When the author was asked to write the following little treatise he acceded to the request with much pleasure, because he had long known that an elementary treatise on Electricity and Magnetism of a somewhat novel character was much needed. In England at the present time it may almost be said that there are two sciences of Electricity - one that is taught in ordinary text-books, and the other a sort of floating science known more or less perfectly to practical electricians, and expressed in a fragmentary manner in papers by Faraday, Thomson, Maxwell, Joule, Siemens, Matthiessen, Clark, Varley, Culley, and others. The science of the schools is so dissimilar from that of the practical electrician that it has been quite impossible to give students any suffiscient, or even approximately sufficient, text-book. It has been necessary to refer them to disjointed treatises in the Reports of the British Association, in the 'Cambridge Mathematical Journal,' the 'Phil. Trans.' and the 'Phil. Magazine.'