THE SENSATIONS OF TONE BibliographicalNote. First EnglishEdition, June, 1875 ; Second Edition, revised and Aj^pendix added,August,1885; ThirdEdition,reprintedfromSecondEdition,June,1895. ON THE SENSATIONS OF TONE AS A PHYSIOLOGICAL BASIS FOR THE THEOEY OF MUSIC BY HERMANN L. F. HELMHOLTZ, M.D. LATE FOREIGN MEMBEE OF THE ROYAL SOCIETIES OF LONDON AND EDINBURGH, PROFESSOR OF PHYSIOLOGY IN THE UNIVERSITY OF HEIDELBERG, AND PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN Trmisluted, thoroughly Revised ami Corrected, rendered conformable to the Fourth (a7id last) GermanEdition of1877,withnumerousadditional Notes and a New additional Appendix bringing doicn information to 1885 and especially adapted to the use of3Iusical Students BY ALEXANDER ELLIS J. B.A., F.R.S., F.S.A., F.C.P.S., F.C.P. T^\^CE PRESIDENT OF THE PHILOLOGICAL SOCIETY, MEMBER OF THE MATHEMATICAL SOCIETY, FORMERLY SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE, AUTHOR OF 'EARLYENGLISHPRONUNCIATION' AND 'ALGEBRAIDENTIFIEDWITH GEOMETRY' THIRD £DITPON LONDON LONGMANS, GREEN, AND CO. AND NEW YORK 1895 All rights reserved PHYSICS DEPT. (JIL.^^Ua^<$>^ ' ABEEDEEN UNIVERSITY PRESS.