a pulley arrangement, 12-13; also 9 et seq.
Leibnitz, on harmony, 33; on international intercourse, 342, footnote.
Lessing, quotation from, 47.
Letters of the alphabet, their symmetry, 94, 97.
Level heights of work, 172-174.
Lever, a, in action, 222.
Leverrier, prediction of the planet Neptune, 29.
Leyden jar, 114.
Liberal education, a, 341 et seq., 359, 371.
Libraries, thoughts stored up in, 237.
Lichtenberg, on instruction, 276, 370.
Licius, a Chinese philosopher, 213.
Liebig, 163, 278.
Life and death, 186.
Light, history of as elucidating how theories obstruct research, 242; Huygens's and Newton's views of, 227-228; its different conceptions, 226; rectilinear propagation of, 194; rôle of, in vision, 81; spatial and temporal periodicity of, explains optical phenomena, 194; numerical velocity of, 58; where does it go to? 199; generally, 48 et seq.
Like effects in like circumstances, 199.
Likeness, 388, 391.
Lilliput, 84.
Lines, straight, their symmetry, 98; curved, their asymmetry, 98; of force, 249.
Links of thought, intermediate, 198.
Liquefaction, latent heat of, 178.
Liquid, efflux, law of, 150; equilibrium, figures of, 4 et seq.; the latter produced in open air, 7-8; their beauty and multiplicity of form, 7, 8; made permanent by melted colophonium, 7.
Liquids, forms of, 1-16; difference between, and solids, 2; their mobility and adaptiveness of form, 3; the courtiers _par excellence_ of the natural bodies, 3; possess under certain circumstances forms of their own, 3.
Living force, 137, 184; law of the conservation of, 149.
Lloyd, observation of the conical refraction of light, 29.
Lobster, of Lake Mohrin, the, 61.
Localisation, cerebral, 210.
Locke, on language and thought, 358.
Locomotive, steam in the boiler of, 219.
Loeb, J., 289, 291, 302.
Logarithms, 195, 219; in music, 103-104.
Logical root, of the principle of energy, 181; of the principle of excluded perpetual motion, 182.
Lombroso, 280.
Lucian, 347.
_Macula acustica_, 272.
Magic lantern, 96.
Magic powers of nature, 189.
Magical power of science, belief in the, 189.
Magnet, a, 220; will compared to the pressure of a, 14; coercive force of a, 216.
Magnetic needle, near a current, 207.
Magnetised bar of steel, 242-243.
Major and minor keys in music, 100 et seq.
Malus, 242.
Man, a fragment of nature's life, 49; his life embraces others, 234.
Mann, 364.
Manuscript in a mirror, 93.
Maple syrup, statues of, on Moon, 4.
Marx, 35.
Material, the relations of work with heat and the consumption of, 245 et seq.
Mathematical methods, their character, 197-198.
Mathematics, economy of, 195; on instruction in, 338-374; C. G. J. Jacobi on, 280.
Matter, constancy of, 203; its nature, 203; the notion of, 213.
Maupertuis, his Latin city, 338.
Maximal and minimal problems, their rôle in physics, 14, footnote.
Mayer, J. R., his conception of energy, 245, 246; his methods of thought, 247; on the conservation of energy, 163, 164, 165, 167, 183, 184; his metaphysical utterances, 183, 246; also 138, 184, 191, 217, 271, 274.
Measurement, definition of, 206.
Measures, international, 108.
Mécanique céleste, 90, 188; sociale, and morale, the, 90.
Mechanical, conception of the world, 105, 155 et seq., 188, 207; energy, W. Thomson on waste of, 175; analogies between ---- and thermal energy, 17 et seq.; equivalent of heat, electricity, etc., 164, 167 et seq.; mythology, 207; phenomena, physical events as, 182; philosophy, 188; physics, 155-160, 212; substitution-value of heat, 178, footnote.
Mechanics, Kirchhoff's definition of, 236.
Medicine, students of, 326.
Melody, 101.
Melsens, 310, 327.
Memory, a treasure-house for comparison, 230; common elements impressed upon the, 180; its importance, 238; science disburdens the, 193.
Mendelejeff, his periodical series, 256.
Mental, adaptation, 214-235; completion of phenomena, 220; imagery, 253; imitation, our schematic, 199; processes, economical, 195; reproduction, 198; visualisation, 250.
Mephistopheles, 88.
Mercantile principle, a miserly, at the basis of science, 15.
Mersenne, 377.
Mesmerism, the mental state of ordinary minds, 228.
Metaphysical establishment of doctrine of energy, 183.
Metaphysical spooks, 222.
Metrical, concepts of electricity, 107 et seq.; notions, energy and entropy are, 178; units, the building-stones of the physicist, 253.
Metronomes, 41.
Meyer, Lothar, his periodical series, 256.
Middle Ages, 243, 349.
Midsummer Night's Dream, 309.
Mill, John Stuart, 230.
Millers, school for, 326.
Mill-wheel, doing work, 161.
Mimicking facts in thought, 189, 193.
Minor and major keys in music, 100 et seq.
Mirror, symmetrical reversion of objects in, 92 et seq.
Miserly mercantile principle at the basis of science, 15.
Moat, child looking into, 208.
Modern scientists, adherents of the mechanical philosophy, 188.
Molecular theories, 104.
Molecules, 203, 207.
Molière, 234.
Momentum, 184.
Monocular vision, 98.
Monotheism of the Christians and Jews, 187.
Montagues and Capulets, 87.
Moon, eclipse of, 219; lightness of bodies on, 4; the study of the, 90, 284.
Moreau, 307.
Mosaic of thought, 192.
Motion, a perpetual, 181; quantity of, 184; the Eleatics on, 158; Wundt on, 158; the Herbartians on, 158.
Motions, natural and violent, 226; their familiar character, 157.
Mountains of the earth, would crumble if very large, 3; weight of bodies on, 112.
Mozart, 44, 279.
Müller, Johann, 291.
Multiplication-table, 195.
Multiplier, 132.
Music, band of, its _tempo_ accelerated and retarded, 53; the principle of repetition in, 99 et seq.; its notation, mathematically illustrated, 103-104.
Musical notes, reversion of, 101 et seq.; their economy, 192.
Musical scale, a species of one-dimensional space, 105.
Mystery, in physics, 222; science can dispense with, 189.
Mysticism, numerical, 33; in the principle of energy, 184.
Mythology, the mechanical, of philosophy, 207.
Nagel, von, 364.
Nansen, 296.
Napoleon, picture representing the tomb of, 36.
Nations, intercourse and ideas of, 336-337.
Natural constants, 193.
Natural law, a, not contained in the conformity of the energies, 175.
Natural laws, abridged descriptions, 193; likened to type, 193.
Natural motions, 225.
Natural selection in scientific theories, 63, 218.