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| Baker B., Copson E. — The mathematical theory of Huygens principle |
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| Предметный указатель |
'Cut' Hankel functions 90
Aether, elastic-solid theory of 20 44 69
Arbitrariness of boundary values 27 38 41 71
Asymptotic behaviour of diffracted wave 95 97 122
Black half-plane, diffraction of plane-polarized light by 120 149
Blackness, definition of 98 124
Blackness, Kirchhoff's definition of 70 98 124
Blackness, Kottler's definition of 98 117
Blackness, unsatisfactory state of theory of 152
Blackness, Voigt's definition of 150
Contact transformations 4 5
Contact transformations, connexion with Huygens' geometrical construction 5
Cylindrical wave-functions 48 49 53
Cylindrical wave-functions, Volterra's general theorem on 54
Cylindrical waves, diffraction of, by black half-plane 97
Cylindrical waves, equation of 45 49
Cylindrical waves, equation of, Hadamard's solution 56
Cylindrical waves, equation, Riesz's solution 54 62
Cylindrical waves, equation, Volterra's solution 56 64
Cylindrical waves, equation, Weber's solution 48
Determinacy, theorem of 40
Diffracted wave, asymptotic behaviour of 95 97 122
Diffraction by thick black screen 101
Diffraction by thin black screen 101
Diffraction of cylindrical waves by black half-plane 97
Diffraction of light 68
Diffraction of plane-polarized light by black half-plane 120 149
Diffraction of plane-polarized light by reflecting half-plane 142
Diffraction of spherical waves by black half-plane 92
Diffraction, formula, Fresnel — Kirchhoff 72
Diffraction, formula, Fresnel's 33
Diffraction, formula, Kirchhoff's 70
Diffraction, formula, Stokes's 32 36
Diffraction, Kirchhoff's theory of 68 79
Diffraction, Kottler's theory of 98
Diffusion 47 53 65
Divergent sound waves, Sommerfeld's conditions 25 28
Eigenfunctions 28
Eigenvalues 27
Elastic-solid theory of the aether 20 44 69
Electromagnetic field, analytical expression of Huygens' principle for 105 114
Electromagnetic field, Maxwell's equations of 102
Electromagnetic theory of light 6 44 102
Electromagnetic waves, forward propagation of 3
Elementary solution, Hadamard's 46
Equation of cylindrical waves 45 49
Equation of cylindrical waves, Riesz's solution of 54 62
Equation of cylindrical waves, Volterra's solution of 56 64
Equation of wave-motions 8
Equation of wave-motions, in n dimensions, Riesz's solution of 66
Equation of wave-motions, in spherical polar coordinates 9
Equation of wave-motions, Poisson's solution of 14
Equivalent layer, Green's 23 55
Forward propagation of electromagnetic waves 3
Forward propagation of plane waves 3 9
Forward propagation of spherical waves 18
Fractional order, integrals of, Riemann — Liouville definition of 57
Fractional order, integrals of, Riesz's 58
Fresnel — Kirchhoff diffraction formula 72
Fresnel's diffraction formula 33
Fresnel's diffraction formula, extension of Huygens' principle 20 22
Fresnel's diffraction formula, integrals 95 141
Geometrical optics, Kirchhoff's theorem on 79
Geometrical optics, theory of wave-propagation, Huygens' 1 19
Green's equivalent layer 23 55
Green's equivalent layer, functions 27
Hadamard's elementary solution 48
Hadamard's solution of equation of cylindrical waves 56
Half-plane, diffraction of cylindrical waves by 97
Half-plane, diffraction of plane waves by 84 120 142
Half-plane, diffraction of spherical waves by 92
Hankel functions 52 87 90
Helmholtz's formula 24 26 28 79
Helmholtz's formula as an analytical expression of Huygens' principle 31 68
Helmholtz's formula, physical meaning of 28
Helmholtz's formula, restrictions on the use of 26
Helmholtz's formula, Sommerfeld's conditions for 25
Helmholtz's formula, Weber's analogue of 51
Huygens' geometrical construction as a contact transformation 4
Huygens' geometrical theory of wave-propagation 1 19
Huygens' principle, analytical expression of, by Helmholtz's formula 31
Huygens' principle, analytical expression of, for electromagnetic field 105 114
Huygens' principle, Fresnel's extension of 20
Huygens' principle, Stokes's approximate formulation of 32
Huygens' principle, verification of, for expanding spherical waves 15
Integrals of fractional order, Riemann — Liouville definition of 57
Integrals of fractional order, Riesz's 58
| Integrals, Fresnel's 95 141
Interference 20 21 92 147
Kirchhoff's definition of blackness 70 98 124
Kirchhoff's diffraction formula 70
Kirchhoff's formula 36 38
Kirchhoff's formula, connexion with Larmor — Tedone formulae 109
Kirchhoff's formula, failure of 109
Kirchhoff's formula, for sources inside a closed surface 38
Kirchhoff's formula, for sources outside a closed surface 37
Kirchhoff's formula, physical interpretation of 42
Kirchhoff's formula, Volterra's analogue of 52
Kirchhoff's theorem on geometrical optics 79
Kirchhoff's theory of diffraction 68 79
Kottler's definition of blackness 98 117
Kottler's formulae 117
Kottler's formulation of Huygens' principle for electromagnetic field 114
Kottler's theory of diffraction 98
Larmor — Tedone formulae 105
Larmor — Tedone formulae, analytical proof of 106
Larmor — Tedone formulae, complex form of 106
Larmor — Tedone formulae, connexion with Kirchhoff's formula 109
Larmor — Tedone formulae, failure of 109
Larmor — Tedone formulae, modification of 109
Light, electromagnetic theory of 6 44 102
Light, rectilinear propagation of 3 20
Luminosity of edge of screen 92 94 123 150
Maggi's transformation 75 80 84 93
Maxwell's equations of electromagnetic field 102
Maxwell's equations of electromagnetic field, many-valued solutions of 124
Maxwell's equations of electromagnetic field, two-dimensional solutions of 130
Mean value, notation for 13
Method of descent 46
Phase of secondary wave 22 33
Physical interpretation of Kirchhoff's formula 42
Plane of diffraction 147
Plane of polarization, rotation of 149
Plane waves, forward propagation of 3 9 19
Plane-polarized light, diffraction of, by black half-plane 120 149
Plane-polarized light, diffraction of, by reflecting half-plane 142
Point-source of light 68
Poisson's formula 14 15 18
Rectilinear propagation of light 3 20 79
Reflecting half-plane diffraction of plane-polarized light by 142
Reflecting screen 124
Retarded values, definition of 32
Riemann surfaces, use of, in diffraction problems 129
Riemann surfaces, use of, in electrostatic problems 127
Riemann — Green theory 56
Riemann — Liouville definition of integrals of fractional order 57
Riesz's integrals of fractional order 58
Riesz's solution of equation of cylindrical waves 54 62
Riesz's solution of equation of wave-motions in n dimensions 66
Rotation of plane of polarization 149
Saltus problems 72 98 152
Secondary wave, phase of 22 33
Sommerfeld's conditions for divergent sound-waves 25 28
Sound waves of small amplitude 6
Sound waves, isotropic spherical 9
Source, double 12
Source, simple 11
Spherical waves, diffraction of, by black half-plane 92
Spherical waves, forward propagation of 18
Spherical waves, velocity potential of 9
Spherical waves, verification of Huygens' principle for 15
Stokes's approximate formulation of Huygens' principle 32
Stokes's diffraction formula 32 36
Velocity of sound 8 9
Velocity potential 6 8
Velocity potential, of double source 12
Velocity potential, of simple source 11
Velocity potential, of spherical waves 9
Voigt's 'blackest' screen 151
Voigt's definition of blackness 150
Volterra's analogue of Kirchhoff's formula 52
Volterra's general theorem on cylindrical wave-functions 54
Volterra's solution of equation of cylindrical waves 56 64
Wave-equation, in spherical polar co-ordinates 9
Wave-equation, many-valued solutions of 132 138
Wave-equation, n-dimensional, Riesz's solution of 66
Wave-equation, one-dimensional 8
Wave-equation, two-dimensional 49
Wave-functions, cylindrical 48 49 53 62
Wave-functions, definition of 8
Wave-motions, difference between, in two and three dimensions 46
Wave-motions, equation of 8
Wave-propagation, Huygens' geometrical theory of 1 19
Weber's analogue of Helmholtz's theorem 51
Weber's solution of equation of cylindrical waves 48
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