In the months covered by this volume, Erasmus experienced sharply deteriorating health and thoughts of approaching death, although he remained active in the promotion of good causes and the defence of his good name. The seemingly imminent threat of religious civil war in Germany affected Erasmus in two ways. First, he made up his mind to leave Germany and return to his native Brabant. However, the arrival in 1533 of a formal invitation from Queen Mary, regent of the Netherlands, coincided with the onset of chronic ill health that would last until the end of his life. Repeated postponements eventually led to an abandonment of the journey altogether. Second, Erasmus did what he could to promote the cause of religious unity. In On Mending the Peace of the Church he urged rulers to enact moderate reforms that would satisfy all parties and avoid confessional division. When Martin Luther responded to this attempt at a "middle path" between "truth and error" in his Letter Concerning Erasmus of Rotterdam (1534), denouncing Erasmus as a skeptic and not a Christian, Erasmus responded indignantly with his Purgation against the Slanderous Letter of Luther. Erasmus' only other work published in this period turned out to be one of his most popular, On Preparing for Death.

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SOUND WAVES THEIR SHAPE AND SPEED 1 I 3 1 o OQ O . 1 o H PREFACE THE question of the influence of the material of which a wind musical instrument is made has not been settled after more than a century of widespread discussion. Is the tone quality of a flute, the tube of which is made of gold, superior to that of a similar flute made of silver or wood If there is a difference, what is the explanation It was this specific question that, in 1900, started the investigations which, having passed much beyond the original inquiry, have furnished the material for the reports here presented. The desire to investigate the physical nature of musical sounds, and the sound-producing characteristics of musical instruments, led to a study of all available methods for recording the forms of sound waves. No device was found which was sufficiently sensitive and free from disturbing in fluences for the proposed investigations, and a new instru ment, the Phonodeik, was developed. Part I of this work describes the phonodeik, and the methods of using it, to gether with illustrations of phonodeik records of sounds of various types, such as voices, musical instruments, bells, fog horns, and the explosive sounds from large guns in action. A chapter is included explaining the photography of sound waves by the electric-spark method, as applied to the study of projectiles in flight and to the acoustics of auditoriums. In 1918 and 1919 the writer organized, and carried out at Sandy Hook Proving Ground an extended series of experi ments on the pressure developed in the sound waves pro PREFACE duced by the discharge of large guns, and for the determina tion of the velocity of the explosive sounds and of the normalvelocity of sound in the free air. Preliminary re ports have been presented to various scientific societies, but the reduction of the large amount of observational material has only recently been completed. A final report covering the several phases of these investigations is now presented as Part II of this work. In the reduction of the observations, a least - squares method of solving the exponential equations involved was prepared by Dean T. M. Focke, Head of the Department of Mathematics, Case School of Applied Science. The first calculations, extending over a period of a year, were made by the writers Research Assistant, Mr. Ralph F, Hovey. The authors Research Associates, Professor John R. Mar tin, 1928, and Dr. Robert S. Shankland, 1932-33, have made the principal calculations relating to the final analysis and determination of the velocity of sound, and have assisted in the preparation of the manuscript. Professor R. S. Buring ton has given valuable aid. The author is especially in debted to Professor J. J. Nassau for advice and suggestions. The author is under obligation to the Chief of Ordnance of the War Department and to the Commanding Officers of Sandy Hook Proving Ground for many privileges and courtesies extended in connection with the experimental work and the preparation of these reports. The Chief of Ordnance has given approval of the free use of all the scientific data obtained at the Proving Ground, and has provided the photographs reproduced in Figures 37, 57, and 63. CASE SCHOOL OP APPLIED SCIENCE, DAYTON C. MILLER. CLEVELAND, OHIO, MABCH, 1937. vi CONTENTS PART I THE PHONODEIK SOUND WAVES AND THEIR SHAPES CHAPTER PAGE I. Sound and Tone Quality Sound Waves 3 TheAnalysis of Complex Sounds 6 II. The Phonodeik Recording Sound Waves 9 Mechanical Principles of the Phonodeik 13 Optical Principles of the Phonodeik 22 Auxiliary Records Time Signals and Axis .... 24 The Phonodeik Laboratory 26 The Projection Phonodeik 30 The Portable Phonodeik 33 Corrections for Resonance Effects 39 III. The Shapes of Sound Waves Interpreting Phonodeik Records 47 Photographs of Sound Waves from Voices and Instru ments 50 IV...