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amount angle anticlastic Applied Forces arbitrary assume beam boundary conditions bounding surface Central Axis centre circular coefficients compression conjugate consequently constant continuous functions coordinate surfaces coordinates cubical dilatation curvature curves cylinder deduce denote differential direction-cosines dxdydz elastic limits element ellipse ellipsoid elongation equal equations of motion equilibrium external forces finite flexion couple functions given Hence homogeneous Hooke's law infinitely small integral irrotational longitudinal magnitude modulus molecules natural normal sections notation orthogonal parallel to Ox perfectly elastic plane of yz plate portion potential energy pressure principal axes produce pure strain Quadric radius represent rotation satisfied shearing stress simple shear small strain solid solid harmonics solution sphere straight line stress components Substituting suppose Surface Tractions surfaces of revolution symmetry tangent temperature tension theorem throughout the body tion torsion transverse section uniform unstrained values vanish velocity vibrations viscosity wire Young's modulus zero
Page 162 - ... the power of any spring is in the same proportion with the tension thereof: that is, if one power stretch or bend it one space, two will bend it two, and three will bend it three, and so forward.
Page 457 - ... that there is no oscillation. When it is left to itself it turns slowly towards the right, gradually undoing part of the effect of the more recent twist, then stops, and twists still more slowly to the left, thus undoing part of the quasi-permanent effect of the earlier twist. Thus the behaviour of such a wire, strictly speaking, is an excessively complex one, depending, as it were, upon its whole previous history ; though, of course, the trace left by each stage of its treatment is less marked...
Page 14 - The four lines of argument which I have now indicated lead all to substantially the same estimate of the dimensions of molecular structure. Jointly they establish with what we cannot but regard as a very high degree of probability the conclusion that, in any ordinary liquid, transparent solid, or seemingly opaque solid, the mean distance between the centres of contiguous molecules is less than the hundred-millionth, and greater than the two thousand-millionth of a centimetre.
Page 165 - The capability which solids possess of being put into a state of isochronous vibration shews that the pressures called into action by small displacements depend on homogeneous functions of those displacements of one dimension. I shall suppose moreover, according to the general principle of the superposition of small quantities, that the pressures due to different displacements are superimposed, and consequently that the pressures are linear functions of the displacements.
Page 15 - To form some conception of the degree of coarse-grainedness indicated by this conclusion, imagine a rain drop, or a globe of glass as large as a pea, to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be coarser grained than a heap of small shot, but probably less coarse grained than a heap of cricketballs.
Page 162 - About two years since I printed this theory in an anagram at the end of my book of the descriptions of helioscopes, viz. ceiiinosssttuu, id est, ut tensio sic vis; that is, the power of any spring is in the same proportion with the tension thereof...
Page 15 - To form some conception of the degree of coarsegrainedness indicated by this conclusion, imagine a globe of water or glass, as large as a football,3 to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be more coarse-grained than a heap of small shot, but probably less coarse-grained than a heap of footballs.
Page 450 - ... 4. An elastic wire, indefinitely extended in one direction, is firmly held in a clamp at the other end. If a series of simple transverse waves travelling along the wire be reflected at the clamp ; show that the reflected waves will have the same amplitude as the incident waves, but that their phase is accelerated by one quarter of a wave length.
Page 34 - Let p be the perpendicular from the centre on the tangent plane at...