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| Hamilton W.R. — The collected mathematical papers. Volume 1: geometrical optics |
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| Предметный указатель |
T, transformation of partial differential equation for V by means of 178
T, transformation of, for change of origin 367
T, V, W, deductions of, from each other 174
Tangential coordinates xxiii xxvi 304 475 503
Teixeira 380
Telescope, uncentred xxvii 367
Telescope, uniaxal crystal as object glass of 340
Telescopes, construction of 104 301 383
Theory of Systems of Rays ix x xix xxii 1 88 163 314 462
Therefore, symbol  for 370
Thin optical system See also Lens; Lenses; Surfaces of revolution
Thin optical system,  for xxviii
Thin optical system, correction of spherical aberration and coma in xxviii. See also Aplanaticity
Thin optical system, factor in T for 403 456 511
Thin optical system, T for xxiv xxviii
Thin pencils See Pencils
Third class, systems of rays of 8 242
Time of passage of light through prism xxvi 305 307 310
Time of propagation as characteristic function xxi 168 277 296 307 329 473 475 489 497
Time, principle of least See Fermat
Time-function See V
Timmermans 463
Trajectories, orthogonal See Orthogonal trajectories
Transformation of coordinates 128 222
Transformation of Legendre 474
Transformation of partial differential equation for V by means of W and T 178 474
Transformation of T for change of origin 367
Transformation, contact xxi 171 474 487
Transformation, homogeneous, of W and T 198 205
Transition line on reflector or refractor 275
Transition planes 270
Transition points 270
Triple object glass 430
U 148
U, development in plane system 153
U, development in series for 149
U, development in system of revolution 155
Umbilics 275 300 475.
Undevelopability, coefficient of 7 33
Undevelopable pencils See Pencils
Undevelopable systems of rays 7
Undistorted image of small plane object 39
Undulatory slowness along ray (v) 168 279 499.
Undulatory theory See also Wave theory
Undulatory theory of Huyghens 313
Undulatory theory of light and prismatic aberration 305 310
Undulatory theory of light of Fresnel 165 280 285 302 314 330
Undulatory theory, application of characteristic function to 277 497
Undulatory theory, components of normal slowness in 172 277 301 327 497.
Undulatory theory, history of 313
Undulatory theory, laws of reflection and refraction in 285 301.
Undulatory theory, medium-function  in 278 497
Undulatory theory, normal velocity of propagation ( ) in 277 280 327 497
Undulatory theory, rays in 278 498
Undulatory theory, T in 489
Undulatory theory, V as time of propagation in, xxi 168 277 296 307 329 473 497
Undulatory theory, W in 278 475 489
Undulatory theory, waves in, and surfaces of constant action 107 259 335
Undulatory velocity along ray  279 498 500.
Uniaxal crystal See Crystal
Uniform media See Media
Unit-wave in any uniform medium, construction for 291
Unit-wave in biaxal crystal 281
V See Medium-function v
V as action xx xxi xxv 111 132 168 328
V as function of final coordinates xx 17 111 488
V as function of initial and final coordinates xx 168 488
V as function, first definition xix 91 105
V as time of propagation in undulatory theory xxi 168 277 307 329 473 497
V for instrument of revolution xxvii 155 298 364
V for plane mirror 297
V for prism 307
V for single uniform medium 208
V for system of curved rays (first definition) 105
V for thin spheric lens, xxvii 365
V for two thin lenses, close together 369
V in dynamics 331 485
V in geometry of surfaces, xxvi 304
V, change in, produced by passage through thin spheric lens xxvii 365
V, characteristic function xix
V, development in plane system 154
V, development in series for 150 364
V, development in system of revolution 156 158 160
V, equations of ray in terms of 111 169 172 498
V, general expression for, for all optical combinations 218
V, maxima and minima of 270
V, medium-functions , v deduced from 169 482
V, partial differential coefficients of, as components of normal slowness 172 277 301 497
| V, partial differential coefficients of, as direction cosines of ray 17 91 297 322
V, partial differential coefficients of, connections of, with those of W 112 184 490
V, partial differential coefficients of, sudden changes in, in reflection or refraction 118 215 218 285 301 325 329
V, partial differential equation (first order) for See Integration; Partial differential equation; Transformation
V, partial differential equation (second order) for 170
V, principal foci and principal rays in terms of 134 276 495
V, unchanged in value by reflection or refraction 117 214 329
V, W, T, deductions of, from each other 174
Vandermonde 64 468
Variational principle and contact transformation xxi 487
Variations, calculus of xx xxv 8 104 107 110 319
Varying action see Action
Velocity of light, Fermat on 316
Velocity of light, Galileo and Descartes on 311
Velocity of light, in emission theory 9 110 147 168 335 500
Velocity of light, Newton on 317
Velocity ray-, lines of single 280 283
Velocity, group 500
Velocity, molecular (v) 168; see also Medium-function v; Undulatory slowness; Velocity of light
Velocity, normal, in biaxal crystal 280
Velocity, normal, lines of single 280 283
Velocity, normal, of wave propagation () 277 327 497
Velocity, normal, planes of single 283
Velocity, undulatory, along ray 279 498 500
Velocity, undulatory, along ray, in biaxal crystal 281
Verdet 281
Vergency 238
Vergency, planes of See Planes of vergency
Vergency, points of See Points of vergency
Vertices of circular image 40
Vertices of mirror 35
Vertices of surface 102 362
Vibrating chords, equation of 96
Vibration, lines of, on Fresnel's wave 288
Vibrations in elastic ether 165 280 313
Virtual caustic 7
Virtual caustic surfaces 7
Virtual foci See Foci; Focus
Virtual intersections of rays 139
Visible image of luminous point 32
Vision, bounding pencil of 31
W, applied to geometry of surfaces xxvi 304 475
W, characteristic or auxiliary function xx xxv 111 147 168 174 473 488
W, development in series for 149 155 364
W, equations of ray in terms of 147 148 180 473 474
W, for focal system of rays 125
W, for instrument of revolution xxvii 155 364 515
W, for parabolic reflector or refractor of revolution 216
W, for single uniform medium 208
W, for thin spheric lens, xxvii 365
W, general expression for, for all optical combinations 218
W, homogeneous transformation of 198
W, in curvilinear coordinates 222
W, in undulatory theory 278 475 489
W, integration of partial differential equation for V by means of xx xxv 146 153 155 178 364 473
W, partial differential coefficients of, and those of 7 199
W, partial differential coefficients of, and those of T 112 184 190 490
W, partial differential coefficients of, sudden changes in, in reflection or refraction 119 218
W, partial differential equations for 178 179
W, principal foci and principal rays in terms of 132 276 495
W, sudden change in, in reflection or refraction xxv 119 214
W, transformation of partial differential equation for V by means of 178
W, V, T, deductions of, from each other 174
Wave in any uniform medium, construction for 291
Wave in any uniform medium, curvature of 131
Wave in biaxal crystal, polarisation of 280
Wave, Fresnel's, application of quaternions to xi xvii
Wave, Fresnel's, cusps and circles of contact on 164 283 302
Wave, Fresnel's, equation of xxvi 280 341
Wave, Fresnel's, equation of, in polar form 282
Wave, Fresnel's, lines of vibration on 288
Wave, Fresnel's, relations of, to surface of components 291 301
Wave, mechanics 500
Wave, normal slowness of propagation of 278. See also Components
Wave, normal velocity of propagation of 277 280 327 497.
Wave, reflected or refracted, construction for 302
Wave, theory and emission theory xxi xxv 107 313 497.
Wave, unit- See Unit-wave; Wave
Waves as surfaces of constant action 107 259
Waves, cutting rays perpendicularly 330 335
Waves, extreme osculating 270
Whittaker 318 468 487
Winkeleikonal 488
Wordsworth xiii xiv xvi
Young 165 314
Zero, differences of xi
Zero-invariant 162
“Hamilton's Equation” for congruences xxii 33 140
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