Acoustical power transmitted in loudspeaker horn 185
Adiabatic curve, non-linearity due to 1 75 180
Aerodynamical forces, self-oscillation due to 140
Amplitude-frequency curves 59 60
Amplitude-frequency modulation in loudspeaker reproduction 78
Amplitude-frequency relation for nonlinear mass-spring system 57 70
Amplitude-frequency relation for thermionic valve circuit 82
Astronomy, differential equations in 21
Bending length of fabric (the heavy elastica) 175 178 179
Bernoulli's equation 11
cnt (Jacobian elliptic cosine) 26
Combination (sum and difference) tones 78
Coulomb damping 101
Creep in eccentrically loaded columns 171
Curved steel shells, impulse tests of 155
Differences, method of, for solving nonlinear D.E. 166 173
Differential equations, methods of solving non-linear 8
Elastica 34
Elastica, heavy 174
Electrical motor-generator, self-oscillations 47
Electrically maintained tuning fork 90
Elliptic cosine 26
Elliptic cosine, graph of 29
Elliptic function  39 40
Elliptic integral 26 36—38
Elliptic sine 26
Energy equality, principle of 104
energy equation 27 55 61
Entrainment (silent zone in valve oscillator) 83
Equivalent linear differential equation 103
Exponential loudspeaker horn, sound waves of finite amplitude in 180
Finite differences, method for solving non-linear D.E. 166 173
Flare in loudspeaker horn, influence of 186
Flexometer for testing fabrics, leather 175
Fourier series solution of non-linear D.E. 29 54
Frequency modulation in loudspeaker reproduction 78
Froude's pendulum 138
Graphical method of solving non-linear D.E. 145
Heart-loop for testing flimsy fabrics 175
Hydro-electric installation, surges in 95
Impulse tests of steel shells 155
Inductive tuning 109
Intermodulation frequencies 75
Isocline method of solving non-linear D.E. 145 158 104
Iteration method of solving non-linear D.E. 48
Jacobian elliptic cosine 26
Jacobian elliptic sine 26
Jump phenomenon 59 70
Linear equivalent of non-linear D.E. 106
Linearization of electrical circuits having non-linear elements 107
Loudspeaker horn, sound waves of finite amplitude in 180
Maclaurin's theorem, used for solving non-linear D.E. 167 177
Mass-spring system, non-linear 17 24 48 52
| Mathieu's equation 113
Mathieu's equation, as stability criterion 188
Mathieu's equation, experimental illustration of unstable solution 117 118 120
Mathieu's equation, solution graphs 115 116
Mathieu's equation, stability chart for 114 116
Melde's experiment 120
Negative resistance 136
Non-linear coupling, oscillation due to 141
Non-linear differential equation, definition of 9
Non-linear element in physical system, stabilization due to 119 121 138 139
Non-linear spring control, method of obtaining 25
Numerical solution of non-linear D.E. 168
Parametric excitation of oscillations 6 119 120
Periodic coefficients, differential equations having 113
Perturbation method for solving nonlinear D.E. 43 50
Plane jet in hydrodynamics 20
Principle of energy equality 104
Relaxation oscillations 6 138 151 153
Relaxation oscillations, periodic time of 154
Relaxation oscillations, waveform of 152
Riccati's equation 12
Self-oscillation due to aerodynamical forces 140
Self-oscillation due to aerodynamical forces, solid friction 135
Self-oscillation of motor-generator combination 47
Ship stabilization 92 95
simple pendulum 31
Simple pendulum with oscillating support 131
Simpson's rule, application to numerical solution of non-linear D.E. 169
Slowly varying amplitude and phase, method for solving non-linear D.E. 87
snt (Jacobian elliptic sine) 20
Sound waves of finite amplitude 1
Sound waves of finite amplitude in loudspeaker horn 180
Stability chart for Mathieu's equation 114 116
Stiffness, definition of 24
Subharmonic, higher orders 66
Subharmonic, mechanism exhibiting 130—132
Subharmonic, order 2 70
Subharmonic, order 3 62
Subharmonic, stability of, order 2 72
Subharmonic, stability of, order 3 188
Subharmonics and relaxation oscillations 84 85
Subharmonics in loudspeaker diaphragms 128
Surges in hydro-electric installation 95
Synchronous electrical motor, stability of 160
Thermionic valve oscillator 41 111
Thermionic valve oscillator, silent zone (entrainment) 83
Thermionic valve, transconductance of 41 110
Unstable subharmonics 72 189
Valve, thermionic, oscillatory circuit 41 111
Valve, thermionic, oscillatory circuit, forced oscillation in 80
Valve, thermionic, oscillatory circuit, silent zone 83
Vibrating thread with periodically variable tension 120
Vibrating thread with periodically variable tension, stability of 125
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