ADAPTED TO THE USE OF THE HIGHER BY OSMUND AIRY, B. A. TRINITY COLLEGE, CAMBRIDGE. ONE OF THE MATHEMATICAL MASTERS OF WELLINGTON College. PUBLIC London and Cambridge: 1870. [All Rights reserved.] 1 PREFACE. THIS is, I imagine, the first time that any attempt has been made to adapt the subject of geometrical optics to the reading of the higher classes in our good schools. That this should be so is the more a matter for remark, since the subject would appear to be peculiarly fitted for such an adaptation. The great simplicity of its primary laws, in the first place, and the very small amount of analysis which, generally speaking, they involve, render the commencement not so unattractive as that of many subjects which are usually taken as the beginning of the second course of mathematical reading: whilst the new ideas and trains of thought which are introduced at every stage appear to me to be at once interesting and valuable. The conception of a virtual image, to take an early instance, is probably an entirely new one to the reader's mind. So also is the idea of a caustic curve, and the subject abounds with similar new considerations. But the chief advantage that this subject possesses appears to me to be the middle position which it holds between the purely theoretical and the purely experimental. It contains sufficient of physical interest to give reality, and the easy and certain experiments by which it can be illustrated are convincing evidences of the correctness of the results, whilst the analysis which is requisite to obtain these results is sufficient to afford the reader, who up till now has been studying Algebra and Euclid, a proof that the said Algebra and Euclid have really some distinct use in explaining the phænomena of common life. When the idea of writing such a book was first suggested to me by my old master, Professor Drew of King's College, I was afraid that there was hardly room, under the present system, for the subject in the course of a boy's school-work: I therefore, after making some progress in it, wrote to obtain the opinion of the head mathematical masters of two or three of our best schools; and I cannot sufficiently acknowledge the courtesy with which these gentlemen gave me the information I required. While acknowledging that the doubt which I had expressed existed in their own minds, they urged me strongly to continue my work, as they fully agreed in recognizing the great use of introducing a subject into school-work which should combine new ideas with practice in former knowledge. |