Transcriber’s Notes: Underscores _ before and after a word or phrase indicate _italics_ in the original text. Equal signs = before and after a word or phrase indicate =bold= in the original text. Small capitals have been converted to SOLID capitals. Illustrations have been moved so they do not break up paragraphs. Deprecated spellings have been preserved. Typographical and punctuation errors have been silently corrected. The list of works by John Tyndall has been moved from the front to the end of the file. POPULAR LECTURES ON SCIENTIFIC SUBJECTS BY HERMANN VON HELMHOLTZ TRANSLATED BY E. ATKINSON, PH.D., F.C.S. FORMERLY PROFESSOR OF EXPERIMENTAL SCIENCE, STAFF COLLEGE SECOND SERIES _WITH AN AUTOBIOGRAPHY OF THE AUTHOR_ [Illustration] LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA 1908 _All rights reserved_ _BIBLIOGRAPHICAL NOTE._ _Issued in Silver Library, March 1893; Reprinted July 1895, May 1898, June 1900, December 1903, August 1908._ PREFACE. The favour with which the first series of Professor Helmholtz’s Lectures has been received would justify, if a justification were needed, the publication of the present volume. I have to express my acknowledgments to Professor G. Croome Robertson, the editor, and to Messrs. Macmillan, the publishers of ‘Mind,’ for permission to use a translation of the paper on the ‘Axioms of Modern Geometry’ which appeared in that journal. The article on ‘Academic Freedom in German Universities’ contains some statements respecting the Universities of Oxford and Cambridge to which exception has been taken. These statements were a fair representation of the impression produced on the mind of a foreigner by a state of things which no longer exists in those Universities, at least to the same extent. The reform in the University system, which may be said to date from the year 1854, has brought about so many alterations both in the form and in the spirit of the regulations, that older members of the University have been known to speak of the place as so changed that they could scarcely recognise it. Hence, in respect of this article, I have availed myself of the liberty granted by Professor Helmholtz, and have altogether omitted some passages, and have slightly modified others, which would convey an erroneous impression of the present state of things. I have also on these points consulted members of the University on whose judgment I think I can rely.