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| Hamilton W.R. — The collected mathematical papers. Volume 1: geometrical optics |
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| Предметный указатель |
Component combinations 214
Components of aberration at mirror 77
Components of normal slowness 172 277 301 327 497
Components of normal slowness, in biaxal crystal 280
Components of normal slowness, sudden changes in, in reflection or refraction 118 215 285 301 325 329
Components of normal slowness, surface of See Surface of components
Composition of partial deviations 253
Compound combinations 214
Computation of aberration coefficients for instrument of revolution 512. See also Aberration coefficients
Condensation See also Density
Condensation, lines of uniform, at principal focus 143
Condition of developability 7
Condition of rectangularity of extraordinary system of rays 7 8 335
Conditions of achromatism 104
Conditions of aplanaticity See Aplanaticity
Congruence xxii xxiv xxvii 15 140 235 345.
Congruence, aberrations of xxii xxv
Congruence, density of, at focus 82
Congruence, density of, at principal focus 85
Congruence, normal xix xxii xxiv xxv 16 350.
Congruence, singularities of xxii xxvii 345 504
Conical locus connected with intersections of ray-lines 252
Conical polarisation 288
Conical refraction x xxi xxv xxvi 164 285 302 303 312 330
Conjugate functions xi
Conjugate guiding axes 232
Conjugate planes of deflexure 241 258
Conjugate planes of vergency 293
Conjugate point 272. See also Transition-point
Connections between partial differential coefficients of characteristic functions 112 184 190 199 490
Conoidal cusps on Fresnel's wave 164 283 302
Constant action See Action principle
Constant of chromatic dispersion 232
Constant of deviation 232 238 241 248
Constants of aberration 299. See also Aberration coefficients
Construction for emergent ray in instrument of revolution 398
Construction for reflected or refracted wave or ray 293 302
Construction for unit-wave in any uniform medium 291
Construction of microscopes and telescopes 104 301 383
Construction of object glass See Object glass
Contact transformations xxi 171 474 487
Contact, circles of, on Fresnel's wave 164 283 302
Contact, normals of circular, on Fresnel's wave 283
Contact, planes of circular, on Fresnel's wave 285
Convergence of system of lenses 423
Cooke 386
Coordinate axes, natural, at principal focus 85 143
Coordinate planes, natural, through any straight ray See Natural coordinate planes
Coordinates, curvilinear 222. See also Marks of position
Coordinates, natural, for systems of rays of the second class 7
Coordinates, oblique and polar 222
Coordinates, tangential xxiii xxvi 304 475 503
Coordinates, transformation of 128 222
Corpuscular theory of light see Emission theory
Couples, algebraic xi
Crystal, biaxal, axes of elasticity in 165 280
Crystal, biaxal, characteristic function for 8
Crystal, biaxal, conical polarisation in 288
Crystal, biaxal, conical refraction in See Conical refraction
Crystal, biaxal, double polarisation in 288
Crystal, biaxal, double refraction in 288 312
Crystal, biaxal, extraordinary refraction in 8 285
Crystal, biaxal, lenses of 293
Crystal, biaxal, medium function v in 282
Crystal, biaxal, propagation of light in 165 280 288 301 330
Crystal, one-axed See Crystal uniaxal
Crystal, reflection at interior surfaces of 8
Crystal, refraction of, and least action 317
Crystal, single-axed See Crystal uniaxal
Crystal, uniaxal, medium function v for 130
Crystal, uniaxal, surfaces cutting rays perpendicularly in 8 335
Crystal, uniaxal, system of rays produced by 8
Crystal, uniaxal, thin lens of xxvi 336
Crystal, uniaxal, used for object glass of telescope 340
Crystal, with two axes See Crystal biaxal
Crystalline media See Media
Crystallized medium of continually varying nature 8
Crystals, osculating focal 8
Cunningham Medal v x
Curvature, axis of, of final ray 232
Curvature, axis of, rotation round 253
Curvature, centres of 475
Curvature, curves of 348 361.
Curvature, line of focal 102
Curvature, lines of See Lines of curvature
Curvature, of caustic curve 83
Curvature, of curve in space 7
Curvature, of ellipsoid, surface of centres of 34 300
Curvature, of general wave surface 131
Curvature, of image (aberrational) xxiii 378 510
Curvature, of locus of focus 432
Curvature, of ray 232
Curvature, of undevelopable pencil 7
Curvature, of undevelopable pencil, point of evanescent 7
Curvature, of undevelopable pencil, surface of centres of 7
Curvatures of caustic surface 45
Curvatures of ellipsoids 304
Curvatures of object glass 384
Curve of double curvature, reflection or refraction from 102
Curve, caustic See Caustic curve
Curve, in space, curvature of 7
Curve, limiting, for general system of rays 349 504
Curve, surface 98
Curved rays, systems of 104 109 168 227 275
Curves of curvature 348 36.
Curves of reflection 24. See also Lines of reflection
Curves, focal 6
Curves, reflecting or refracting, focal lengths of 6
Curves, refracting,  for any number of 417
Curvilinear coordinates 222. See also Marks of position
Cusp on caustic curve 83
Cusp on caustic surface 366
Cusp-rays 283 303
Cusps, conoidal, on Fresnel's wave 164 283 302
Cylinder of rays emergent from biaxal crystal 288 303
Cylinder, indicating, of deflexion 241
Cylindrical surfaces, T for system of 493
Czapski xxiv
D'Alembert, principle of 315
Darboux 475
de Broglie 277 500
Deductive method 314
Defects of imagery See Aberrations; Aplanaticity; Astigmatism; Coma; Curvature; Distortion
Deflected lines 241
Deflexion 243
Deflexion, indicating cylinder of 241
Deflexure, axis and radius of 244
Deflexure, centre of, and focus by projection 245
Deflexure, conjugate planes of 258
Deflexure, planes of extreme See Planes of extreme deflexure
Deflexures, extreme 243
Deflexures, of surfaces 241
density See also Condensation
Density along ray 32 52 464
Density at caustic surface 82
Density at focus 82
Density at principal focus 83 85 143
Density of reflected light 32 51
Density of refracted light 94
Density on plane of aberration through focus 53 54 58
Density on plane through principal focus 83 143
Density, differing from observed intensity of light 87
Density, geometrical xxv 87
Density, lines of uniform 86
Density, near caustic surface 54
Derivatives, partial See Partial differential coefficients
Descartes xix 89 295 311 312 317 330 473
Descartes, analogy to geometry of xix 295 330 473
Developable pencils see Pencils developable
Developable surfaces xxvii 351. developable
| Developable surfaces, angle of intersection of 334 351 464
Developable surfaces, bases of 348
Developable surfaces, near singular curve 504
Developable surfaces, T for refracting system of 493
Developable systems of rays 7
Deviation, constant of 232 238 241 248
Deviations, partial, composition of 253
Diametral parabola 63
Diametral surface for system of rays of the second class 7
Differences of Zero xi
Differences, equation in 413—416 418 422 424
Differences, finite 69 96
Differential coefficients, partial see Partial differential coefficients
Differential equation of bases of developable surfaces 348 359 504
Differential equation of focal mirrors 11 28
Differential equation of focal refractors 90
Differential equation of lines of reflection 24
Differential equation of lines of refraction 95
Differential equations See also Partial differential equation
Differential equations of motion (dynamical) xi 331 485
Differential equations of ray in atmosphere xix xxv 105 326
Differential equations of ray in canonical form 171 182
Differential equations of ray in curvilinear coordinates 227
Differential equations of ray in general medium xxv 110 172 180 224 325
Differential equations of ray in oblique coordinates 224
Dioptrics, fundamental formula of 89
Direct aplanaticity See Aplanaticity direct
Direction cosines of ray as partial differential coefficients of V 17 91 297 322
Direction cosines, dependence of, on extreme coordinates 169 297
Directrix of undevelopable pencil 7
Dispersion, chromatic 16 232
Distance, apparent, of luminous point 32
Distortion (aberrational) xxiii 378 510
Distortion, eye-axes and object-axes of 256
Distortion, planes of no 256
Distortions of objects viewed from each other 256
Disturbance, principle of accumulated 313
Dollond 303
Double achromatic object glass See Object glass
Double lens See Lenses two;
Double polarisation in biaxal crystal 288
Double refraction in biaxal crystal 288 312
Dunkel 349
Dupin 246 274 304 463 464
Dynamics, application of characteristic function to x xi xxi xxvi 9 301 311 330 484
Dynamics, General Method in, xi 301 485
Edgeworth, Mlss xiii
Eikonal xxiii 488.
Elastic ether, vibrations in 165 280 313
Elasticity, axes of, in biaxal crystal 165 280
Elements of arrangement of near luminous paths 232 238 241 248 253 256 262
Elements of position of ray 15
Elimination of incident variables in reflection or refraction 214
Elimination of intermediate variables in calculation of T 217 370 408 413 493 507
Ellipse of aberration at any point of ray xxii 42
Ellipse of aberration at principal focus xxii 47 83 86
Ellipses of constant density or uniform condensation at principal focus 85 143
Ellipsoid mirror of revolution 11
Ellipsoid, perpendicular to rays in instrument of revolution xxiii xxvi 300 503
Ellipsoid, surface of centres of 34 300
Ellipsoids giving lines of vibration on Fresnel's wave 288
Ellipsoids, results respecting curvatures of 304
Elliptic integrals 85 86 300
Elliptical image of planet's disc 39
Elliptical section of thin pencil of rays xxii 31 42
Emanating systems 6 7
Emission theory xxi xxv 10 107 497
Emission theory, history of 313
Emission theory, medium-function v as velocity in 9 110 147 168 335 500
Emission theory, surfaces of constant action in See Action
Energy, biaxal 285
Envelope of Cartesian surfaces 89
Envelope of ellipsoids and hyperboloids 13
Envelope of spheres 15
Eppenstein xxiv
Epstein 502
equation See also Differential equation; Partial differential equation
Equation in differences 413—416 418 422 424
Equation of Fresnel's wave, polar form of 282
Equation of Fresnel's wave, xxvi 280 341
Equation of the characteristic function 107 109 168
Equations of motion (dynamical) xi 331 485
Equations of ray 16 345.
Equations of ray, in instrument of revolution xxvii 299 365 366 376 457 508
Equations of ray, in terms of S 268
Equations of ray, in terms of T 180 299 493 494 508
Equations of ray, in terms of V 111 169 172 498
Equations of ray, in terms of W 147 148 180 473 474
Equations of the Fifth Degree, Insolubility of xi
Ether, elastic, vibrations in 165 280 313
Euclid 315
Euler xv 304 317 331
Evolutes 360
Exdiametral rays See Rays exdiametral
Extraordinary reflection 118 214.
Extraordinary refraction 118 214.
Extraordinary systems of rays 6 107—144 147 164—293 324—330.
Extreme deflexure, axes of 241
Extreme deflexure, planes of See Planes of extreme deflexure
Extreme deflexures 243
Extreme foci by projection 7 138
Extreme osculating action-surfaces or waves 270
Extreme osculating focal systems 126 478
Extreme osculating foci 274 480
Extreme projection, planes of See Planes of extreme projection
Extreme virtual foci 7 140
Extreme virtual foci, planes of See Planes of extreme virtual foci
Eye-axes and object-axes of distortion 256
Factor in T for thin optical system 403 456 511
Faraday xiii
Fermat 316 317
Fermat, principle of least time of 316 463 487 499 500
Figure of eight curve of aberration xxii 44
Finite differences, calculus of 69 96
First class, system of rays of 7 15 17.
Flatness of image, condition for 510
Flatness of locus of primary focus 431
Fluctuating functions xi
Focal centres and images xviii 421 509
Focal centres of thick lens 395 410 419 509
Focal centres of two hemispheres 397
Focal centres of two thick lenses 397
Focal coordinates in plane system 6
Focal crystals, osculating 8
Focal curvature, line of 102
Focal curves 6
Focal distance, osculating 29
Focal distances See also Focal lengths
Focal distances for general system 353 361
Focal distances for reflection at mirror 23 25
Focal inflection, directions of, on mirror 51
Focal length of focal refractor 92
Focal length of instrument with three refracting media 420
Focal length of system of refracting surfaces of revolution close together 423 441
Focal length of thick lens 395
Focal length of two hemispheres 397
Focal lengths See also Focal distances
Focal lengths of instrument of revolution dependent on 299
Focal lengths of mirror for parallel incident rays 99
Focal lengths of thin lens of uniaxal crystal xxvi 336
Focal lines xxii 44 240.
Focal lines in instrument of revolution 378 383 385 457
Focal mirrors 11 28
Focal mirrors, osculating 26
Focal planes 239. See also Planes of vergency
Focal points 508
Focal reflectors, osculating 135 275
Focal refractors 89
Focal refractors, osculating 92 135 275
Focal surfaces, osculating 7
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