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### Contents

ABSTRACT DYNAMICS | 1 |

Fluid pressure depending on external forcesSurfaces of equal | 4 |

Partly rewritten | 9 |

Small addition | 12 |

Attraction of a spherical surface of which the density varies | 18 |

Rate of increase of pressurePressure in a calm atmosphere | 29 |

PotentialForce in terms of the potentialEquipotential sur | 36 |

Greens problem reduced to the proper general solution | 56 |

to 324 Same as old 331 to | 325 |

to 336 Same as old 318 to 328 with some alterationsco | 326 |

A homogeneous ellipsoid is a figure of equilibrium of a | 327 |

Equilibrium ellipsoid of three unequal axesGeneral problem | 334 |

Addition including slightly disturbed equilibrium new | 337 |

Some addition | 338 |

Digression on spherical harmonicsHarmonic spheroidHar | 341 |

Same as nonmathematical portion of old | 343 |

Reference to Tide Predicter added | 58 |

Addition | 62 |

Second investigation of attraction of ellipsoidElliptic | 66 |

Small addition | 76 |

Centre of gravityCentrobaric bodies proved possible | 82 |

Some alteration | 90 |

Rodrigues coordinates new | 95 |

Addition | 96 |

Small addition | 97 |

STATICS OF SOLIDS AND FLUIDS | 98 |

Somewhat altered | 100 |

Rewritten and enlarged | 101 |

Rewritten | 102 |

Addition | 107 |

Additiontransient terrestrial nutation of 306 days new | 108 |

Slight alteration | 110 |

Additionrolling and spinning bodies new | 111 |

Additiondynamics of twist in kinks new | 123 |

Equilibrium of a flexible and inextensible cordCatenary | 128 |

Small alteration | 130 |

Additionintegral curvature horograph new | 137 |

Spiral springsSpiral spring of infinitely small inclination | 144 |

Elastic curve transmitting force and coupleKirchhoffs | 151 |

Flexure of a plane elastic plateDefinitionsGeometrical | 174 |

Some alteration | 184 |

Plate bent by any forcesConditions of equilibriumEqua | 188 |

190j Addition 198 Rewrittendegrees of freedomgeometrical slide new | 198 |

Symmetrical flexure of flat ringFlexure of flat ring | 200 |

Slight alteration | 201 |

Transmission of force through an elastic solidHomogeneous | 206 |

Slight addition | 212 |

Homogeneousness definedMolecular hypothesis assumes | 216 |

Units of length and time new | 223 |

VOL II | 225 |

Fundamental problems of mathematical theoryConditions | 233 |

Part omitted | 245 |

St Venants application to torsion problemsTorsion pro | 246 |

Small addition | 267 |

by a single bending stress by simultaneous | 268 |

Case of 647 independently investigatedRapid decrease | 274 |

Footnote new | 276 |

Definition of Principal axes new | 282 |

Reference added | 283 |

Problem of 696 solved for spherical shellDilatation proved | 286 |

Slight addition | 289 |

Considerable addition new | 293 |

Surfacetractions givenComponent tractions on any spheri | 294 |

Small alteration | 317 |

Old 329 rewritten and extended | 318 |

Old 330with considerable additionsignoration of coordinates new | 319 |

Physical problems relative to plane rectangular and circular | 344 |

345 i to xxviii Oscillations with frictiondissipation of energyposi tional and motional forcesgyrostaticsstability new | 345 |

Harmonic spheroidal levels of high ordersUndulation of level | 352 |

Determinateness of potential through space from its value over | 358 |

Figure of the sea level determinable from measurements | 367 |

and 374 Same as old | 373 |

to 380 Same as old 375 to 379 with alterations | 374 |

Hydrostatic examples resumedNo mutual force between por | 379 |

and 382 Same as old | 380 |

to 386 Same as old 381 to 384 Old 385 and 386 omitted | 383 |

398 Harmonic analysis new | 393 |

Equilibrium of rotating spheroid of heterogeneous liquid | 398 |

Addition on calculating machines new | 401 |

Rewritten | 404 |

Laplaces hypothetical law of density within the earthAs | 406 |

Footnote quoted from old 830 compare with new 830 | 408 |

Rewritten | 409 |

Comparison of Laplaces hypothesis with observationThe | 415 |

Numerical estimates of the amount of tidal frictionSecular | 420 |

Part rewritten | 429 |

Rewritten | 431 |

Extendedbifilar balance new | 435 |

Part rewritten | 443 |

Slightly altered and part omittel | 451 |

Advance in knowledge of tides since the first editionThe | 452 |

and 454 Rewritten | 453 |

455 | 455 |

458 | 458 |

Equations of Equilibrium of an Elastic Solid deduced from | 461 |

On the Secular Cooling of the Earth | 468 |

and 479 Small addition | 478 |

APPENDIX E On the Age of the Suns Heat | 485 |

f and 492 Slight alteration | 491 |

Integral of normal attraction over a closed surface new | 493 |

494 a to q Theory of potentialattraction of ellipsoids new | 494 |

APPENDIX F On the Size of Atoms | 495 |

Small addition | 496 |

Example added | 501 |

APPENDIX G On Tidal Friction by G H Darwin | 503 |

Small alterations and additions | 505 |

Part rewritten | 506 |

Slight alteration | 507 |

519 | |

520 | |

523 | |

524 | |

525 | |

527 | |

8 | |

Appendix B I Tidepredicter new 29 II Equationsolver new III to VI Mechanical integrator new VII Harmonic analyser new | 29 |

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### Common terms and phrases

according acting action amount angle applied approximately attraction axes axis becomes body called centre components condition consider constant corresponding couple curvature curve denote density determined direction distance distribution disturbing earth edge elastic ellipsoid ellipticity energy equal equations equilibrium example expression external figure flexure fluid force function given gives gravity harmonic heat Hence homogeneous inertia infinitely infinitely small integral length liquid mass matter mean motion normal parallel perpendicular plane plate portion positive potential present pressure principal probable problem produce proved radius remark resultant rigid rotation round shows sides simple solid solution space spherical surface square strain stress substance suppose surface temperature theory tides tion traction uniform unit whole wire zero