Action, least, discontinuous motions 455
Action, least, examples on this test 458
Action, least, Hamilton's generalisation into Varying Action 442
Action, least, Jacobi's test that the action is a minimum 458
Action, least, two theorems 447
Airy, G.B., form of an electric cable payed out from a ship 597
Airy, G.B., governors 105 107
Airy, G.B., numerical verification of an expansion by Fourier's rule 615
Approximations, second, change of type and period 356
Approximations, second, examples 364
Approximations, second, general theory 360
Approximations, second, what terms rise in order 355
Ball, Sir R., theorems on the oscillations of a suspended body 133 214
Bernoulli, D., motion of a chain suspended by one end 599
Bernoulli, D., transference of oscillations 94
Bertrand, relative motion 25
Bertrand, remarks on a theorem of Poisson 495 497
Bertrand, theorem on (u, v) 498
Billiards, final rectilinear motion Ex. 2
Billiards, impact of two balls Ex. 3
Billiards, path of the centre Ex. 1
Billiards, some numerical results 239
Billiards, various results Ex. 4
Biquadratic, analysis for dynamics 285
Biquadratic, conditions of stability 287
Boole, proof of Lagrange's variation formula 478
Boomerang, described with general theory 210
Boomerang, G.T., Walker's memoir on the motion 210
Booth, arc of herpolhode 171 Ex.
Bour, Ed., reduction of the number of variables in theoretical dynamics, referred to 512
Bour, Ed., relative vis viva 42
Bourget, oscillations of tight connected strings 621
Bryan, G.H., a graphic illustration 467 Ex.
Bryan, G.H., report on Thermodynamics 461
Canonical elements, defined 489 491
Canonical elements, the constants in Jacobi's complete integral form a canonical set 496
Centrifugal force, compound c.f. 26
Centrifugal force, the centrifugal forces E 112 311 389
Chandler, S.C., motion of the pole in the earth 534
Changing bodies, equations of motion 22
Changing bodies, Liouville J., Darwin, Kelvin, Tisserand, Gylden, Helmert 24
Chree, C., motion of a tight string, effect of a sensible thickness 612
Clairaut, relative motion 25
Cone rolls on a moving sphere 209
Conjugate functions, applied to a heterogeneous membrane 642
Conjugate functions, applied to a network 421
Conjugate functions, theory explained 459 641
Conjugate functions, vortex motion 475
Conjugate line, defined 174
Conjugate line, theorems on its motion 175
Contact transformation, generalised Matthieu's rule 500
Coriolis, billiards 239
Coriolis, relative motion 25
Coriolis, vis viva with moving axes 30
Cournot, motion of a body on a plane quoted 240 249
Cube, oscillates on the summit of a sphere 252 Ex.
Cyclical motions, Szily's theorem 462 Ex.
Cyclical motions, the fundamental theorems 461
Cyclical motions, various references 461
Cylinder, steady motion with its edge on a plane, and the oscillations 244 Ex.
Darboux, elimination of the time in Lagrange's equations 451
Darboux, on an equation of Poisson 599
Darboux, theorem on what intersections of quadrics could be polhodes 150 Ex.
Darwin, changing body 22
Darwin, effect of geological changes on the earth's axis of rotation 540
Day, other causes 539 540
Day, the length is not affected by the attraction of the sun 539
De Morgan, discontinuity in the arbitrary functions 615
De Morgan, exceptional cases in the theory of maxima 455
Differential equations, many degrees of freedom 262
Differential equations, minors zero 272 see
Differential equations, Sturm's theorem on differential equations of the second order 427
Differential equations, the complementary function 325
Differential equations, the string differential equation 587
Differential equations, two degrees of freedom 260
Differential equations, types of motion 264
Disc or hoop, a disc spun about a diameter 244 Ex.
Disc or hoop, general equations 244
Disc or hoop, horizontal ring rotating on the summit of a sphere 208
Disc or hoop, rolls with plane vertical 15 244
Disc or hoop, steady motion and oscillations 244 Ex.
Discontinuity, discontinuous agitating force 413
Discontinuity, discontinuous motions 455
Discontinuity, the arbitrary functions in the theory of sound may be discontinuous 615
Dixon, A.C., memoir on a Theorem of Jacobi 201
Donkin, normal transformation 482
Donkin, proof that  489
Donkin, reduction in the number of variables 512
Donkin, rule for transformation of coordinates in Hamilton's equations 500
Donkin, string with attached mass 622 Ex.
Donkin, string with periodic force and piano string 619 620
Donkin, the constants in Jacobi's integral form a canonical set 496
Donkin, theorem on reciprocal functions 487
Drift of shot, general explanation 210
Electric cable, effect of friction 598
Electric cable, form of, when payed out from a ship 597
Ellery, Huygliens' parabolic pendulum, referred to 107
Ellipsoid, axis vertical oscillates on a plane 252 Ex.
Ellipsoid, conjugate Ellipsoid 174 183 Ex.
Ellipsoid, motion of a contracting ellipsoid centre fixed 24 Ex.
Ellipsoid, roots of discriminant 63
Ellipsoid, two intersect in a polhode 150 175
Energy of oscillation, effects of an increase of inertia 76
Energy of oscillation, effects of an increase of inertia, and introduction of a constraint 78
Energy of oscillation, energy of a tight oscillating string 627
Energy of oscillation, intensity of a wave 627
Energy of oscillation, mean kinetic and potential 72
Energy, steady motion 99
Energy, test of stability 96
Energy, the determinant 99
Energy, the determinant, with examples 102
Euler, J.A., path of a billiard ball 239
Euler, L., complementary functions in precession 532
Euler, L., how changed if A, B, C were unequal 540
Euler, L., the ten-monthly period 533
Evans, Sir John, experiments on bodies which spin in one direction only 253
Ewing, speed governor 107
Ferrers, geometrical construction for the angular velocity in space of the instantaneous axis 169
Ferrers, on Sylvester's top 149
Ferrers, solution of a Tripos Problem quoted 130
Finite differences, applications to particles, rods, discs 418
Finite differences, chain of gyrostats, rods 419
Finite differences, chain of particles 402
Finite differences, four propositions 430 440
Finite differences, network 420
Finite differences, Sturm's theorems 433
Finite differences, theory of equations of Differences 422
Finite differences, two kinds of motion 411
Forced oscillations, Herschel's theorem 334
Forced oscillations, illustrations 340
Forced oscillations, infinite string 618
Forced oscillations, interval between cause and effect 352
Forced oscillations, magnification 337 346
Fourier, his use of the series for  599
Fourier, the rule for expansion in series 398
Free oscillations, general form of the fundamental determinant 310
Free oscillations, gradual disappearance of free oscillations 321 331
Free oscillations, imaginary roots 319
Free oscillations, the three potentials 309 311
Free oscillations, theorem on real roots 315
Frost, P., his Solid Geometry quoted 199
Frost, P., moving axes 5
Gallop, a rolling disc 244
Gallop, on the rise of a spinning top 243
Gascheau, referred to 109
Geometry of moving axes, applications to the theory of curves and surfaces 21
Geometry of moving axes, condition that a line OM is fixed in space 15
Geometry of moving axes, motion of OM in space 19
Gilbert, relative motion 42 44 Ex.
Gray and Mathews, Treatise on Bessel functions 600 600
| Greenhill, drift of Shot 210
Greenhill, elliptic functions quoted 203
Greenhill, geometrical representation of the time of a small oscillation of a top 205
Greenhill, gyrostat 44 Ex.
Greenhill, integrable cases of a top motion 207
Greenhill, memoirs on the motion of a top 201 201
Greenhill, oscillation of a heterogeneous chain 600 Ex.
Greenhill, problem on vortex motion 476
Greenhill, solution of Euler's equations 137
Gylden, changing body 22
Gyrostat, a general case 45
Gyrostat, application of Lagrange's equations 44
Gyrostat, chain of gyrostats 419
Gyrostat, effect of rotation of the earth 43
Gyrostat, some examples on suspended and other gyrostats 10 15
Gyrostat, various examples 46 205
Hamilton, Sir W.R., applied to the solution of the general equations of motion 463
Hamilton, Sir W.R., examples 477
Hamilton, Sir W.R., examples on the principal and characteristic functions 467
Hamilton, Sir W.R., principle of varying action 442
Hamilton, Sir W.R., some general cases in which these can be integrated 476
Hamilton, Sir W.R., the differential equations which these functions must satisfy 468
Hayward, R.B., equations of moving axes 5
Helmert, changing body 24
Helmholtz, motion of a plucked string 614 614
Helmholtz, pianoforte string 620
Helmholtz, practical analysis of a sound 340
Helmholtz, reciprocal Theorem in dynamics  492
Helmholtz, the relation of Fourier's series to the human ear 615
Hemming, G.W., treatise on Billiards quoted 239
Herpolhode, cone of herpolhode 159
Herpolhode, geometrical properties of the herpolhode 470
Herpolhode, Poinsot's definition 151
Herpolhode, when  191
Herschel, theorem on forced vibrations 334
Hess, his integral for the motion of some tops 212
Hess, reduction 212
Huyghens, his parabolic pendulum explained 106
Impulses on a loose string 583
Impulses on a membrane 640
Impulses on a tight string 620
Impulses, impact of rods 626
Impulses, jerks in machinery 349
Impulses, no forces 146
Impulses, steady motion disturbed 118
Impulses, top 209
Indeterminate multipliers, applied to Hamilton's equations 502
Indeterminate multipliers, oscillations about equilibrium 48
Initial motions, loose string 589
Instantaneous axis, Poinsot's theorem on its motion in space 168
Instantaneous axis, the cone 159
Invariable line 141
Invariable line, the invariable cone 159
Invariable line, velocity in its sphero-conic 164 165
Inversion, deduced from the principle of least action with examples 459
Inversion, relations between the pressures 459
Isolation, method of, determinant to find the constants of integration separately 366
Isolation, method of, repeated roots 369
Jacobi, rule for transformation of coordinates 490
Jacobi, solution of Euler's equations 137
Jacobi, test that the "action" is a real minimum 458
Jacobi, the complete integral of Hamilton's differential equation 470
Jacobi, theorem on (u, v) 498
Jellett, approximate solution of a top problem 243
Jullien, referred to 109
Kater, test that a support is firm 342
Kelvin, Lord, chain of gyrostats 419
Kelvin, Lord, changing body 22
Kelvin, Lord, motion of a body about a centre of force 557 Ex.
Kirchhoff, solution of Euler's equations 139
Klein and Sommerfeld, motion of a top 201
Klein and Sommerfeld, on Hess' integral 212
Koenigs, theorem on polhodes 150 Ex.
Korteweg, D.J., on second approximations 355
Kowalevski, her integral for the motion of some tops 213
Lagrange's equations, bordered determinant 64
Lagrange's equations, change of the independent variable t (two proofs) 458
Lagrange's equations, elimination of the time from Lagrange's equations 458
Lagrange's equations, energy 72
Lagrange's equations, equal roots 61
Lagrange's equations, indeterminate multipliers 48
Lagrange's equations, invariants 68
Lagrange's equations, principal oscillations 53
Lagrange's equations, separation of roots of the determinant 58
Lagrange, a tight chain of particles 402
Lagrange, general transformation from Cartesian to other coordinates 460
Lagrange, motion of a top 200
Lagrange, small oscillations of a suspended body 214
Lagrange, stability of three mutually attracting particles 108
Lagrange, the variation formula 478
Lagrange, the variation formula, extension 479
Lagrange, the variation formula, variation of parameters 509
Lamb, H. Encyc. Brit. "Dynamics" quoted 205 Ex.
Lamb, H., reciprocal theorems in dynamics 492
Lane-Fox, remarks on the Boomerang 210
Langley, S.P., experiments on a disc falling in air 210
Larmor, J., inversion of dynamical problems 459
Larmor, J., on Least action when applied to the modified Lagrangian function 450
Latitude, variation of, Albrecht and Forster's observations 535
Latitude, variation of, Chandler's observations and Newcomb's Theory 534
Latitude, variation of, maps of the path of the pole 535
Latitude, variation of, Turner 535
Lecornu, L., the impossible motions of a rod 255
Legendre, motion when referred to 184
Levi-Civita, on stationary motion 213
Liouville, J., changing body 22
Liouville, J., moving axes 5
Liouville, R., his discussion of Hess' integral 212
Lottner, relative motion 42 46 Ex.
MacCullagh, construction for a body under no forces 152
MacCullagh, geometrical interpretation 515
MacCullagh, geometrical solution of Euler's equations 153
MacCullagh, potential of a body at a distant point 513
Mackinlay, text book of Gunnery quoted 210
Magnus, deviation of projectiles quoted 210
Maxwell, essay on Saturn's rings 557 Ex.
Maxwell, on Governors 107
Membrane, equation in a series to find the load to produce a given period 639 639 474
Membrane, heterogeneous membranes 641
Membrane, vibrations due to a periodic force, or a blow 640
Membrane, vibrations when bounded by a rectangle 635
Moon, two important constants 556
Moscow collections, memoirs on Hess' integral 212
Moving axes, equations of motion and examples 10
Moving axes, fundamental theorem 4
Moving axes, fundamental theorem, oblique axes 7
Moving axes, fundamental theorem, vectors 5
Moving axes, geometry of 16
Moving axes, rolling hoop 15
Moving axes, small oscillations 15
Moving axes, top, axis vertical 15
Moving axes, uniaxal bodies 12
Multipliers, method of, equal roots 392
Multipliers, method of, extension to other cases in dynamics (1) symmetrical determinant 384 386
Multipliers, method of, extension to other cases in dynamics (2) skewed determinant 389
Multipliers, method of, Fourier's rule 398
Network of particles, conjugate functions 421
Network of particles, quadrilateral openings 420
No forces, conjugate line 174
No forces, Correlated bodies 192
No forces, MacCullagh 152
No forces, motion of principal axes 176
No forces, motion under 137
No forces, Poinsot 143
No forces, resistance of the air 147
No forces, sphero-conics 161
No forces, Stone's theorem 183 Ex.
No forces, sudden action of forces 146
No forces, Sylvester's and Poinsot's measures of the time 196 198
No forces, uniaxal bodies 180
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