Chapter XVIII: Appendix: I (2)

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.

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.

"Mr. T. J. McCormack, by his effective translation, where translation was no light task, of this masterly treatise upon the earliest and most fundamental of the sciences, has rendered no slight service to the English speaking student. The German and English languages are generally accounted second to none in their value as instruments for the expression of scientific thought; but the conversion bodily of an abstruse work from one into the other, so as to preserve all the meaning and spirit of the original and to set it easily and naturally into its new form, is a task of the greatest difficulty, and when performed so well as in the present instance, merits great commendation. Dr. Mach has created for his own works the severest possible standard of judgment. To expect no more from the books of such a master than from the elementary productions of an ordinary teacher in the science would be undue moderation. Our author has lifted what, to many of us, was at one time a course of seemingly unprofitable mental gymnastics, encompassed only at vast expenditure of intellectual effort, into a study possessing a deep philosophical value and instinct with life and interest. 'No profit grows where is no pleasure ta'en,' and the emancipated collegian will turn with pleasure from the narrow methods of the text-book to where the science is made to illustrate, by a treatment at once broad and deep, the fundamental connexion between all the physical sciences, taken together."--_The Mining Journal_, London, England.

"As a history of mechanics, the work is admirable."--_The Nation_, New York.

"An excellent book, admirably illustrated."--_The Literary World_, London, England.

"Sets forth the elements of its subject with a lucidity, clearness, and force unknown in the mathematical text-books ... is admirably fitted to serve students as an introduction on historical lines to the principles of mechanical science."--_Canadian Mining and Mechanical Review_, Ottawa, Can.

"A masterly book.... To any one who feels that he does not know as much as he ought to about physics, we can commend it most heartily as a scholarly and able treatise ... both interesting and profitable."--A. M. Wellington, in _Engineering News_, New York.

"The book as a whole is unique, and is a valuable addition to any library of science or philosophy.... Reproductions of quaint old portraits and vignettes give piquancy to the pages. The numerous marginal titles form a complete epitome of the work; and there is that invaluable adjunct, a good index. Altogether the publishers are to be congratulated upon producing a technical work that is thoroughly attractive in its make-up."--Prof. D. W. Hering, in _Science_.

"There is one other point upon which this volume should be commended, and that is the perfection of the translation. It is a common fault that books of the greatest interest and value in the original are oftenest butchered or made ridiculous by a clumsy translator. The present is a noteworthy exception."--_Railway Age_.

"The book is admirably printed and bound.... The presswork is unexcelled by any technical books that have come to our hands for some time, and the engravings and figures are all clearly and well executed."--_Railroad Gazette_.

TESTIMONIALS OF PROMINENT EDUCATORS.

"I am delighted with Professor Mach's _Science of Mechanics_."--_M. E. Cooley_, Professor of Mechanical Engineering, Ann Arbor, Mich.

"You have done a good service to science in publishing Mach's _Science of Mechanics_ in English. I shall take every opportunity to recommend it to young students as a source of much interesting information and inspiration."--_M. I. Pupin_, Professor of Mechanics, Columbia College, New York.

"Mach's _Science of Mechanics_ is an admirable ... book."--_Prof. E. A. Fuertes_, Director of the College of Civil Engineering of Cornell University, Ithaca, N. Y.

"I congratulate you upon producing the work in such good style and in so good a translation. I bought a copy of it a year ago, very shortly after you issued it. The book itself is deserving of the highest admiration; and you are entitled to the thanks of all English-speaking physicists for the publication of this translation."--_D. W. Hering_, Professor of Physics, University of the City of New York, New York.

"I have read Mach's _Science of Mechanics_ with great pleasure. The book is exceedingly interesting."--_W. F. Magie_, Professor of Physics, Princeton University, Princeton, N. J.

"The _Science of Mechanics_ by Mach, translated by T. J. McCormack, I regard as a most valuable work, not only for acquainting the student with the history of the development of Mechanics, but as serving to present to him most favorably the fundamental ideas of Mechanics and their rational connexion with the highest mathematical developments. It is a most profitable book to read along with the study of a text-book of Mechanics, and I shall take pleasure in recommending its perusal by my students."--_S. W. Robinson_, Professor of Mechanical Engineering, Ohio State University, Columbus, Ohio.

"I am delighted with Mach's 'Mechanics.' I will call the attention to it of students and instructors who have the Mechanics or Physics to study or teach."--_J. E. Davies_, University of Wisconsin, Madison, Wis.

"There can be but one opinion as to the value of Mach's work in this translation. No instructor in physics should be without a copy of it."--_Henry Crew_, Professor of Physics in the Northwestern University, Evanston, Ill.

POPULAR SCIENTIFIC LECTURES.

A PORTRAYAL OF THE SPIRIT AND METHODS OF SCIENCE.

By DR. ERNST MACH.

PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE UNIVERSITY OF VIENNA.

Translated by THOMAS J. McCORMACK.

_Third Edition, Revised Throughout and Greatly Enlarged._

Cloth, Gilt Top. Exhaustively Indexed. Pages, 415. Cuts, 59. Price, $1.50.

TITLES OF THE LECTURES.

The Forms of Liquids.

The Fibres of Corti.

On the Causes of Harmony.

On the Velocity of Light.

Why Has Man Two Eyes?

On Symmetry.

On the Fundamental Concepts of Static Electricity.

On the Principle of the Conservation of Energy.

On the Economical Nature of Physical Inquiry.

On the Principle of Comparison in Physics.

On the Part Played by Accident in Invention and Discovery.

On Sensations of Orientation.

On the Relative Educational Value of the Classics and the
Mathematico-Physical Sciences.

A Contribution to the History of Acoustics.

Remarks on the Theory of Spatial Vision.

On Transformation and Adaptation in Scientific Thought.

PRESS NOTICES.

"A most fascinating volume, treating of phenomena in which all are interested, in a delightful style and with wonderful clearness. For lightness of touch and yet solid value of information the chapter 'Why Has Man Two Eyes?' has scarcely a rival in the whole realm of popular scientific writing."--_The Boston Traveller_.

"Truly remarkable in the insight they give into the relationship of the various fields cultivated under the name of Physics.... A vein of humor is met here and there reminding the reader of Heaviside, never offending one's taste. These features, together with the lightness of touch with which Mr. McCormack has rendered them, make the volume one that may be fairly called rare. The spirit of the author is preserved in such attractive, really delightful, English that one is assured nothing has been lost by translation."--Prof. Henry Crew, in _The Astrophysical Journal_.

"A very delightful and useful book.... The author treats some of the most recondite problems of natural science, in so charmingly untechnical a way, with such a wealth of bright illustration, as makes his meaning clear to the person of ordinary intelligence and education.... This is a work that should find a place in every library, and that people should be encouraged to read."--_Daily Picayune_, New Orleans.

"In his translation Mr. McCormack has well preserved the frank, simple, and pleasing style of this famous lecturer on scientific topics. Professor Mach deals with the live facts, the salient points of science, and not with its mysticism or dead traditions. He uses the simplest of illustrations and expresses himself clearly, tersely, and with a delightful freshness that makes entertaining reading of what in other hands would be dull and prosy."--_Engineering News_, N. Y.

"The general reader is led by plain and easy steps along a delightful way through what would be to him without such a help a complicated maze of difficulties. Marvels are invented and science is revealed as the natural foe to mysteries."--_The Chautauquan_.

"The beautiful quality of the work is not marred by abstruse discussions which would require a scientist to fathom, but is so simple and so clear that it brings us into direct contact with the matter treated."--_The Boston Post_.

"A masterly exposition of important scientific truths."--_Scotsman_, Edinburgh.

"These lectures by Dr. Mach are delightfully simple and frank; there is no dryness or darkness of technicalities, and science and common life do not seem separated by a gulf.... The style is admirable, and the whole volume seems gloriously alive and human."--_Providence Journal_, R. I.

"The non-scientific reader who desires to learn something of modern scientific theories, and the reasons for their existence, cannot do better than carefully study these lectures. The English is excellent throughout, and reflects great credit on the translator."--_Manufacturer and Builder_.

"We like the quiet, considerate intelligence of these lectures."--_Independent_, New York.

"Professor Mach's lectures are so pleasantly written and illumined with such charm of illustration that they have all the interest of lively fiction."--_New York Com. Advertiser_.

"The literary and philosophical suggestiveness of the book is very rich." _Hartford Seminary Record_.

"All are presented so skilfully that one can imagine that Professor Mach's hearers departed from his lecture-room with the conviction that science was a matter for abecedarians. Will please those who find the fairy tales of science more absorbing than fiction."--_The Pilot_, Boston.

"Professor Mach ... is a master in physics.... His book is a good one and will serve a good purpose, both for instruction and suggestion."--Prof. A. E. Dolbear, in _The Dial_.

"The most beautiful ideas are unfolded in the exposition."--_Catholic World_, New York.

THE ANALYSIS OF THE SENSATIONS

By DR. ERNST MACH.

PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE UNIVERSITY OF VIENNA.

Pages, 208. Illustrations, 37. Indexed.

(Price, Cloth, $1.25.)

CONTENTS.

Introductory: Antimetaphysical.

The Chief Points of View for the Investigation of the Senses.

The Space-Sensations of the Eye.

Space-Sensation, Continued.

The Relations of the Sight-Sensations to One Another and to the
Other Psychical Elements.

The Sensation of Time.

The Sensation of Sound.

Influence of the Preceding Investigations on the Mode of Conceiving
Physics.

"A wonderfully original little book. Like everything he writes a work of genius."--_Prof. W. James_ of Harvard.

"I consider each work of Professor Mach a distinct acquisition to a library of science."--_Prof. D. W. Hering_, New York University.

"There is no work known to the writer which, in its general scientific bearings, is more likely to repay richly thorough study. We are all interested in nature in one way or another, and our interests can only be heightened and clarified by Mach's wonderfully original and wholesome book. It is not saying too much to maintain that every intelligent person should have a copy of it,--and should study that copy."--_Prof. J. E. Trevor_, Cornell.

"Students may here make the acquaintance of some of the open questions of sensation and at the same time take a lesson in the charm of scientific modesty that can hardly be excelled."--_Prof. E. C. Sanford_, Clark University.

"It exhibits keen observation and acute thought, with many new and interesting experiments by way of illustration. Moreover, the style is light and even lively--a rare merit in a German prose work, and still rarer in a translation of one."--_The Literary World_, London.

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Transcriber's note:

_Underscores_ have been used to indicate _italic_ fonts.

End of Project Gutenberg's Popular scientific lectures, by Ernst Mach