. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 408 Hence RICE cos {N"P"M") = 66 (6162)" AET. K (10) and similar results can be obtained for the other pairs of axes. A glance at Fig. 4 shows that the rectangle P'M'Q'N' has suffered a shear to the shape P"M"Q"N". (It is in general also subject to a rotation.) The shear is measured by the angle L"P"N" whose sine is by equation (10) equal to 66/(^162)^ If the strains are sufficiently small we can simplify this. Recalhng
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 408 Hence RICE cos {N"P"M") = 66 (6162)" AET. K (10) and similar results can be obtained for the other pairs of axes. A glance at Fig. 4 shows that the rectangle P'M'Q'N' has suffered a shear to the shape P"M"Q"N". (It is in general also subject to a rotation.) The shear is measured by the angle L"P"N" whose sine is by equation (10) equal to 66/(^162)^ If the strains are sufficiently small we can simplify this. Recalhng the original definitions of the era coefficients in (4), we see that ^11 — 1, 622 — 1, 633 — 1, 623, 632, 631, ei3. 612, 621. X' Fig. 4 are small compared to unity if the relative displacement of two points is a small fraction of their distance apart. Hence, by (9), ei, 62, ez each differ from unity by a small amount. Also in the definition of ee the third term is the product of two small quantities, the second term differs from 621 by a small fraction of 621, and the first term differs from e^ by a small fraction of 612. Thus, apart from a neghgible error, the sine of L"P"N" is equal to 612 + 621. The angle being also small in this case, its value, that is the shear of the lines originally parallel to OX' and OY', is practically 612 + 621," this in fact measures very closely the amount by which the angle between these lines has changed. 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
Size: 1483px × 1686px
Photo credit: © The Book Worm / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, booksubjectscience, booksubjectthermodynamics
