A History of the Theory of Elasticity and of the Strength of Materials: pts. 1-2. Saint-Venant to Lord KelvinUniversity Press, 1893 |
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a₁ aeolotropic angle angle of friction applied axes axis b₁ body body-forces Boussinesq central line Clebsch coefficients constants cos² cross-section crystal cylinder deals deduces differential direction discussion dx dy dy dz elastic solid elastic theory equations equilibrium ether expressions finite flexure force functions given Hence homogeneous homogeneous function infinitely integral investigation isotropic Kirchhoff Lamé load longitudinal magnetisation memoir mid-plane motion Neumann obtained parallel perpendicular plane plate pressure principal problem pulverulent mass radius referred remarks rigid Saint-Venant Saint-Venant's shews shifts Sir William Thomson solution spherical harmonics strain strain-energy stresses stretch supposed surface T₁ theory of elasticity Thomson and Tait torsion traction transverse Treatise velocity vibrations wire y₁ zero Εωκ
Popular passages
Page 452 - In the first place we must not listen to any suggestion that we must look upon the luminiferous ether as an ideal way of putting the thing. A real matter between us and the remotest stars I believe there is, and that light consists of real motions of that matter, motions just such as are described by Fresnel and Young, motions in the way of transverse vibrations.
Page 382 - The state of the case is shortly this : — The hypothesis of a perfectly rigid crust containing liquid violates physics by assuming preternaturally rigid matter and violates dynamical astronomy in the solar semi-annual and lunar fortnightly nutations ; but tidal theory has nothing to say against it On the other hand the tides decide against any crust flexible enough to perform the nutations correctly with a liquid interior, or as flexible as the crust must be unless of preternaturally rigid matter.
Page 428 - 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 366 - From thermodynamic theory* it is concluded that cold is produced whenever a solid is strained by opposing, and heat when it is strained by yielding to, any elastic force of its own, the strength of which would diminish if the temperature were raised ; but that, on the contrary, heat is produced when a solid is strained against, and cold when it is strained by yielding to, any elastic force of its own, the strength of which would increase if the temperature were raised.
Page 452 - If I knew what the electro-magnetic theory of light is, I might be able to think of it in relation to the fundamental principles of the wave theory of light. But it seems to me that it is rather a backward step from an absolutely definite mechanical notion that is put before us by Fresnel and his followers to take up the so-called Electro-magnetic theory of light in the way it has been taken up by several writers of late.
Page 420 - Vol. I, part II, §832, Lord Kelvin and Professor Tait remark that " The precise circumstances under which elastic bodies break have not hitherto been adequately investigated by experiment. It seems certain that rupture cannot take place without difference of stress in different directions. One essential element therefore is the difference between the greatest and least of the three principal stresses. How much the tendency to break is influenced by the amount of the intermediate principal stress...
Page 437 - ... be invoked minutely accurate experimental measurement to find how nearly the law of simple proportionality holds through finite ranges of contraction and elongation. The answer happily for mathematicians and engineers is that Hooke's law is fulfilled, as accurately as any experiments hitherto made can tell, for all metals and hard solids each through the whole range within its limits of elasticity...
Page 69 - Jf ist; nach einer mehrfach ausgesprochenen Ansicht hat es weder den einen noch den anderen Werth und ist verschieden bei verschiedenen Substanzen. Bei den meisten Körpern, bei denen man eine gleiche Elasticität in verschiedenen Richtungen annehmen kann, stellt sich der experimentellen Bestimmung dieses Verhältnisses der Umstand hindernd in den Weg, dafs bei ihnen, auch bei sehr kleinen Formänderungen, bleibende Dehnung und elastische Nachwirkung in erheblichem Grade sich zeigen. Es ist dieses...