country with the higher practical requirements of optical science, would doubtless be able to evolve corollaries of the greatest importance bearing upon this question.
My chief object in working out the scheme of Applied Optics herein explained, has been to arrive at a complete system of algebraic formulæ of the second order which can be applied to any optical system likely to occur in practice with results which in general very closely approach to accuracy. I have therefore confined myself for the most part to the attainment of those practical conditions which have to be fulfilled by the best optical constructions conditions which include, and run closely parallel to, Von Seidel's five well-recognised conditions.
As far as I know, there is only one work in the English language professing to give a sketch of Von Seidel's methods, and that is Professor Silvanus Thompson's Contributions to Photographic Optics,[1] after Otto Lummer, while there are numerous accounts of his methods published in German works, and several treatises built upon them, such as Steinheil and Voit's Handbuch der Angewandten Optik,[2], 1891, and Von Rohr's Theorie und Geschichte des photographischen Objective,[3] the latter a most instructive and valuable work ; and last, but not least, Dr. Siegfried Czapski's new edition of Der Theorie des optischen Instrumenten,[4] 1904. This last work is a philosophical, broad, and general survey of the various problems which have to be faced, and if possible solved, by the optical designer who would rise superior to mere rule of thumb. But its perusal requires in many respects a higher level of mathematical training than is necessary for the understanding of this treatise.
In the German language there exists quite a mine of optical literature written by men who are practical opticians as well as mathematical experts, while we have scarcely anything of a corresponding nature in the English tongue.
The fact that such works as I have just mentioned have been published in Germany (as first editions, at any rate) for so many years, and yet no demand has ever arisen for English translations, is only too painful evidence of the apathy with which the Science of Optics has been regarded in this country.
There are, of course, various works on geometrical optics which have more or less recently emanated from our universities, such as Heath's Geometrical Optics,[5] Parkinson's Optics,[6] Pendlebury's Lenses and
