which are only of theoretical importance or of interest from a mathematical point of view, and of little value to the practical optician, such as, for instance, the theory of caustics, planes of unit magnification, etc., about which the more mathematical student can obtain full information from various contemporary works of well-known repute, such as those mentioned above, as well as Coddington's work, which, however, is now out of print and often difficult to procure.
It will be observed that I have not given the lines of reasoning by which the formulæ of the first approximation are arrived at; for I have assumed that the student will bring with him to the study of this work a knowledge of such elementary optical formulae. For those who wish to enter upon it without that knowledge I do not know a better book to recommend as a clearly written first guide to the formulæ of the first approximation than Todhunter's Optics (in Part II. of his Natural Philosophy for Beginners, 1877, which I believe is also out of print) or Lardner's Optics, and the series of articles on “Applied Optics” by Dr. Drysdale in the British Optical Journal.
I think it must be conceded that, while the method of investigating the foci of oblique and eccentric pencils of finite or large aperture explained in this work leads to novel and highly important formulæ of the second approximation, and some others which are novel in many respects, it also opens out possibilities of working out formulæ of the third and in some cases the fourth approximations, which in the hands of a skilful mathematician may lead to new and useful results of great importance; while the application of the differential method of Coddington and other workers to infinitely narrow pencils is exceedingly limited in its scope and results, as I shall show.
At first sight it seems a remarkable thing that a system of surfaces bound by the simplest of all known curves, namely, the circle, with their centres on a common axis, should give rise to problems which, if solved to a high degree of exactitude, are of such extraordinary complexity.
I gladly take the present opportunity of expressing my thanks to Sir W. de W. Abney and Professor Silvanus P. Thompson for much kind encouragement and valuable help; and also to Dr. Moritz von Eohr for allowing me to reproduce some of his diagrams on Plate XXIV.
In conclusion, I shall be only too glad if any technical errors or obscurities, which must, in spite of all care, exist in a work of this kind, are pointed out to me.
H. DENNIS TAYLOR
