An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and…

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Byerly, William Elwood, 1849-1935 Byerly, William Elwood, 1849-1935
English
Ever wondered how we can break down complex things—like sound waves or heat patterns—into simple, repeating parts? That's the magic of Fourier series, and Byerly's book is like finding the original instruction manual. Written over a century ago, this isn't just math; it's a time capsule from when scientists were first figuring out how to translate the physical world into a language of equations. It's for the curious reader who wants to see where our modern understanding of waves, heat, and vibration really began, straight from the source. Think of it as a historical detective story, but the mystery is how to describe a perfect musical note with math.
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almost every music teacher has hitherto undertaken to teach Singing. This book will not, I am sure, add to the mystery. A careful perusal of its contents should clear away many misconceptions, and place the student on the right road to that end which he or she has in view. PREFACE TO THE FOURTH EDITION. That another large edition of this little Manual should be called for in so comparatively short a time is sufficiently encouraging testimony of the worth of the book and the favour it has found at the hands of students of singing and others--a result the more gratifying to the publishers since hitherto it has been issued with an anonymous title-page. Often has the authorship of the little volume been industriously defended and disputed--not by myself--both in this country and America; but, on the whole, the identity of its originator has been well maintained. For my part matters might have remained so, especially as I am not insensible to the fact that there is much "preaching" herein--as indeed there must be in such a work, and some of the advice is of such a nature that its giver runs the risk of being placed upon an exceeding high pinnacle of moral excellence, or of being accounted the personification of all the virtues--both of which distinctions might scarcely be merited. The appearance of my name upon the title-sheet is the result of no wish of mine, and I have consented to it only out of deference to the pressing request of the publishers. A chapter on the Physiological Surroundings of the Voice has been added to this edition. FREDERICK J. CROWEST. PREFACE TO THE SEVENTH EDITION. Once again my publishers have informed me of the necessity for reprinting this Manual, which has been so successful both here, in America, and in the Colonies. I have nothing to alter in the work, but I must express my thanks for the marked support that has been given to this straightforward advice. Did space permit, much might be said relative to that growing complaint, "Teachers' (or Board School) Laryngitis" as it is called. For some time past I have been authorized to make observations at the chief Throat Hospitals in connection with this constantly increasing mischief, arising from an injurious use of the voice in Teaching, and which only proper Voice Production will remedy. While I cannot give advice here, I shall be happy to answer any communications of sufferers from this complaint. FREDERICK J. CROWEST. 24 AMPTHILL SQUARE, LONDON, N.W. CONTENTS. _Page_ PRELIMINARY REMARKS 9 ON HABITS, DIET, &c. 13 Early Rising--Cleanliness--The Hair--The Teeth--Exercise--Dress-- Diet--Smoking--Late Hours--General Morality. PRONUNCIATION AND STUDY OF WORDS 21 Nervousness--Pronunciation--Vowel-Sounds--Consonants--English-- Emphasis--Position of Lips--Study of "Words"--General Education--Dramatic Study. VOICES AND THEIR VARIOUS QUALITIES 28 Voices and their Names--Compass--Soprano--Mezzo-Soprano-- Mezzo-Contralto--Contralto--Alto--Tenore-Leggiero--Tenore-Robusto-- Barytone and Basso-Cantante--Bass--Buffo--Qualities of Voices. INSTRUCTION, BOOKS AND MASTERS 47 Schools of Singing--Masters--Institutions--A First Opinion--Bad Lessons--Bad Teachers--Books of Exercises. PRACTICE 53 Individuality--Perseverance--Facial Expression--Self-Accompaniment-- Position of Body, Arms, Hands, Throat, Tongue, Larynx-- Head-Singing--Throatiness--Clearing the Throat--High Notes--The Scale--Forte, Mezzo-Voce, and Piano--Tone--Chest, Falsetto, and Head--Scale Practice--First Exercises (_with Examples_)--Duration of Practice--Singing in Tune--How to Begin--Variety--Chorus Singing--Humming--Studying Songs--Imitation--General Musical Study. ON STYLE AND EXPRESSION 71 Traditional Styles--Modern German _Lieder_--"The Cathedral School"--Oratorio (_with Examples_)--Opera--Ballads--Recitative (_with Examples_)--Slurring--Sentiment--Decision--Imitation--Public Singing--"Holding" an Audience--Mistakes in Public. ON TIME IN SINGING 87 The Metronome--Accent--Exercises: four beats to the bar; three beats to the bar; two beats to the bar. ON THE CHOICE OF MUSIC 103 Music to Suit the Voice--"Original Keys"--Execution--Fashion-- Forming a "Repertoire." PHYSIOLOGICAL SURROUNDINGS 109 The Larynx--The Thyroid--The Pharynx--The Voice; A Wind, Reed, or String Instrument. EXERCISES 115 Exercises 1, 2, for Uniting Notes--Exercise 3, for...

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So, what's this book actually about? Forget a traditional plot with characters. The 'story' here is a scientific quest. Over a hundred years ago, mathematicians and physicists had a powerful new tool: Joseph Fourier's idea that any messy, complicated wave could be built by adding together perfect, smooth sine waves. Byerly's Treatise was a key guidebook that showed engineers and scientists how to actually use this tool for real-world problems.

The Story

The book systematically walks you through the mathematics of Fourier series—those sums of sines and cosines. Then, it shows how to apply this math to solve physics problems in three specific shapes: spheres, cylinders, and the simpler rectangles mentioned in the full title. It's answering questions like, 'If you heat one edge of a metal plate, how does the temperature spread?' or 'What are the vibration modes of a drumhead?'

Why You Should Read It

There's a unique clarity here. Byerly writes with a pre-computer age focus on fundamental understanding and elegant analytical solutions. You get to see the logical structure of the subject laid bare, without the shortcuts of modern software. It feels like sitting with a brilliant, patient professor from another era. The value isn't in learning the latest techniques, but in appreciating the classic, rock-solid foundations of a field that powers everything from image compression to quantum mechanics.

Final Verdict

This is not a casual read. It's perfect for students of physics or engineering who want historical context, for mathematicians who appreciate classic texts, or for any scientifically-minded reader with some calculus under their belt who enjoys seeing how big ideas were first captured and explained. It's a book for someone who asks 'why?' as much as 'how?'



📢 Public Domain Content

Legal analysis indicates this work is in the public domain. Access is open to everyone around the world.

William Sanchez
1 year ago

Simply put, the atmosphere created is totally immersive. I would gladly recommend this title.

Donna Lopez
5 months ago

Good quality content.

4.5
4.5 out of 5 (2 User reviews )

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