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- The steady motion of a spherical vortex.
*Edinburgh Mathematical Society. Proceedings.*, 15 (1896-97), 76-80. - The fluted vibrations of a circular vortex ring with a hollow core.
*London Mathematical Society. Proceedings.*, 28 (1897), 97-119. - Note on the transformations of the equations of hydrodynamics.
*Edinburgh Mathematical Society. Proceedings.*, 16 (1897-98), 36-38. - Some muiltiform solutions of the partial differential equations of physical mathematics and their applications.
*London Mathematical Society. Proceedings.*, 30 (1899), 121-163. - The use of multiple space in applied mathematics.
*British Association for the Advancement of Science. Report of the Annual Meeting.*, (Bradford, 1900), 644-646. - Oblique incidence of a train of plane waves on a semi-infinite plane.
*Edinburgh Mathematical Society. Proceedings.*, 19 (1900-01), 71-77. - A problem in conduction of heat.
*Philosophical Magazine*, S.6, 4 (1902), 162-165. - The use of contour integration in the problem of diffraction by a wedge of any angle.
*Philosophical Magazine*, S.6, 5 (1903), 374-379. - The use of Green's functions in the mathematical theory of the conduction of heat.
*Edinburgh Mathematical Society. Proceedings.*, 21 (1902-03), 40-64. - The scattering of waves by a cone.
*Philosophical Magazine*, S.6, 20 (1910), 690-691. - The Green's function for a wedge of any angle, and other problems in the conduction of heat.
*London Mathematical Society. Proceedings.*, S.2, 8 (1910), 365-374. - A problem in the linear flow of heat, discussed from the point of view of the theory of integral equations.
*Edinburgh Mathematical Society. Proceedings.*, 30 (1911-12), 97-106. - Integral equations and the determination of Green's functions in the theory of potential.
*Edinburgh Mathematical Society. Proceedings.*, 31 (1912-13), 71-89. - Functions of positive type and their application to the determination of Green's functions.
*Messenger of Mathematics*, 42 (1912-13), 135-140. - The relation between pure and applied mathematics.
*Australasian Association for the Advancement of Science. Report of Meeting.*, 14 (Melbourne, 1913), 6-18. - The scattering of sound waves by a cone.
*Mathematische Annalen*, 75 (1914), 133-147. - The Green's function for the equation nabla²u + k²u = 0.
*London Mathematical Society. Proceedings.*, S.2, 13 (1914), 236-257. - The Green's function for the equation nabla²u + k²u = 0. Second paper.
*London Mathematical Society. Proceedings.*, S.2, 16 (1917), 84-93. - Problems in conduction of heat.
*Philosophical Magazine*, S.6, 38 (1919), 200. - Diffraction of waves by a wedge of any angle.
*London Mathematical Society. Proceedings.*, S.2, 18 (1920), 291-306. - Bromwich's method of solving problems in the conduction of heat.
*Philosophical Magazine*, S.6, 39 (1920), 603-611. - The cooling of a solid sphere with a concentric core of a different material.
*Cambridge Philosophical Society. Proceedings.*, 20 (1921), 399-410. - Operational methods in mathematical physics.
*Mathematical Gazette*, 14 (1928), 216-225. - Operational methods in mathematical physics.
*Mathematical Gazette*, 22 (1938), 264-280. - (With J.C. Jaeger) Some problems in the mathematical theory of the conduction of heat.
*Philosophical Magazine*, S.7, 26 (1938), 473-495. - (With J.C. Jaeger) On Green's functions in the theory of heat conduction.
*American Mathematical Society. Bulletin.*, 45 (1939), 407-413. - (With J.C. Jaeger) A problem in conduction of heat.
*Cambridge Philosophical Society. Proceedings.*, 35 (1939), 394-404. - (With J.C. Jaeger) The determination of Green's function for the equation of conduction of heat in cylindrical coordinates by the Laplace transformation.
*London Mathematical Society. Journal.*, 15 (1940), 273-281. - (With J.C. Jaeger) Some two-dimensional problems in conduction of heat with circular symmetry.
*London Mathematical Society. Proceedings.*, S.2, 46 (1940), 361-388. - A simple application of the Laplace transformation.
*Philosophical Magazine*, S.7, 30 (1940), 414-417. - (With J.C. Jaeger) The determination of Green's function for line sources for the equation of conduction of heat in cylindrical coordinates by the Laplace transformation.
*Philosophical Magazine*, S.7, 31 (1941), 204-208. *Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat*. London: Macmillan, 1906. xvii + 434pp. 2nd, revised edition in two vols.,*Introduction to the theory of Fourier's series and integrals*(London: Macmillan, 1921), xii + 323pp., and*Introduction to the mathematical theory of the conduction of heat in solids*(London: Macmillan, 1921), xii + 268pp.; Japanese translation by Takemae Genzo:*Fourier kyûsû**oyobi sekibun ron*(Tokyo: Uchida-Rôkaku-Ho, 1927), xii + 482 pp., and*Netsu dendô**ron*(Tokyo: Uchida-Rôkaku-Ho, 1928), xv + 405 pp.- (With J.C. Jaeger)
*Operational methods in applied mathematics*. Oxford: Clarendon Press, 1941. xvi + 264p.