TABLE OF CONTENTS.

vii

CHAPTER LXX. LENSES.

Forms of lenses, 1000. Principal focus, 1001. Optical centre, 1002. Conjugate foci.

Image erect or inverted, enlarged or diminished, 1003. Formulæ, 1004. Conjugate

foci on secondary axis, 1005. March of conjugate foci, 1006. Construction for image,

1007. Size of image, 1008. Example, 1009. Image on cross-wires, 1010. Aberra-

tion of lenses, 1011. Virtual images, 1012. Concave lens, 1013. Focometer, 1014.

Refraction at a single spherical surface, 1015. Refraction through a sphere, 1016.

Camera obscura, 1017. Photographic camera and photography, 1018. Projection;

Solar microscope and magic lantern, 1019, 1020,

pp. 1013-1030.

CHAPTER LXXI. VISION AND OPTICAL INSTRUMENTS.

Construction of eye, 1021. Its optical working, 1022. Adaptation to distance, 1023.

Binocular vision. Data for judgment of distance, 1024. Stereoscope, 1025. Visual

angle; Magnifying power, 1026. Spectacles, 1027. Magnification by a lens. Sim-

ple microscope, 1028. Compound microscope and its magnifying power, 1029.

Astronomical telescope and its magnifying power; Finder, 1030.

Place for eye;

Bright spot and its relation to magnifying power, 1031. Terrestrial eye-piece, 1032,

Galilean telescope. Its peculiarities. Opera-glass, 1033. Reflecting telescopes,

1034. Silvered specula, 1035. Measure of brightness; intrinsic and effective, 1036.

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, 1037. 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, 1038. Light

received from a star increases with power of eye-piece till magnifying power

is 1039. Illumination of image on screen is proportional to solid angle subtended

by lens. Appearance presented to eye at focus, 1040. Field of view in astronomical

telescope, 1041. Cross-wires, and their adjustment for preventing parallax, 1042.

Line of collimation, and its adjustment, 1013. Micrometers, 1044, pp. 1031-1058.

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CHAPTER LXXII. DISPERSION. STUDY OF SPECTRA.

Analysis of colours by prism, 1045, 1046. Newton's method of obtaining the solar

spectrum, 1047. Modes of obtaining a pure spectrum either virtual or real, 1048.

Fraunhofer's lines, 1049. Invisible ends of spectrum, 1050. Phosphorescence and

fluorescence, 1051. Decomposition of white light, 1052. Spectroscope, 1053. Use

of collimator, 1054. Classes of spectra, 1055. Spectrum analysis, 1056. Inferences

from dark lines in solar spectrum, 1057. Observations of chromosphere. Spectra of

nebulæ, 1058. Doppler's principle, 1059. Spectra of artificial lights. Bodies

illuminated by monochromatic light, 1060. Brightness and purity of spectra, 1061.

Chromatic aberration, 1062. Achromatism. "Dispersive power," 1063, 1064.

Achromatic eye-pieces, 1065. Rainbows, primary, secondary, and supernumerary,

1066, .

pp. 1031-1086.

Sundry additions; goniometers, convex lenses, nodal points,

pp. 1086-1088*.

CHAPTER LXXIII. COLOUR.

Colour of opaque bodies, 1067. Of transparent bodies. Superposition of coloured glasses,
1068. Colours of mixed powders, 1069. Mixture of coloured lights. Different
compositions may produce the same visual impression, 1970. Methods of mixture:

glass plate; rotating disc; overlapping spectra. A mixture may be either a mean or

a sum. Colour equations, 1071. Helmholtz's crossed slits, and Maxwell's colour-

box, 1072. Results of observation: substitution of similars; personal differences;

any four colours are connected by one equation; any five colours yield one match by

taking means. Sum of colours analogous to resultant of forces. Mean analogous to

centre of gravity, 1073. Cone of colour. Hue, depth, and brightness. Complemen-

taries. All hues except purple are spectral, 1074. Three primary colour-sensations,

red, green, and violet, 1075. Accidental images, negative and positive, 1076.

Colour-blind vision is dichroic, the red primary being wanting, 1077. Colour and

musical pitch, 1078,

pp. 1087-1098.

CHAPTER LXXIV. WAVE THEORY OF LIGHT.

Explanation of rectilinear propagation.
Two wave-surfaces in non-isotropic

Principle of Huygens. Wave-front, 1079.

Spherical wave-surface in isotropic medium.

medium, 1080. Construction for wave-front in refraction. Law of sines, 1081.

Reflection, 1082. Newtonian explanation of refraction. Foucault's crucial experi-

ment, 1083. Principle of least time. Application to reflection and refraction.

More exact statement of the principle. Application to foci and caustics. Zus a

minimum or maximum, 1083. Application to terrestrial refraction. Rays in air are

concave towards the denser side, 1084. Calculation of curvature of horizontal or

nearly horizontal rays, 1085. Of inclined rays, 1086. Astronomical refraction, 1088.

Mirage, 1089. Curved rays of sound, 1090. Calculation of their curvature, 1091.

Diffraction fringes, 1092. Gratings, 1093. Principle of diffraction spectrum, 1094.

Practical application, and deduction of wave-lengths, 1095. Retardation gratings,

1096. Reflection gratings, 1097. Standard spectrum, 1098. Wave-lengths, 1099.

Colours of thin films, 1100,

pp. 1099-1118.

CHAPTER LXXV. POLARIZATION AND DOUFLE REFRACTION.

Experiment of two tourmalines. Polarizer and analyser, 1101. Polarization by reflec-

tion. The transmitted light also polarized. Polarizing angle, 1102. Plane of

polarization, 1103. Polarization by double refraction, 1104. Explanation of double

refraction in uniaxal crystals. Wave-surface for ordinary ray spherical, for extra-

ordinary ray spheroidal. Extraordinary index. Property of tourmaline, 1105.

Nicol's prism, 1106. Colours produced by thin plates of selenite, 1107. Rectilinear

vibration changed to elliptic. Analogy of Lissajous' figures. Resolution of elliptic

vibration by analyser. Why the light is coloured. Why a thick plate shows no

colour. Crossed plates, 1108. Plate perpendicular to axis shows rings and cross,

1109. Explanation, 1110., Crystals are isotropic, uniaxal, or biaxal, 1111. Rota-

tion of plane of polarization. Quartz and sugar. Production of colour, 1112.

Magneto-optic rotation. Kerr's results, 1113. Circular polarization a case of ellip-

tic. Quarter-wave plates. Fresnel's rhomb. How to distinguish circularly-polarized

from common light, 1114. Discussion as to direction of vibration in plane-polarized

light, 1115. Vibrations of ordinary light, 1116. Polarization of dark heat-rays,

REDUCTION TO C.G.S. MEASURES. (See page 48.)

[cm. denotes centimetre(s); gm. denotes gramme(s).]

The velocity acquired in falling for one second in vacuo, in any part of Great Britain, is about 32.2 feet per second, or 9.81 metres per second.

The pressure of one atmosphere, or 760 millimetres (29.922 inches) of mercury, is 1.033 kilogramme per sq. centimetre, or 14.73 lbs. per square inch.

The weight of a litre of dry air, at this pressure (at Paris) and 0° C., is 1·293 gramme. The weight of a cubic centimetre of water is about 1 gramme.

The weight of a cubic foot of water is about 62.4 lbs.

The equivalent of a unit of heat, in gravitation units of energy, is

772 for the foot and Fahrenheit degree.

1390 for the foot and Centigrade degree.
424 for the metre and Centigrade degree.

42400 for the centimetre and Centigrade degree.

In absolute units of energy, the equivalent is—

41.6 millions for the centimetre and Centigrade degree;

or 1 gramme-degree is equivalent to 41 6 million ergs.

ACOUSTICS.

CHAPTER LXII.

PRODUCTION AND PROPAGATION OF SOUND.

866. Sound is a Vibration.-Sound, as directly known to us by the sense of hearing, is an impression of a peculiar character, very broadly distinguished from the impressions received through the rest of our senses, and admitting of great variety in its modifications. The attempt to explain the physiological actions which constitute hearing forms no part of our present design. The business of physics is rather to treat of those external actions which constitute sound, considered as an objective existence external to the ear of the percipient.

It can be shown, by a variety of experiments, that sound is the result of vibratory movement. Suppose, for example, we fix one end C of a straight spring CD (Fig. 592) in a vice A, then draw the other end D aside into the position D', and let it go. In virtue of its elasticity (§ 126), the spring will return to its original position; but the kinetic energy which it acquires in re

C

turning is sufficient to carry it to a nearly Fig. 592.-Vibration of Straight Spring. equal distance on the other side; and it

thus swings alternately from one side to the other through distances very gradually diminishing, until at last it comes to rest. Such movement is called vibratory. The motion from D' to D", or from D" to D', is called a single vibration. The two together constitute a