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Page viii
... proved • Green's problem , reduced to the proper general solution of Laplace's equation ; solved synthetically in terms of par- ticular solution of Laplace's equation - Isolation of effect by closed portion of surface - Green's problem ...
... proved • Green's problem , reduced to the proper general solution of Laplace's equation ; solved synthetically in terms of par- ticular solution of Laplace's equation - Isolation of effect by closed portion of surface - Green's problem ...
Page ix
... proved - Chasles ' comparison between the po- tentials of two confocal homoeoids - Proof of Poisson's theorem regarding attraction of elliptic homoeoid - Law of attraction when a uniform spherical shell exerts no action on an internal ...
... proved - Chasles ' comparison between the po- tentials of two confocal homoeoids - Proof of Poisson's theorem regarding attraction of elliptic homoeoid - Law of attraction when a uniform spherical shell exerts no action on an internal ...
Page x
... proved - Equilibrium of constrained rigid body— Example . Two constraints ; -the four equations of equi- librium found ; and the two factors determining the amounts of the constraining forces called into action- Equations of equilibrium ...
... proved - Equilibrium of constrained rigid body— Example . Two constraints ; -the four equations of equi- librium found ; and the two factors determining the amounts of the constraining forces called into action- Equations of equilibrium ...
Page xi
... stated in advance - Laws for flexure of elastic plate assumed in advance - Stress - couple acting across a normal 604-608 609-613 614-626 section - Twisting components proved equal round any two perpendicular CONTENTS . xi.
... stated in advance - Laws for flexure of elastic plate assumed in advance - Stress - couple acting across a normal 604-608 609-613 614-626 section - Twisting components proved equal round any two perpendicular CONTENTS . xi.
Page xii
... proved by Kirchhoff - Kirchhoff's boundary equations investi- gated - Distribution of shearing force determined , which produces same flexure as a given distribution of couple round axes perpendicular to boundary - Uniform distribu ...
... proved by Kirchhoff - Kirchhoff's boundary equations investi- gated - Distribution of shearing force determined , which produces same flexure as a given distribution of couple round axes perpendicular to boundary - Uniform distribu ...
Contents
ABSTRACT DYNAMICS | 1 |
Fluid pressure depending on external forcesSurfaces of equal | 4 |
Conditions of equilibrium of a particleEquilibrium of | 8 |
Partly rewritten | 9 |
Small addition | 12 |
Rate of increase of pressurePressure in a calm atmosphere | 29 |
PotentialForce in terms of the potentialEquipotential sur | 36 |
Potential in free space cannot have a maximum or minimum | 49 |
Slight alteration | 316 |
Small alteration | 317 |
Old 329 rewritten and extended | 318 |
Old 330with considerable additionsignoration of coordinates new | 319 |
Loss of apparent weight by immersion in a fluidLemma | 320 |
to 324 Same as old 331 to | 325 |
to 336 Same as old 318 to 328 with some alterationscon | 326 |
A homogeneous ellipsoid is a figure of equilibrium of a | 327 |
Greens problem reduced to the proper general solution | 56 |
Reference to Tide Predicter added | 58 |
Addition | 62 |
Second investigation of attraction of ellipsoidElliptic | 66 |
Small addition | 76 |
Origin of spherical harmonic analysis of Legendre and | 84 |
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 |
Exhaustion of potential energyGreens methodExhaustion | 152 |
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 |
longitudinal extension different for different substances | 222 |
Units of length and time new | 223 |
Small addition | 225 |
Fundamental problems of mathematical theoryConditions | 233 |
St Venants application to torsion problemsTorsion pro | 240 |
Part omitted | 245 |
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 |
cal surface concentric with origin harmonically expressed | 294 |
Small alterations and additions | 298 |
Plane strain definedProblem for cylinders under plane | 300 |
Addition | 312 |
Equilibrium ellipsoid of three unequal axesGeneral problem | 334 |
Transition to hydrodynamicsImperfectness of elasticity | 336 |
Addition including slightly disturbed equilibrium new | 337 |
338 | 338 |
Some addition | 340 |
Digression on spherical harmonicsHarmonic spheroidHar | 341 |
Same as nonmathematical portion of old | 343 |
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 |
Figure of the sea level determinable from measurements | 367 |
and 374 Same as old | 373 |
Hydrostatic examples resumedNo mutual force between por | 379 |
to | 380 |
and | 382 |
to | 386 |
Equilibrium of rotating spheroid of heterogeneous liquid | 398 |
Addition on calculating machines new | 401 |
Rewritten | 404 |
Footnote quoted from old 830 compare with new 830 | 405 |
Slight alteration | 408 |
409 Rewritten | 409 |
Comparison of Laplaces hypothesis with observationThe | 415 |
Numerical estimates of the amount of tidal frictionSecular | 420 |
427 | 427 |
Part rewritten | 429 |
Rewritten | 431 |
Extendedbifilar balance new | 435 |
Part rewritten | 443 |
Slightly altered and part omittel | 451 |
Same as part of old 451old 452 omitted | 452 |
and 454 Rewritten | 453 |
455 | 455 |
Small omission | 458 |
Advance in knowledge of tides since the first editionThe | 460 |
99 | 467 |
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 | 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 |
Part rewritten | 506 |
Slight alteration | 507 |
519 | |
520 | |
525 | |
527 | |
Other editions - View all
Common terms and phrases
amount analytical angle angular velocity anticlastic applied forces attraction axes axis brium catenary centimetre centre of gravity centre of inertia centrobaric co-ordinates components condition confocal curvature curve cylinder denote density diagram direction displacement distance distribution ds ds dx dy dz earth edge elastic solid ellipsoid elliptic equal equili equilibrium equipotential equipotential surface expression external point finite flexural rigidity fluid friction function given harmonic Hence homoeoid homogeneous infinitely small integral isotropic mass matter modulus moment of inertia motion normal section osculating plane parallel particle plate position pressure problem radius rectangular resultant force rigid body rotation round shell solid angle solid harmonic solution space sphere spherical harmonic spherical surface spheroid spiral strain stress substance suppose synclastic tangent theorem tion torsion traction twist uniform unit of length whole wire zero