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• W2012178800 abstract "IN a recent paper (Proc. Lond. Math. Soc., April 11, 1889), Prof. Karl Pearson has discussed at some length the possible forms of the additional terms which may be introduced into the general equations of elasticity by a consideration of the mutual action of the molecules and the ether, and has examined what physical phenomena may admit of explanation in this way. In particular, certain terms which thus appear admissible are made to yield a theory of the phenomenon known as “elastische Nachwirkung,” or “after-strain.” The attempt to explain such a comparatively slow process by the intervention of the ether certainly invites scrutiny, and in fact a very slight examination serves, I think, to show that the theory in question rests on a mistake. The author, after writing down the equations which (on his view) represent the steady application of stress to a portion of matter, proceeds to integrate them in the usual way by assuming a time-factor emt, and arrives at a quadratic in m2 whose roots are μ/μ' and (3λ + 2μ)/(3λ' + 2μ'), where λ, μ are the ordinary elastic constants of Lame, and λ', μ' are the coefficients of the additional terms referred to. He continues:—“Now m cannot be positive, so long at least as we are dealing with elastic-strain. For λ' and μ' are small as compared with λ and μ, the effects we are considering being only of the second order. Hence m2 is large, and if m were positive the strain would rapidly grow immensely large, which is contrary to experience. Thus, we must give m the negative values – √(μ/μ') and – √{(3λ + 2μ)/(3λ' + 2μ')}.” The positive values of m are certainly inconvenient, but they are on the same footing with the negative ones; all are solutions of the author's equations, and all are required for the purpose of satisfying arbitrary initial conditions. The proper inference is surely that the substance is unstable, so long as the constants μ/μ' and 3λ' + 2μ' are (as the author has tacitly assumed them to be) positive. If, to avoid this disaster, we change the signs of these constants, we get circular instead of exponential functions, and all analogy to elastic after-strain of course disappears. In its place we have vibrations (not molecular, but “molar”) whose period is intrinsic to the substance and independent of the dimensions of the portion considered. To what physical reality these may correspond I do not undertake to say." @default.
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• W2012178800 date "1890-03-01" @default.
• W2012178800 modified "2023-09-27" @default.
• W2012178800 title "On a Certain Theory of Elastic After-Strain" @default.
• W2012178800 doi "https://doi.org/10.1038/041463b0" @default.
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