# Green, George (1793-1841) (DNB00)

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**GREEN**, GEORGE (1793–1841), mathematician, was born at Sneinton, near Nottingham, in 1793. His father was a miller with private means. While a very young child he showed great talent for figures. In 1828 his ‘Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism’ was published by subscription at Nottingham. In this essay he first introduced the term ‘potential’ to denote the result obtained by adding the masses of all the particles of a system, each divided by its distance from a given point; and the properties of this function are first considered and applied to the theories of magnetism and electricity. This was followed by two papers communicated by Sir Edward Ffrench Bromhead to the Cambridge Philosophical Society: (1) ‘On the Laws of the Equilibrium of Fluids analogous to the Electric Fluid’ (12 Nov. 1832); (2) ‘On the Determination of the Attractions of Ellipsoids of Variable Densities’ (6 May 1833). Both papers display great analytical power, but are rather curious than practically interesting.

In October 1833 he entered Caius College, Cambridge, as a pensioner. At the following Easter he was head of the freshman's mathematical list, and was elected a scholar. In 1835 he was again first in mathematics, and finally took his degree as fourth wrangler in January 1837, the second being Professor Sylvester. ‘Green and Sylvester were the first men of the year, but Green's want of familiarity with ordinary boys' mathematics prevented him from coming to the top in a time race. It was a surprise to every one to find Griffin and Brumell had beaten him.’ He seems not to have been connected with any of the eminent men who passed with him. No contribution of his appears in Gregory and Ellis's ‘Cambridge Mathematical Journal.’ The few papers he wrote were all read before the Cambridge Philosophical Society, where he found companionship with men of his own age. Bishop Harvey Goodwin writes: ‘I was twice examined by Green. He set the problem paper in two out of three of my college examinations; I am not sure about the third. He never assisted as far as I know in lectures. This possibly might be owing to his habits of life. His manner in the examination room was gentle and pleasant.’

Immediately upon the completion of his first term at Cambridge he read (16 Dec. 1833) before the Edinburgh Royal Society a paper ‘On the Vibrations of Pendulums on Fluid Media.’ The problem here considered is that of the motion of an elastic fluid agitated by the small vibrations of a solid ellipsoid moving parallel to itself. After taking his degree he again applied himself to original research, and on 15 May 1837 he read a paper ‘On the Motion of Waves in a variable Canal of small depth and width,’ and on 18 Feb. 1839 a supplement to the same. On 11 Dec. 1837 he read two of his most valuable memoirs (1) ‘On the Reflection and Refraction of Sound,’ (2) ‘On the Reflection and Refraction of Light at the common surface of two non-crystallised Media.’ The question discussed is that of the propagation of normal vibrations through a fluid. From the differential equations of motion is deduced an explanation of a phenomenon analogous to that known in optics as total internal reflection, when the angle of incidence exceeds the critical angle. By supposing that there are propagated, in the second medium, vibrations which rapidly diminish in intensity and become evanescent at sensible distances, the change of place which accompanies this phenomenon is clearly brought into view. Supplementary to these he read on 6 May 1839 another paper ‘On the Reflection and Refraction of Light at the common surface of two crystalline Media,’ doing for the theory of light what in the former had been done for that of sound. Green here for the first time enunciates the principle of the conservation of work, which he bases on the assumption of the impossibility of a perpetual motion. On 20 May 1839 he read his last paper, ‘On the Propagation of Light in Crystalline Media.’ This finishes the record of one who ‘as a mathematician stood head and shoulders above all his companions in and outside of the university.’

He was elected to a Perse fellowship at Caius College on 31 Oct. 1839, but through ill-health returned to his home at Sneinton, where he died, aged 47, and was buried on 4 June 1841.

[Green's Mathematical Papers, with brief Memoir by N. M. Ferrers, 1871; information from Bishop Harvey Goodwin and private sources.]