. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. STRAINED ELASTIC SOLIDS 399 and the strain is "; Nevertheless, on account of the proviso mentioned above, we can regard the strain as being homogeneous throughout any assigned physically small element of volume. If the length actually contracts, the extension du/dx' is negative. As another simple example consider again the case in which all particles are displaced parallel to OX', but now taking the displacement to be a function of y', the distance o
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. STRAINED ELASTIC SOLIDS 399 and the strain is "; Nevertheless, on account of the proviso mentioned above, we can regard the strain as being homogeneous throughout any assigned physically small element of volume. If the length actually contracts, the extension du/dx' is negative. As another simple example consider again the case in which all particles are displaced parallel to OX', but now taking the displacement to be a function of y', the distance of the particle from a plane parallel to which the displacement takes place. Now choose Q', the neighbor of P', to be a point such that P'Q' is perpendicular to the direction of the displacements. M Q. 0 Fig. 1 Thus if x', y', z' are the coordinates of P' and x, y, z are the coordinates of its displaced position P, X = x' + u(y'), y = y', z = z'. Also if x', y' + t]', z' are the coordinates of the undisplaced position Q' of the "neighbor," its displaced coordinates are x' + u{y' + 7,0, y' + -n', z'- The displacement P'P is u{y') and the displacement Q'Q is u{y' + r]') or u{y') + (du/dy'W. Hence MQ in Fig. 1 is. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Donnan, F. G. (Frederick George), 1870-1956; Haas, Arthur Erich, 1884-1941. New Haven, Yale University Press; London, H. Milford, Oxford University Press
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