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according acting action amount angle applied attraction axes axis becomes body called centre circular components condition consider constant corresponding couple course curvature curve denote density determined direction displacement distance distribution disturbing earth edge elastic element ellipsoid energy equal equations equilibrium example expression external figure fixed flexure fluid follows force function given gives gravity harmonic Hence homogeneous inertia infinitely infinitely small integral internal length mass matter mean middle motion normal section parallel particle perpendicular plane plate portion position potential present pressure principal problem produce proved radius reference remark respectively resultant rigid rotation round sides simple solid solution space sphere spherical surface spiral square strain stress substance suppose surface theorem theory tion traction twist uniform unit weight whole wire zero
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.