Unpublished manuscript, 'On certain functions connected with tesseral harmonics, with applications' by A H [Arthur Herbert] Leahy The transformation of a zonal harmonic referred to a pole on a sphere to another pole on the same sphere, and its expression in a series containing the 2n + 1 harmonics of the same order referred to this new pole, is an operation frequently employed in physical research. The purpose of this paper is the investigation of certain functions of the angular distance between the poles which occur when a general tesseral harmonic is transformed from one pole and plane to another pole and another plane of reference. Includes eight geometrical diagrams and a detailed table of contents. Subject: Mathematics Received 24 March 1894. Read 24 May 1894. Communicated by [William Mitchinson] Hicks. Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 56 of the Proceedings of the Royal Society as 'On certain functions connected with tesseral harmonics, with applications'. 1894