Treatise on Natural Philosophy, Volume 1, Part 2

Front Cover
At the University Press, 1883 - Mechanics, Analytic - 527 pages

From inside the book

Contents

Reference to Tide Predicter added
58
Addition
62
Second investigation of attraction of ellipsoidElliptic
68
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
Elastic curve transmitting force and coupleKirchhoffs
151
Flexure of a plane elastic plateDefinitionsGeometrical
172
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
Small addition
225
Fundamental problems of mathematical theoryConditions
233
St Venants application to torsion problemsTorsion pro
240
VOL II
241
Part omitted
245
Torsional rigidity less in proportion to sum of principal
258
axesGeometrical interpretation of distortion in normal
265
Small addition
267
681685
268
by a single bending stress by simultaneous
272
Footnote new
276
Application to problem of 696General problem of 696
280
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 alterations and additions
298
Plane strain definedProblem for cylinders under plane
300
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
Extended to include old 342 with addition
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
Comparison of Laplaces hypothesis with observationThe
415
Numerical estimates of the amount of tidal frictionSecular
420
427 Rewritten
427
Part rewritten 431 Rewritten
431
Extendedbifilar balance new Appendix B I Tidepredicter new II Equationsolver 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
458 Small omission
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
Greens problem reduced to the proper general solution
501
APPENDIX G On Tidal Friction by G H Darwin
503
Part rewritten
506
Slight alteration
507
nateSimultaneous electric influences in spaces separated
511
Old 520 rewritten including part of
519
Distribution of electricity on an ellipsoidal conductor new
520
777778
521
Attraction of Homoeoids new including old
523
to
525
and
527

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Page 9 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 9 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 478 - I infer that the general climate cannot be sensibly affected by conducted heat, at any time more than 10,000 years after the commencement of superficial solidification. No doubt, however, in particular places there might be an elevation of temperature by thermal springs, or by eruptions of melted lava, and everywhere vegetation would, for the first...
Page 460 - On the whole we may fairly conclude that, whilst there is some evidence of a tidal yielding of the earth's mass, that yielding is certainly small, and that the effective rigidity is at least as great as that of steel.
Page 479 - Do not the vast masses of basalt, the general appearances of mountain ranges, the violent distortions and fractures of strata, the great prevalence of metamorphic action (which must have taken place at depths of not many miles if so much), all agree in demonstrating that the rate of increase of temperature downwards must have been much more rapid, and in rendering it probable that volcanic energy, earthquake shocks, and every kind of so-called Plutonic action, have been, on the whole, more abundantly...
Page 216 - A body is called homogeneous when any two equal, similar parts of it, with corresponding lines parallel and turned towards the same parts, are undistinguishable from one another by any difference in quality.
Page 478 - Such is, on the whole, the most probable representation of the earth's present temperature, at depths of from 100 feet, where the annual variations cease to be sensible, to 100 miles ; below which the whole mass, or all, except a nucleus cool from the beginning, is (whether liquid or solid) probably at, or very nearly at, the proper melting temperature for the pressure at each depth.
Page 485 - It is thus shown that, although mechanical energy is indestructible, there is a universal tendency to its dissipation, which produces gradual augmentation and diffusion of heat, cessation of motion, and exhaustion of potential energy through the material universe.2 The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws.
Page 471 - ... the substances, combining together, may be again separated electrolytically by thermo-electric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfil the expectations of its ingenious inventor by going for ever.
Page 492 - HEAT. The sun being, for reasons referred to above, assumed to be an incandescent liquid now losing heat, the question naturally occurs, How did this heat originate ? It is certain that it cannot have existed in the sun through an infinity of past...

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