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| Hamilton W.R. — The collected mathematical papers. Volume 1: geometrical optics |
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| Предметный указатель |
Malus, on caustic surfaces and foci 51 120 299 315 384
Malus, on density 34 51 52 464
Malus, on general systems of rays 1 8 345
Malus, on intersections of rays 252
Malus, on lines of reflection and refraction 24 94 95 96
Malus, on rays in atmosphere 105
Malus, on reflection and refraction from curve of double curvature 103
Malus, on uniaxal crystals, xxvi 339
Malus, theorem of xix xxii xxvi 90 97 315 333 463. theorem
Marginal rays 429
Marks of position 222
Mathematical optics, division of, into two parts 298
Mathematical optics, fundamental formula of See Fundamental formula
Mathematical optics, fundamental problem of 169
Mathematical optics, science of 314
Mathematical optics, view of xxvi 295 297
Maupertuis 317
Maxima and minima in deductions of characteristic functions from each other 174
Maxima and minima in elimination in reflection or refraction 214. See also Stationary value
Maxima and minima of time or action 270 318
Measure of colour  168. See also Chromatic index
Mechanics See Dynamics
Mechanics, wave 500
Medals v x xi
Media, general (heterogeneous anisotropic) xx xxv 8 109—111 168—277 324—330
Media, general, in dynamics 486
Media, ordinary (homogeneous isotropic) xix xx xxiv xxv 1—104 146—163 364—460
Media, ordinary, of varying density (heterogeneous isotropic) xix xxv 104.
Media, uniform or crystalline (homogeneous anisotropic) xx xxv 8 111—144 147 175—277 277—293 326.
Medium, single uniform, characteristic functions for 207
Medium-function  , and partial differential equation for V xxv 170 301
Medium-function , connections of partial differential coefficients of, with those of v and  207
Medium-function , deduced from V 169 482
Medium-function , in dynamics 484
Medium-function , in undulatory theory 278 497
Medium-function v See also Refractive power
Medium-function v as molecular velocity of light in emission theory 9 109 147 168 335
Medium-function v as undulatory slowness 168 279 499
Medium-function v for atmosphere 104
Medium-function v for biaxal crystal 282
Medium-function v for general medium 9 109 147 168 324
Medium-function v for ordinary medium 147 324
Medium-function v for uniaxal crystal 130
Medium-function v in dynamics 484 501
Medium-function v, connections of partial differential coefficients of, with those of , and 207
Medium-function v, deduced from V 169 482
Metaphysics xiii
Method, General, in Dynamics xi 301 485
Methods of analysis and synthesis 314
Methods, inductive and deductive 314
Meusnier 97
Microscopes, construction of 301
Minimal surfaces See Surfaces of least area
Mirror See also Hemisphere; Reflector; Surface; Surface of revolution
Mirror, caustic surfaces for reflection at 22 25
Mirror, components of aberration at 77
Mirror, developable pencils for reflection at 22
Mirror, directions of focal inflection on 51
Mirror, ellipsoid, of revolution 11
Mirror, focal distances of 23 25
Mirror, hyperboloid, of revolution 11
Mirror, image of planet formed by 37
Mirror, lines of reflection on xxiv 24 94
Mirror, paraboloids of revolution osculating 23 25 27
Mirror, parallel rays reflected at 23 28 99
Mirror, plane 11
Mirror, plane, characteristic function V for 297
Mirror, principal foci for 35
Mirror, rays diverging from a point reflected at 25 36 94
Mirror, reflection at 9
Mirror, vertices of 35
Mirrors, combination of two, reflecting parallel incident rays 37
Mirrors, focal 11
Mirrors, focal, differential equation of 28
Mirrors, focal, osculating 26
Mirrors, images formed by 37
Molecular emission, hypothesis of 107. See also Emission theory
Molecular velocity v 168. See also Emission theory; Medium-function v
Monge 88 94—99 101 304 360 361
Motion of bodies, characteristic function applied to x xi xxi xxvi 9 301 311 330 484
Motion, equations of See Equations of motion
Muir 21
Murnaghan 502
N, constant, connected with aberrations 429 433 441 442 443 447 451 452
Natural axes at principal focus 85 143
Natural coordinate planes through ray 138 140 240.
Natural coordinates for systems of rays of the second class 7
Newton 89 312 313 314 317
Nodal points 395 508.
Normal congruence See Congruence normal
Normal slowness of propagation 278
Normal slowness of propagation, components of See Components
Normal surfaces See Surfaces cutting system of rays perpendicularly
Normal velocity of propagation ( ) 277 280 327 497.
Normals of circular contact on Fresnel's wave 283
Normals relations of surfaces to xxvi 304
Number of rays through a point 346
O, constant, connected with aberrations 430 441 443 452
Object glass, thin double achromatic xxiv xxvii xxviii 379 383 407 430 434 451. two
Object glass, thin triple 430
Object glass, uniaxal crystal as 340
Object small plane, undistorted image of 39
Object-axes and eye-axes of distortion 256
Objects, visible magnitudes and distortions of, viewed from each other 256
Oblique aplanaticity See Aplanaticity
Oblique coordinates 222
Oblique exdiametral rays in instrument of revolution 299 364 367 376 383 457 506 509
Oblique indiametral rays in instrument of revolution 407—454
Oblique plane, ray-lines from 241 248 252
One-axed crystal See Crystal uniaxal
Optic axes in biaxal crystal 283
Optical combination See Combination
Optical instruments, fundamental problem of 297. See also Instrument of revolution; Lens; Lenses; Mirror; Object glass; Reflector; Refractor; Surface; Surfaces of revolution; Telescope
Optical systems, fundamental formula of 109
Optics, application of analysis to 17 88
Optics, history of xxvi 311
Optics, mathematical, division into two parts 298
Optics, mathematical, fundamental formula of See Fundamental formula
Optics, mathematical, fundamental problem of 169
Optics, mathematical, science of 314
Optics, mathematical, view of xxvi 295 297
Optics, physical, characteristic function may be applied to 301
Orbits, astronomical 330
Orders of aberration xxiv 49
Ordinary media See Media
Ordinary reflection, analytic expressions of law of 9. See also Reflection
Ordinary refraction, analytic expressions of law of 88. See also Refraction
Ordinary systems of reflected rays 9. See also Systems of rays
Ordinary systems of refracted rays 88. See also Systems of rays
Orthogonal trajectories, theorem of 333. See also Huyghens Theorem Theorem
Osculating action-surfaces, extreme 270
Osculating focal crystals 8
Osculating focal distance 29
Osculating focal mirrors 26
Osculating focal reflectors 135 275
Osculating focal refractors 92 135 275
Osculating focal surfaces 7
Osculating focal systems 125 478
Osculating foci 30 35
Osculating foci, extreme 274 480
Osculating hyperboloid for ray-lines from oblique plane 248
Osculating sphere to perpendicular surface 49
Osculating spheroids 132
Osculating waves, extreme 270
Osculation of surfaces of constant action 133 270 479
Osculation, plane of, of osculating focal system 126 134 479
Oughtred 370
Parabola, diametral 63
Parabolic reflector or refractor of revolution 216
Paraboloid, auxiliary, for ray-lines from oblique plane 248 252
| Paraboloid, guiding See Guiding paraboloid
Paraboloids of revolution osculating a mirror 23 25 27
Parallel rays incident on combination of mirrors 37
Parallel rays incident on instrument of revolution 364 376 383 429 457 508
Parallel rays incident on mirror 23
Parallel rays incident on mirror, foci for 23 28 99
Parallel rays incident on mirror, lines of reflection for 28
Parallel rays incident on refractor 93
Partial differential coefficients of caustic surface 355 361
Partial differential coefficients of characteristic functions, changes in, due to reflection or refraction See Reflection or refraction
Partial differential coefficients of characteristic functions, connections between 112 184 190 199 490
Partial differential coefficients of V as components of normal slowness 172 277 301 497.
Partial differential coefficients of V as direction cosines of ray 17 91 297 322.
Partial differential coefficients of v, , , connections between 207
Partial differential equation (first order), for I, in atmosphere 106
Partial differential equation (first order), for T 178
Partial differential equation (first order), for V See also Integration; Transformation
Partial differential equation (first order), for V, in dynamics 331 485
Partial differential equation (first order), for V, in extraordinary systems xxv 147 170 178 301 328 474
Partial differential equation (first order), for V, in oblique coordinates 224
Partial differential equation (first order), for V, in ordinary systems xx xxv 18 146 322 364 473
Partial differential equation (first order), for V, in plane systems 153
Partial differential equation (first order), for V, in systems of revolution 155
Partial differential equation (first order), for W 178
Partial differential equation (first order), of caustic surfaces 357
Partial differential equation (first order), of pencils or surfaces of rays 19 91 346
Partial differential equation (second order), expressing condition of rectangularity of extraordinary system of rays 8 335
Partial differential equation (second order), for T 180
Partial differential equation (second order), for V 170
Partial differential equation (second order), for W 179
Partial differential equation (second order), of vibrating chords 96
Partial differential equation (second order), peculiar to spheric surfaces 97
Partial differential equation (second order), representing crystals with given caustic surface 8
Partial differential equations See also Singular primitives
Partial differential equations (second order) connected with reflecting or refracting surfaces 94—101
Paths of light xxvi 311.
Paths of planets xxvi 311.
Pencil of vision, bounding 31
Pencils of reflected system 17
Pencils of refracted system 91
Pencils, caustic 270
Pencils, definition of 18
Pencils, developable 7 19.
Pencils, developable, and undevelopable, difference between 32
Pencils, developable, connections of characteristic functions with 120 477
Pencils, developable, for reflection at mirror 22
Pencils, developable, in extraordinary systems 120 477
Pencils, developable, symmetrically situated with respect to planes of extreme projection 138
Pencils, partial differential equation of 19 91 346
Pencils, thin and undevelopable xxii 7 30
Perpendicular surfaces See Surfaces cutting system of rays perpendicularly
Perturbations of orbits 330
Petzval's condition 431
Phillips xxvii 383 405 407 438
Physical optics, characteristic function may be applied to 301
Picard 349 504
Plana xxvi 315 333 464
Plane mirror See Mirror plane
Plane of aberration through any point of ray xxii 40
Plane of aberration, through one of two foci on ray, xxii 42
Plane of aberration, through one of two foci, density on 53 54 58
Plane of aberration, through principal focus, xxii 47 83 141
Plane of curvature of ray 232
Plane of dispersion 232
Plane of osculation of osculating focal system 126 134 479
Plane surfaces, media bounded by 177 217 493
Plane systems of rays 6 153. indiametral
Plane, reflecting or refracting curves 6
Planes of circular contact on Fresnel's wave 285
Planes of deflexure, conjugate 241 258
Planes of extreme deflexure 241 245 253.
Planes of extreme projection 137 141 238 240 245 253.
Planes of extreme virtual foci 7 141.
Planes of no distortion 256
Planes of single normal velocity 283
Planes of vergency 238 258
Planes of vergency, conjugate 293
Planes of vergency, real or imaginary 239 253
Planes, focal 239. See also Planes of vergency
Planes, guiding 232
Planes, natural coordinate, through ray See Natural coordinate planes
Planes, principal, of congruence 140. See also Natural coordinate planes
Planes, separating 270
Planes, transition 270
Planet, image of 37 94 420
Planet, paths or orbits of xxvi 311 330
Plate, refraction through 419 421
Poetry xiii
Poggendorff 306 309 310
Point, conjugate 272. See also Transition-point
Point, group- 501
Point, of evanescent curvature 7
Point, transition- 270
Points of vergency 240 265 274.
Points of vergency, aberrations near 275
Points of vergency, loci of 240. See also Caustic surfaces
Points, cardinal 508
Points, focal 508
Points, limit, of congruence xxii 140.
Points, nodal 395 508.
Points, principal, in instrument of revolution 457 508
Polar coordinates 222
Polar equation of Fresnel's wave 282
Polarisation in biaxial crystal 280
Polarisation in biaxial crystal, conical 288
Polarisation in biaxial crystal, double 288
Poncelet xiv
Potter xxvi 305 307 309 310
Power of system of refractors 423
Power of thick lens 395
Power of thin lens 365 370 423
Power of two hemispheres 397
Power of two thick lenses 397
Power, refractive, of medium 91 104.
Prange xxiv 475 487
President of Royal Irish Academy v x xiv
Primary focus See Focus primary
Primitives, singular See Singular primitives
Principal axes in instrument of revolution 366
Principal axes of deflexure 244
Principal rays 130 241 275.
Principal rays, in instrument of revolution 300 366 377
Principal relations, calculus of xi
Principal, caustic 362
Principal, circles of deflexure 244
Principal, coefficient of aberration 161
Principal, foci or focus See Foci; Focus
Principal, planes of congruence 140. See also Natural coordinate planes; Planes of extreme projection; Planes of extreme virtual foci
Principal, points of instrument of revolution 395 419 457 508.
Principal, virtual foci 7
Principle of accumulated disturbance 313
Principle of least time See Fermat
Principles of constant, least, stationary and varying action See Action
Prism, passage of light through xxvi 305 307 310
Prisms, ordinary and extraordinary 177 184.
Probabilities xi
Problem, fundamental, of mathematical optics 169
Problem, fundamental, of optical instruments 297
Professorship of Astronomy x
Projection, foci by 7 135 240 241 245
Projection, planes of extreme See Planes of extreme projection
Propagation of light See also Slowness; Velocity
Propagation of light, in biaxal crystal 165 280 288 301 330
Propagation of light, rival theories of 107 313
Ptolemy 312 315 316
Pycnoid 83
Q-coefficients in expansion for T 298. See also Aberration coefficients
Quadrature of section of caustic surface 300
Quaternions xi xiii xv xvii
Quetelet xvii 332 333 463
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