Last updated 10th July 2024: Online ordering is currently unavailable due to technical issues. We apologise for any delays responding to customers while we resolve this. For further updates please visit our website https://www.cambridge.org/news-and-insights/technical-incident
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 20 January 2009
This paper is a sequel to an earlier one containing a tensor formulation and generalisation of well-known solutions of Laplace's equation and of the classical wave-equation. The partial differential equation considered was
where 
was that of an n-dimensional flat space. It is shown below that similar solutions exist for any n-dimensional space of constant positive or negative curvature K.
page 24 note 1 Proc. Edinburgh Math. Soc. (2), 2 (1930–1931), 181.Google Scholar
page 26 note 1 Ruse, , Proc. London Math. Soc., 32 (1931), 90.Google Scholar
page 26 note 2 See the paper quoted above and also Ruse, , Quarterly J. of Math. (Oxford), 3 (1932), 15.Google Scholar
page 26 note 3 Synge, , Proc. London Math. Soc, 32 (1931), 241.CrossRefGoogle Scholar
page 26 note 4 Ruse, , Quarterly J. of Math. (Oxford), 1 (1930), 146.Google Scholar
page 26 note 5 Etherington, , Phil. Mag., 15 (1933), 761.CrossRefGoogle Scholar
page 26 note 6 Darboux, , Lecons sur la theorie gene'rale des surfaces, Vol. II, Book V, Ch. V (p. 450, § 536 in 2nd edition, Paris 1915).Google Scholar
page 28 note 1 Ruse, , Quarterly J. of Math. (Oxford), 1 (1930), 148;Google ScholarcfDuschek-Mayer, , Lehrbuchder Differentialgeometrie, Vol. II (Leipzig, 1930), p. 143.Google Scholar
page 33 note 1 A treatise on differential equations (5th ed., 1921), p. 534, § 276.Google Scholar
page 35 note 1 Darboux, , op. cit., Vol. III, Book VII, Ch. XI (p. 394, § 782 in 1st edition, 1894).Google Scholar
page 35 note 2 CfDarboux, , op. cit., Vol. III, p. 396, §783, formula (6).Google Scholar
page 35 note 3 Euler, , Opera omnia, 1st series, Vol. 13 (Leipzig 1913), p. 212et seq.;Google Scholar also Oeuvres de Laplace, Vol. IX (Paris 1893), p. 41,Google Scholar § IX ; and Darboux, , op. cit., Vol. II, Book IV, Ch. III (p. 54 in 2nd ed.).Google Scholar
page 36 note 1 Darboux, , op. cit., Vol. II, p. 65, equation (26).Google Scholar
page 36 note 2 The £ of (4.3) are of course different from the £ of (3.15).
page 38 note 1 We are assuming h > 0 for the sake of the argument. If is the timeof dispatch and the time of reception.
page 39 note 1 Ruse, , “On the definition of spatial distance in general relativity,” Proc. Roy. Soc., Edinburgh, 52 (1931–2), 183–194, and in particular p. 193. For other workon the definition of spatial distanceCrossRefGoogle Scholar see Whittaker, E. T., Proc. Roy. Soc. (A) 133 (1931),93;CrossRefGoogle ScholarKermack, M'Crea, and Whittaker, , Proc. Roy. Soc, Edinburgh, 53 (1932-3), 35;Google ScholarRuse, , Proc. Roy. Soc, Edinburgh, 53 (1932-3), 79;CrossRefGoogle ScholarEtherington, , loc cit. supra;Google ScholarWalker, , Quarterly J. of Math. (Oxford), 4 (1933), 71 ; Temple, Proc Roy. Soc. (A) 168 (1938), 136.Google Scholar
You have
Access
