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Societies and Academies

Nature volume 104, pages 365367 (04 December 1919) | Download Citation



LONDON. Royal Society, November 20.—Sir J. J. Thomson, president, in the chair.—W. J. Johnston; A linear associative algebra suitable for electro-magnetic relations and the theory of relativity. The algebra is based on four fundamental units i, j, k, o. The square of each unit is -1, while the other binary-products are polar (ij/=-ji, io=-oi, etc.). This algebra is associative. i, j, k are interpreted as mutually rectangular unit vectors in Euclidean space, while o is a unit vector in the fourth dimension perpendicular to the other three. Let ω be the pure imaginary scalar ct√ -1 and W=c-1,φ√-1, where φ is the scalar potential, then if (F, G, H) is the ordinary vector potential the vector

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