## A Treatise on the Mathematical Theory of Elasticity |

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Page 466 is essentially illegible. So the first sentence of the .pdf file: "This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project

to make the world’s books discoverable online" does not seem entirely true.

The word "carefully" seems to be an overstatement.

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Page 20 is partly blank.

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### Other editions - View all

### Common terms and phrases

applied approximation Article axes of x axis beam bending body forces boundary conditions central-line centre centroid coefficients components of strain const constants coordinates corresponding cos2 couple cross-section curvature curve cylinder deflexion denote determined dilatation direction displacement ellipsoid elliptic equal equations of equilibrium extension flexural formula free from traction given harmonic function Hooke's Law integral isotropic length linear elements load longitudinal Lord Rayleigh method middle surface normal sections obtained parallel Phil plane strain plate Poisson's ratio pressure principal axes prism problem quadratic function quantities radius right angles rigidity rotation satisfies the equation shearing strain shearing stress simple shear sin2 solid harmonics solution sphere statically equivalent strain-components strain-energy-function stress-components stress-couples stress-system surface tractions symmetry tangent tangential traction tension theorem theory torsion transformed twist unstrained unstressed values vanish velocity vibrations waves Young's modulus

### Popular passages

Page 2 - ... 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 15 - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...

Page 297 - It is not improbable that the surface waves here investigated play an important part in earthquakes, and in the collision of elastic solids. Diverging in two dimensions only, they must acquire at a great distance from the source a continually increasing preponderance.

Page 4 - The modulus of the elasticity of any substance is a column of the same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression, as the length of the substance is to the diminution of its length.

Page 188 - ... surface of the body, and the positive direction of the axis of z to- be that which goes into the interior of the body. The local effect of force applied at the origin being very great, we suppose the origin to be excluded by a hemispherical surface. The displacement expressed by (15) could be maintained in the body by tractions over the plane boundary, which are expressed by the equations ' AX Y = ^ Ay Z -0 ' *° 5' ^~U> and by tractions over the hemispherical boundary, which are expressed by...

Page 4 - This introduction of a definite physical concept, associated with the coefficient of elasticity which descends, as it were from a clear sky, on the reader of mathematical memoirs, marks an epoch in the history of the science.

Page 11 - One of the advantages of this method, of great importance, is, that we are necessarily led by the mere process of the calculation, and with little care on our part, to all the equations and conditions which are requisite and sufficient for the complete solution of any problem to which it may be applied.

Page 170 - ... the equilibrium state) acting through the displacements from the unstressed state to the state of equilibrium.

Page 42 - The strain quadric has the property that the reciprocal of the square of its central radius vector in any direction is proportional to the extension of a line in that direction. If the...