CHAPTER LIV. NUMERICAL EVALUATION OF SOUND.

Loudness, pitch, and character.-Pitch depends on frequency.-Period and frequency are reciprocals.-Wave-length is distance travelled in one period.—Velocity is wave-length multiplied by frequency.-Character or timbre.-Musical intervals.-Gamut.→→Temperament.-Absolute pitch.-Limits of musical pitch.-Minor scale.-Pythagorean scale. Methods of counting vibrations.-Syren.-Vibroscope for writing vibrations.Phonautograph.-Tonometer.-Pitch modified by relative motion,

CHAPTER LV. MODES OF VIBRATION.

pp. 816-827.

Longitudinal and transverse vibrations.-Transverse vibrations of strings.-Their velocity of propagation and frequency.-Sonometer.-Harmonics.-Overtones not always harmonics.-Strings vibrating in segments.-Segmental vibration of strings.-Sympathetic vibration or resonance. - Sounding-boards.- Longitudinal vibrations of strings.-Stringed instruments.-Transversal vibrations of rigid bodies.-Plates and bells.— Tuning-fork.-Affected by temperature.-Mounted fork.-Law of linear dimensions.— Organ-pipes.-Mouth-piece.-Pitch depends on column of air.-Overtones of open and stopped pipes.-Nodes and antinodes.-Stationary undulations.-Wave-length of fundamental note.-Wave-lengths of overtones.-Analogous laws for certain vibrations of rods and strings.-Application to measurement of velocity of sound in various substances.-Reed-pipes.-Opposite effect of temperature.-Wind-instruments. - Mano

metric flames,

pp. 828-846.

CHAPTER LVI. ANALYSIS OF VIBRATIONS. CONSTITUTION OF

SOUNDS.

Optical examination of sonorous vibrations. Lissajous' experiment.-Composition of two simple vibrations in perpendicular directions.-Unison gives an ellipse which can be inscribed in a given rectangle.-General equations to Lissajous' figures.-Optical tuning.-Other modes of exhibiting the composition of rectangular vibrations.-Blackburn's pendulum.-Elastic rod.-Character.-Form of vibration.-Resolution of periodic motions by Fourier's theorem.-Every periodic vibration consists of a fundamental simple vibration and its harmonics.-Every musical note consists of a fundamental note and its harmonics.-Constitution of a vibration defined.—Corresponds to character of resulting sound.-The harmonics which are present in a note may or may not have their origin in segmental vibrations of the instrument.-Combinations of stops in organs. -Helmholtz's resonators.-Adaptation to manometric flames. Human voice.-Vowel sounds.-Experiments of Willis, Wheatstone, and Helmholtz, .

pp. 847-858.

CHAPTER LVIA. CONSONANCE, DISSONANCE, AND RESULTANT

TONES.

Concord and Discord.-Examples.-Consonant intervals can be more accurately identified than dissonant.-Dissonance depends on the jarring effect of beats not too slow nor too rapid.-33 beats per second give a maximum of discomfort.-Proof that all beats are due to imperfect unison.-Beating notes must be near in pitch.--Helmholtz's calculation of amounts of dissonance.-Discordant elements in an imperfect concord.-Resultant tones.-Difference-tones discovered by Sorge and Tartini.-Erroneously attributed to coalescence of beats.-Summation-tones.-Resultant-tones occur when small quantities of the second order are sensible.-Beats of resultant-tones, .

pp. 859-861.

CONTENTS.

OPTICS.

CHAPTER LVII. PROPAGATION OF LIGHT.

xxi

Light. Hypothesis of ather capable of propagating transverse vibrations.- Excessive shortness and excessive frequency of luminous waves.-Strength of shadows.-Rectilinear propagation.-Diffraction an exception.-Images produced by small apertures.Images of sun.—Shadows; umbra and penumbra.-Velocity of light.-Seven and a half circumferences of the earth per second.-Fizeau's experiment with toothed-wheel. Foucault's experiment with rotating mirror.-Ingenious method of keeping rate of rotation constant.-Mode of reducing the observations.-Resulting velocity 298 million metres per second, or 185,000 miles per second.-Velocity deduced from eclipses of Jupiter's satellites.-From aberration of stars.-Sun's distance deduced from Foucault's determination of velocity.-Photometry, principles of. - Photometers of Bouguer, Rumford, Foucault, and Bunsen,

CHAPTER LVIII. REFLECTION OF LIGHT.

pp. 865-882.

Plane of incidence and reflection.-Angles of incidence and reflection equal.-Apparatus for verification.-Artificial horizon. -Regular and irregular reflection. Lookingglasses.-Speculum metal.-Silvered specula.-Plane mirrors.-Position and size of image. Images by successive reflections.-Parallel mirrors.-Mirrors at right angles. -Kaleidoscope.-Pepper's ghost.-Deviation produced by rotating a mirror.-Hadley's sextant.-Spherical mirror.-Centre of curvature.-Principal and secondary axes.-Principal focus of concave mirror.-Parabolic mirrors.-Spherical aberration.-Conjugate foci.-Formula for conjugate focal distances.-Formation of real images.Position of principal focus.-March of conjugate foci.-Construction for position and size of image.-Calculation of size of image.-Phantom bouquet.-Images on screen. -Image as seen directly.-Caustic surface.-Primary and secondary foci.-Primary and secondary focal lines on a screen.-Virtual image in concave mirror.-Distinction between real and virtual images. -Convex mirrors.-Cylindric mirrors.-Anamorphosis.-Ophthalmoscope and laryngoscope,

CHAPTER LIX. REFRACTION.

pp. 883-907.

Sudden change of direction.-Sunbeam entering water.-Coin in basin.-Stick appears broken.-Refractive powers of different media.--The denser usually the more refractive.-Law of sines.-Apparatus for verification.-Index of refraction.-Table of indices.-Critical angle and total reflection.-Mirage as explained by Monge.-Camera lucida. Caustic by refraction at a plane surface, and apparent position of virtual image.-Refraction through parallel plate.-Multiple images in plate.-Candle in looking-glass.-Prism or wedge.-Refraction through it.-Displacement of objects seen through it.—Investigation of formulæ.-Geometrical construction for deviation, and proof of minimum deviation.-Conjugate foci with respect to prism in position of minimum deviation.-Double refraction.-Iceland-spar. Ordinary and extraordinary image, pp. 908-928.

CHAPTER LX. LENSES.

Forms of lenses.-Converging and diverging, or convex and concave.-Principal axis.Principal focus.-Optical centre.-Secondary axes.-Conjugate foci.-Comparative sizes of object and image.-Whether image will be erect or inverted.-Investigation of formulæ for focal length and conjugate focal distances.-Conjugate foci on secondary axis.-March of conjugate foci.-Minimum distance between object and real image is four times focal length.-Construction for position and size of real image.-Calculation

of size. Example.-Image on cross-wires.-Cross-wires at conjugate foci.-Aberration of lenses.-Virtual images, and formulæ relating to them.-Concave lenses.-Focometer. Refraction at a single spherical surface.-Camera obscura. - Photographic camera.-Example of photographic processes.-Projection of experiments on screens.Solar microscope.-Magic-lantern.-Photo-electric microscope,

pp. 929-945.

CHAPTER LXI.-VISION AND OPTICAL INSTRUMENTS. Description of the eye.-Adaptation to different distances.-Binocular vision.-Data for judgment of distances.-Perception of relief.-Stereoscope.-Visual angle (plane) or apparent length.-Apparent area or solid visual angle.-Magnifying power.-Spectacles.—Magnifying lens.-Visual angle in different positions of lens.—Simple microscope.-Compound microscope.-Magnifying power computed and observed.-Astronomical telescope.—Magnifying power computed and observed.—Finder.—Bright spot.— Magnifying power deduced from comparison of object-glass with bright spot.-Terrestrial eye-piece.—Galilean telescope.-Its peculiarities.-Opera-glass.-Reflecting tele, scopes.—Herschelian and Newtonian.-Magnifying power. Gregorian and Cassegranian.-Silvered specula.-Measure of brightness.—Intrinsic and effective.-Intrinsic brightness is-Surfaces are equally bright at all distances.-Image formed by theoretically perfect lens has same intrinsic brightness as object; but effective brightness may be less.-Same principle applies to mirrors.-Reason why high magnification often produces loss of effective brightness. —Intrinsic brightness of image in theoretically perfect telescope is equal to brightness of object.—Effective brightness is the same, if magnifying power does not exceed and is less for higher powers.-Actual telescopes always give images less bright than the objects.-Brightness of stars indeterminate. Light received from star increases with power of eye-piece till magnifying power is -Brightness of image on screen is proportional to solid angle subtended by lens.-Appearance presented to eye at focus.-Cross-wires of telescopes.-Adjustment for preventing parallax.-Line of collimation and its adjustment, .

0

e

e

pp. 946-972.

CHAPTER LXII. DISPERSION. STUDY OF SPECTRA. Analysis of colours by prism.-Solar spectrum.-Modes of obtaining a pure spectrum either virtual or real.-Dark lines.-Invisible portions of spectrum.-Heating and chemical power.-Phosphorescence and fluorescence.-Ultra-violet rays not altogether invisible. -Spectroscope.-Different modes of determining positions of lines. Train of prisms.— Use of collimator.-Different classes of spectra.-Solar, continuous, bright-line.-Spectrum analysis.-Reversal of bright lines.-Analysis of solar atmosphere.-TelespectroBright lines in spectrum of sun's edge. Observation of prominences by method of wide slit.-Spectra of nebulæ.-Displacement of lines by approach or recess. -Huggins' recent observations.-Analysis of artificial lights.-Bodies illuminated by monochromatic light.-Chromatic aberration.-Possibility of achromatism.-Conditions of achromatism. Dispersive power.-Impossibility of complete achromatism.-Huygenian and other achromatic eye-pieces. - Rainbows, primary, secondary, and superpp. 973-999.

scope.

numerary,

CHAPTER LXIII. COLOUR.

Nature of colour in bodies.—Opaque and transparent.-Effect of superposing coloured glasses.-Colours of mixed powders.-Mixtures of colours.-Different compositions may produce the same visual impression.—Methods of mixing colours.-By sheet of glass.-By rotating disc.-By overlapping spectra. — Distinction between mean and

sum of given colours.-Colour equations.-Helmholtz's observations with crossed slits. -Maxwell's colour-box.-Results of observation.-Substitution of similars.- Personal differences.—All colours except purple are spectral.—Any four colours are connected by one definite relation.—Any five colours yield one definite match by taking means.— Mean of colours analogous to centre of gravity.-Sum of colours analogous to resultant of forces.-Cone of colour.-Three co-ordinates answering to hue, depth, and brightness. -Complementary colours.-Three primary colour-sensations, red, green, and blue.Three sets of nerves.-Accidental images, negative and positive.-Colour-blind vision is dichroic, the red primary being wanting.-Colour and musical pitch, pp. 1000-1011.

CHAPTER LXIV. WAVE THEORY OF LIGHT.

Principle of Huygens.-Wave-front.-Explanation of rectilinear propagation.-Spherical wave-surface in isotropic medium.-Two wave-surfaces in non-isotropic medium.— Construction for wave-front in refraction.-And in reflection.-Law of sines deduced. ---Newtonian explanation of law of sines.-Foucault's crucial experiment.-Principle of least time.-Application to reflection and refraction. More exact statement of the principle.-Application to conjugate foci and caustics.-Zus a minimum or maximum. -Application to terrestrial refraction.-Rays in air are concave towards the denser side.-Correction for refraction opposite to that for curvature of earth.-Calculation of curvature of a nearly horizontal ray.-Influence of pressure, temperature, and vertical change of temperature.-Average curvature or of earth's curvature.-Not owing to earth's curvature.-Curvature of inclined rays.-General formula.-Astronomical refraction.—Mirage.—Sinuous rays.-Condition of inverted images.-Analogy of total reflection.-Experiment of artificial mirage.-Diffraction fringes produced by narrow slit.—Analogy of sound.-Diffraction by a grating.-Explanation of purity of spectrum. Spectra of different orders.—Ångstrom's observations.-Calculation of wavelengths.—Standard diffraction-spectrum.-Contrasted with prismatic spectra.-Imaginary standard based on wave-frequency.-Examples of wave-lengths.-Colours of thin films, pp. 1012-1031.

CHAPTER LXV. POLARIZATION AND DOUBLE REFRACTION. Experiment of two tourmalines.-Polarizer and analyzer.-Polarization tested by variation of brightness.-Polarization by reflection.-Malus' polariscope.-Polarizing angle.Brewster's criterion.-Polarization of the transmitted light.-Polarization never favours reflection. Definition of plane of polarization.-Direction of vibration.-Polariza. tion by double refraction. - Explanation of double refraction in uniaxal crystals.—— Wave-surface for ordinary ray spherical, for extraordinary ray spheroidal.-Absorption by tourmaline.-Nicol's prism.-Colours produced by thin plates of selenite.-Rectilinear vibration changed to elliptic.-Analogy of Lissajous' figures.-Resolution of elliptic vibration by analyzer.-Circular polarization a case of elliptic.-Why the light is coloured.—Why a thick plate shows no colour.-Crossed plates.-Plate perpendicular to axis shows rings and cross.-Changes on rotating analyzer.-Explanation of these phenomena.-Crystals are isotropic, uniaxal, or biaxal.-Rotation of plane of polarization.—Quartz and sugar.-Production of colour.-Magneto-optic rotation.-Connection between rotation and crystalline form.-Condition of converting rectilinear into circular vibration.-Quarter-wave plates.-Fresnel's rhomb.-Effect of combining two.-Discussion as to direction of vibration in plane polarized light.-Fresnel's view established by Stokes.-Vibrations of ordinary light,—Polarization of obscure radiation, pp. 1032–1050.