GREEN, George.

On the Laws of the Reflexion and Refraction of Light at the common Surface of two non-crystallized Media...Read December 11, 1837.

Pages 1-24. Large 4to. [Cambridge]: Transactions of the Cambridge Philosophical Society, Vol. VII, Part I, [1837]. [bound with]:—. “VI. Supplement to a Memoir on the Reflexion and Refraction of Light...Read May 6, 1839.” Pages [113]-20. Large 4to. [Cambridge]: Transactions of the Cambridge Philosophical Society, Vol. VII, Part I, [1839]. [bound with]:—. “VII. On the Propagation of Light in Crystallized Media...Read May 20, 1839.” Pages [121]-140. Large 4to. [Cambridge]: Transactions of the Cambridge Philosophical Society, Vol. VII, Part II, [1839]. Extracts from the Transactions of the Cambridge Philosophical Society. Green (1793-1841), an extraordinary self-taught mathematician, matriculated at Caius College in 1833, at the age of 40. Due to the importance of the above publications, he was elected as Perse Fellow of Caius in 1839. Green is primarily known for his work in electricity and magnetism and for the formula connecting surface and volume integrals (Green’s Theorem) still used in the solution of partial differential equations. Green’s general mathematical theory of potential development led, through Kelvin and Maxwell, to the mathematical theories of electricity of the twentieth century. He coined the term “potential.” “Of interest to the strength of materials is Green’s paper ‘On the Laws of Reflexion and Refraction of Light at the Common Surface of Two Non-crystallized Media’ in which he takes up problems of elasticity. This paper started a controversy which gave rise to two schools on the theory of elasticity, the differences between these schools promoting interest in the experimental determination of elastic contents... “‘Supplement to a Memoir...’ is on the reflexion and refraction of light, following and amplifying the works of Cauchy and Airy while following Lagrange in the method of integration. In it Green applies a formula representing a system of molecules acting on each other, as well as applying the general method of Lagrange’s Méchanique analitique to a theory of light... “In the paper ‘On the Propagation of Light...’ Green uses the vis-viva theorem (conservation of mechanical energy) to simplify Cauchy’s treatment of the same subject... “Though these papers more immediately relate to the wave theory of light, Todhunter indicates the importance of their ‘demonstration of the body shift-equations for free vibrations of an elastic solid.’ Green’s method of obtaining body shift-equations has been followed by the majority of upholders of multi-constancy ever since, including Thomson and Kirchhoff. Pearson objects to this method on many points; in particular he denies the linearity of the stress-strain relation and calls the bi-constant argument on which the method is based ‘fallacious’.”–Roberts & Trent, Bibliotheca Mechanica, pp. 145-46. Fine copies. Ex Bibliotheca Mechanica. ❧ D.S.B., XV, pp. 199-201.

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