This work was originally meant to be a continuation of the series Electromagnetic Induction and its Propagation, published in The Electrician in 1885-6-7, but left unfinished. Owing, however, to the necessity of much introductory repetition, this plan was at once found to be impracticable, and was, by request, greatly modified. The result is some thing approaching a connected treatise on electrical theory, though without the strict formality usually associated with a treatise. As critics cannot always find time to read more than the preface, the following remarks may serve to direct their attention to some of the leading points in this volume. The first chapter will, I believe, be found easy to read, and may perhaps be useful to many men who are accustomed to show that they are practical by exhibiting their ignorance of the real meaning of scientific and mathematical methods of enquiry.