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| Hamilton W.R. — The collected mathematical papers. Volume 1: geometrical optics |
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| Предметный указатель |
Radical constants of aberration 299. See also Aberration coefficients
Radii of curvature of caustic surface 46
Radii of curvature of undevelopable pencil 7
Radii of object glass 384
Radius of curvature of curve in space 7
Radius of deflexure 244
Rahn 370
Ray, central, in instrument of revolution 300 366
Ray, curvature of 232
Ray, definition of 15
Ray, direction cosines of, as partial differential coefficients of V 17 91 297 322
Ray, direction cosines of, dependent on extreme coordinates 169 297
Ray, elements of position of 15
Ray, emergent, construction for, in instrument of revolution 398
Ray, equations of See Equations; Differential equations
Ray, reflected or refracted, construction for 293 302
Ray, undulatory slowness along 168 279 499
Ray, undulatory velocity along 279 498 500
Ray, undulatory velocity along, in biaxal crystal 281
Ray-lines 233 238.
Ray-lines, from oblique plane 241 248 252
Ray-lines, intersections of 238 252 253
Ray-velocity, lines of single 280 283
Rayleigh 148 488
Rays in atmosphere xxv 104 326
Rays in history of optics 312
Rays in undulatory theory 278 498
Rays, curved 104 109 168 227 275
Rays, cusp- 283 303
Rays, cut perpendicularly by surfaces See Ellipsoid; Surfaces cutting system of rays perpendicularly
Rays, diverging from point, incident on mirror 25 36 94
Rays, diverging from point, on refractor 93 94
Rays, exdiametral 454 455 456. 364 367 376 383 457 506 509
Rays, indiametral 396 432 450 451 455 458
Rays, intersections of See Intersections; Caustic; Foci; Focus; Points of vergency
Rays, marginal 429
Rays, number of, through a point 346
Rays, oblique See Oblique
Rays, parallel See Parallel rays
Rays, principal See Principal rays
Rays, surfaces of 346. See also Pencils; Developable surfaces
Rays, systems of See Systems of rays
Rays, theory of systems of See Theory
Reciprocal surfaces 164 291 292 301
Rectangular systems of rays 16 138.
Rectangularity of extraordinary system of rays, condition of 7
Rectangularity of extraordinary system of rays, expressed by partial differential equation 8 335
Rectilinear congruence See Congruence
Rectilinearity, law of 411
Reflected ray, construction for 293 302
Reflected rays, ordinary systems of 9. See also Systems of rays
Reflected system, axes of 34
Reflected system, pencils of 17
Reflecting curve, caustics of 102
Reflecting hemisphere 389 390
Reflecting surface See Mirror; Reflector; Surface
Reflection at interior surface of crystal 8
Reflection from curve of double curvature 102
Reflection or refraction, maxima or minima of time or action-function for 270
Reflection or refraction, ordinary or extraordinary, formula, laws or rules of 118 214 285 301 325
Reflection or refraction, sudden changes due to, in partial differential coefficients (first order) of V 118 215 285 301 325 329
Reflection or refraction, sudden changes due to, in partial differential coefficients (second order) of F 118 218
Reflection or refraction, sudden changes due to, in partial differential coefficients (second order) of T 218
Reflection or refraction, sudden changes due to, in partial differential coefficients (second order) of W 119 218
Reflection or refraction, sudden changes due to, in T, xxv 214 388
Reflection or refraction, sudden changes due to, in V (zero) 117 214 329
Reflection or refraction, sudden changes due to, in W xxv 119 214
Reflection, history of law of 312
Reflection, lines of xxiv 24 94
Reflection, ordinary, analytic expressions of law of 9
Reflection, ordinary, and least action xxiv 10
Reflection, ordinary, systems of rays produced by 16
Reflector See also Mirror; Surface
Reflector,  ,  for 391
Reflector, lines of reflection on xxiv 24 94
Reflector, of revolution, parabolic, T for 216
Reflector, separating lines on 275
Reflector, transition-line on 275
Reflectors, combinations of 93 214
Reflectors, osculating focal 135 275
Refracted ray, construction for 293 302
Refracted rays, ordinary systems of 88. See also Systems of rays
Refracted systems, principal properties of 91
Refracting curve, caustics of 102
Refracting hemisphere 389
Refracting sphere, for 395
Refracting surface See Refractor; Surface
Refraction at spheric surface 162 338 442
Refraction at surface of revolution, xxv 160
Refraction of crystals, and least action 317
Refraction of spheric lenses 364
Refraction of system of revolution 160
Refraction through thin spheric lens 162 365
Refraction, change of density at 94
Refraction, conical x xxi xxv xxvi 164 285 302 303 312 330
Refraction, double 288 312
Refraction, extraordinary at surface of revolution 336
Refraction, extraordinary in biaxal crystals 8 285
Refraction, extraordinary, law of 118 214.
Refraction, from curve of double curvature 102
Refraction, history of law of 312
Refraction, index of See Refractive index; Refractive power
Refraction, lines of xxv 92 94
Refraction, lines of, extraordinary 8
Refraction, ordinary, law of 88 411
Refraction, ordinary, law of, and least action xxiv 89 317
Refraction, ordinary, law of, and least time 316
Refraction, ordinary, systems of rays produced by 91
Refraction, through plate 419 421
Refraction, through prism see Prism
Refractive index 146 316 324.
Refractive power of medium 91 104.
Refractor of revolution, and for 391
Refractor of revolution, parabolic, T for 216
Refractor of revolution, T for 388
Refractor, lines of refraction on xxv 92 94
Refractor, rays diverging from a point incident on 93 94
Refractor, separating lines on 275
Refractor, transition line on 275
Refractors See also Surfaces
Refractors, combinations of 93 214
Refractors, focal 89
Refractors, osculating focal 92 135 275
Refractors, system of 423
Reversion of series xxv 55 465
Revolution, optical instrument of See Instrument of revolution
Revolution, parabolic reflector or refractor of 216
Revolution, refracting surface or surfaces of 160. See also Refractor; Surface; Surfaces
Revolution, systems of rays of xxv 155 159 160
Robb v
Robinson 468
Roemer 311
Rohr 395
Rotation round-axis of curvature of ray 253
Ruled surface 15. See also Pencil; Surface of rays
S 268
S and points of vergency 268
S and principal foci and principal rays 276 495
Salmon 33 140 283
Schroedinger 277 500
Schwarzschild xxiv 488
Second class, system of rays of 7 15 242
Seidel 148 429 434 435 510
Separating lines on reflector or refractor 275
Separating planes 270
Series for T 298
Series for U 149
Series for V 150 154 156 158 160 364
Series for W 149 155 364
Series, Lagrange's 154
| Series, Laplace's 70 82 145 148 149 466
Series, reversion of xxv 55 465
Sine condition 406
Single normal velocity, lines of 280 283
Single normal velocity, planes of 283
Single ray-velocity, lines of 280 283
Single-axed crystal See Crystal uniaxal
Singular primitives or solutions 23 100 347 349 357 359 505
Singularities of congruence xxii xxvii 345 504
Slowness, normal 278
Slowness, normal, components of See Components
Slowness, undulatory, along ray (v) 168 279 499
smith 48 488
Snellius 301 312 316 326
Solutions, singular See Singular primitives
Sonnet xvi
Southall 44 162 395 431 435
Southey xiii
Sphere See also Hemisphere
Sphere, a-parabolicity for 425
Sphere, osculating perpendicular surface 49
Sphere, refracting, for 395
Spheric inflexion, directions of, on surfaces cutting rays perpendicularly 48 87
Spheric lenses See Lens; Lenses
Spheric surface, refraction at 162 338 442
Spheric surfaces, partial differential equation peculiar to 97
Spherical aberration See Aberration; Aberrations; Aplanaticity direct
Spheroids of Brewster 8
Spheroids of constant action 133. See also Action
Spheroids of constant action as waves in undulatory theory 259
Spheroids, osculating 132
Stationary action See Action
Stationary length, line of 319
Stationary value of T with respect to intermediate variables 217 370 408 413 493
Steward 296 406 488 489
Study 487
Sturm xxii 44
Supplement, first xxv 107
Supplement, second xxv 145
Supplement, third xxv 164
Surface of centres of ellipsoid 34 300
Surface of centres of undevelopable pencil 7
Surface of components 291 303
Surface of components, and Fresnel's wave 291 301
Surface of revolution, extraordinary refraction at 336
Surface of revolution, reflecting See also Mirror; Reflector
Surface of revolution, reflecting, lateral and longitudinal aberrations of 390
Surface of revolution, reflecting, T for 390
Surface of revolution, refracting See also Refractor
Surface of revolution, refracting, for 409
Surface of revolution, refracting, longitudinal aberration of xxv 160
Surface of revolution, refracting, T for 389
Surface, diametral, for system of rays 7
Surface, guiding 235
Surface, limiting for general system of rays 358
Surface, ruled 15. See also Pencil; Surface of rays
Surface, spheric, refraction at 162 338 442
Surfaces of circular profile 103
Surfaces of constant action See Action
Surfaces of least area 7
Surfaces of rays 346. See also Pencils; Developable surfaces
Surfaces of revolution, refracting system of any number of See also Instrument of revolution
Surfaces of revolution, refracting system of any number of, for 417—420 423 426 431 434 455
Surfaces of revolution, refracting system of any number of, for 426 431 433 434 455
Surfaces of revolution, refracting system of any number of, close together: aberration coefficients for 457
Surfaces of revolution, refracting system of any number of, condition of direct aplanaticity for 434 435 447 451 452
Surfaces of revolution, refracting system of any number of, condition of oblique aplanaticity for 435 447 451 452
Surfaces of revolution, refracting system of any number of, constants M, N, O for See M N 0
Surfaces of revolution, refracting system of any number of, focal lengths and aberrations of 441 444
Surfaces of revolution, refracting system of any number of, focus of, for direct rays 429
Surfaces of revolution, refracting system of any number of, focus of, for oblique rays 431 453
Surfaces of revolution, refracting system of any number of, longitudinal aberration of 427 429 441
Surfaces of revolution, refracting system of any number of, T for 426 431 434 445 454
Surfaces of revolution, refracting system of two, for 418 419 420.
Surfaces, Cartesian 89
Surfaces, caustic See Caustic surfaces
Surfaces, cutting system See also Action surfaces theorem theorem
Surfaces, cutting system of rays perpendicularly 7 14 90 97 138 233 315 330 334
Surfaces, cutting system, as envelopes of spheres 15 463
Surfaces, cutting system, directions of spheric inflexion on 48 87
Surfaces, cutting system, for curved rays 105
Surfaces, cutting system, in uniaxal crystal 8 335
Surfaces, cutting system, lines of curvature on 19
Surfaces, cylindrical, T for system of 493
Surfaces, deflexures of 241
Surfaces, developable See Developable surfaces
Surfaces, isoplatal 7
Surfaces, osculating focal 7
Surfaces, plane, media bounded by 177 217 493
Surfaces, reciprocal 164 291 292 301
Surfaces, reflecting and refracting See also Mirrors; Reflectors; Refractors; Surfaces of revolution
Surfaces, reflecting and refracting, determined by caustic surfaces 97
Surfaces, reflecting and refracting, determined by lines of reflection and refraction 94
Surfaces, reflecting and refracting, partial differential equations connected with 94—101
Surfaces, reflecting and refracting, relations of, to their normals xxvi 304
Symmetrical optical instrument See Instrument of revolution
Synthesis, method of 314
System of bodies, motion of xi 9 331
System of rays, definition of a 15
System of rays, surfaces perpendicular to See Ellipsoid; Surfaces cutting system of rays perpendicularly
System of refracting surfaces See Surfaces; Lens; Lenses
Systems of curved rays 104 109 168 227 275
Systems of rays, classification of 15
Systems of rays, developable 7. See also Pencils developable
Systems of rays, extraordinary 6 107—144 147 164—293
Systems of rays, in general 1 6 345
Systems of rays, of revolution xxv 155 159 160
Systems of rays, of the first class 7 15 17
Systems of rays, of the second class 7 15 242
Systems of rays, of the third class 8 242
Systems of rays, osculating focal 125 478
Systems of rays, plane 6 153. indiametral
Systems of rays, produced by single-axed crystal 8
Systems of rays, rectangular 16 138.
Systems of rays, theory of see Theory
Systems of rays, undevelopable 7. See also Pencils
Systems of reflected rays, ordinary 9
Systems of refracted rays, ordinary 88
T for hemisphere 389
T for instrument of revolution xxiii xxvi xxvii 298 376 412 434 455 503 508 512
T for paraboloid of revolution 216
T for single uniform medium 208
T for surface of revolution 388
T for system of circles 412
T for system of plane, cylindrical or developable surfaces 493
T for system of surfaces of revolution, close together 426 431 434 445 454
T for thick lens See
T for thin lens, of uniaxal crystal xxvi 337
T for thin lens, xxvii 369
T for thin system xxiv xxviii.
T for two thick lenses See
T for two thin lenses (close together) xxvii 369
T for uncentred telescope xxvii 367
T, approximate method of calculating 372 390 408 507
T, auxiliary or characteristic function xx xxv 168 174 488 492
T, elimination of intermediate variables in calculating 217 370 408 413 493 507
T, equations of ray in terms of 180 299 493 494 508
T, extended to curvilinear coordinates 222
T, factor in, for thin system 403 456 511
T, general expression for, for all optical combinations 218
T, homogeneous transformation of 205
T, in undulatory theory 489
T, integration of partial differential equation for V by means of 178
T, partial differential coefficients of, deduced from those of W 199 490
T, partial differential coefficients of, sudden changes in, in reflection or refraction 218
T, partial differential equation (first order) for 178
T, partial differential equation (second order) for 180
T, principal foci and principal rays in terms of 276 496
T, stationary value of, with respect to intermediate variables 217 370 408 413 493
T, sudden change in, in reflection or refraction xxv 214 388
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