Absolute System of Units of System Absolute Volume I: Gauss and Weber’s and Gauss I: Volume Edited by Andre Koch Torres Assis Assis Torres Koch Andre by Edited Wilhelm Weber’s Main Works on Works Main Weber’s Wilhelm Electrodynamics Translated into English into Translated Electrodynamics Assis Wilhelm Weber’s Main Works on Electrodynamics Volume I Apeiron 978-1-987980-23-3 Weber’s Weber’s law applied to and electromagnetism gravitation for more https://www.ifi.unicamp.br/~assis 30than years: obtain obtain high precision absolute measures of electric charge, electric and resistance. force electromotive current, on working been has Assis Torres Koch Andre Editor: the Prof. About perform perform high precision piles the of unifilar galvanic composition and bifilar magnetometers, magnetic measurements including and the the electrochemical equivalent of work in Weber's was physics to water. and implement extend the A absolute large portion system of of units. In particular, he created methods to effectively This This volume also contains translations of other Weber papers and by Gauss, Wöhler up Association to created by 1842. Gauss They deal and with Weber, their the instruments Magnetic to milligram and milligram second). In he measures particular, obtained absolute of the Earth's by magnetic assisted he was in the paper, force As he acknowledged bar. and magnetized of the magnetic ways. moment in many Weber Wilhelm of a It It begins with Gauss's work on the absolute of measure the Earth's of system In the absolute this Gauss introduced work force. magnetic on based measured were magnitudes units in which electromagnetic the dimensions of length, mass and time (specifically millimeter, This This is the first of English”. into 4 Translated volumes on Electrodynamics of Works the book “Wilhelm Weber’s Main Wilhelm Weber’s Main Works on Electrodynamics Translated into English Volume I: Gauss and Weber’s Absolute System of Units edited by André Koch Torres Assis Apeiron Montreal Published by C. Roy Keys Inc. 4405, rue St-Dominique Montreal, Quebec H2W 2B2 Canada http://redshift.vif.com First Published 2021 Library and Archives Canada Cataloguing in Publication Title: Wilhelm Weber’s main works on electrodynamics translated into English / edited by André Koch Torres Assis. Names: Weber, Wilhelm Eduard, 1804-1891, author. | Assis, André Koch Torres, 1962- editor. Description: Includes bibliographical references and indexes. | Contents: Volume I: Gauss and Weber’s Absolute System of Units Identifiers: Canadiana (print) 20210279079 | Canadiana (ebook) 20210279095 | ISBN 9781987980233 (v. 1 ; softcover) | ISBN 9781987980240 (v. 1 ; PDF) Subjects: LCSH: Electrodynamics. Classification: LCC QC631 .W4313 2021 | DDC 537.6—dc23 Front cover of Volume I: The picture on the cover of Volume I shows Carl Friedrich Gauss (1777-1855) and his collaborator Wilhelm Weber (1804-1891). Source: Friedrich Zöllner, Wis- senschaftliche Abhandlungen, Volume 2, Part I (L. Staackmann, Leipzig, 1878), frontispiece. Wilhelm Weber’s Main Works on Electrodynamics Translated into English Volume I: Gauss and Weber’s Absolute System of Units Edited by Andre Koch Torres Assis 2 Contents 1 General Introduction 7 1.1 Weber’s Life and Works ............................. 8 1.2 Weber’s Elektrodynamische Maassbestimmungen ................ 8 1.3 Practical Aspects of the Project ........................ 9 1.4 Acknowledgments ................................ 10 2 Introduction to Volume I 13 3 Some Personal Notes from the Translators 15 3.1 Why Did I Decide to Work in this Project of the English Translation of We- ber’s Main Works on Electrodynamics ..................... 15 3.2 Why to Work for the Spreading of Weber’s Ideas ............... 20 3.3 How We Got Interested in Weber’s Electrodynamics ............. 21 3.4 Participating in the Weber Project ....................... 23 3.5 Buried Treasure in Weber’s Research ...................... 25 3.6 Some Personal Notes ............................... 27 3.7 Weber and the Manhattan Project: How I Learned about Weber’s Electrody- namics ...................................... 28 3.7.1 Moon’s Model of the Nucleus ...................... 29 4 Wilhelm Weber’s Works Translated into English, French and Portuguese 31 5 [Gauss, 1832, Abstract of the Paper:] Intensitas vis magneticae terrestris ad mensuram absolutam revocata 37 6 Editor’s Introduction to Gauss’ Work on the Absolute Measure of the Earth’s Magnetic Force 47 7 [Gauss, 1833] The Absolute Measure of the Earth’s Magnetic Force 49 7.1 .......................................... 52 7.2 .......................................... 53 7.3 .......................................... 54 7.4 .......................................... 55 7.5 .......................................... 55 7.6 .......................................... 56 7.7 .......................................... 57 7.8 .......................................... 58 7.9 .......................................... 60 3 7.10 .......................................... 61 7.11 .......................................... 62 7.12 .......................................... 65 7.13 .......................................... 65 7.14 .......................................... 65 7.15 .......................................... 66 7.16 .......................................... 67 7.17 .......................................... 69 7.18 .......................................... 70 7.19 .......................................... 71 7.20 .......................................... 72 7.21 .......................................... 72 7.22 .......................................... 74 7.23 .......................................... 75 7.24 .......................................... 77 7.25 .......................................... 77 7.26 .......................................... 78 7.27 .......................................... 80 7.28 .......................................... 80 8 [Gauss, 1837] Introduction to the Results of the Observations Made by the Magnetic Association in the Year 1836 81 9 [Weber, 1837a] Remarks on the Arrangement of Magnetical Observatories, and Description of the Instruments to be Placed in Them 85 9.1 Remarks on the Separate Parts of the Magnetic Observatory, and of the Mag- netic Instruments ................................. 90 9.2 Explanation of Plate III ............................. 94 9.3 Expense of Building and Furnishing a Magnetic Observatory ......... 99 10 [Weber, 1837b] Description of a Small Portable Apparatus for Measuring the Absolute Intensity of Terrestrial Magnetism 103 10.1 The Parts of the Small Apparatus ....................... 104 10.2 Observations to be Made with This Apparatus ................ 105 10.2.1 The Experiments of Deflection ..................... 105 10.2.2 Experiments of Vibration ........................ 106 10.3 Application of the Observations ......................... 107 10.4 Calculation, According to the Above Rules, of the Observations Made with the Small Measuring Apparatus ......................... 116 10.5 Examination of the Result ............................ 119 10.6 On the Advantages of the Dimensions Selected for the Small Measuring Ap- paratus ...................................... 120 11 [Gauss, 1838] On a New Instrument for the Direct Observation of the Changes in the Intensity of the Horizontal Portion of the Terrestrial Mag- netic Force 123 4 12 [Weber, 1838] Observations on the Arrangement and Use of the Bifilar Magnetometer 135 12.1 General Observations .............................. 136 12.2 On the Separate Parts of the Bifilar Magnetometer .............. 143 12.3 On the Use of the Bifilar Magnetometer .................... 146 13 [Weber, 1839] On a Transportable Magnetometer 151 13.1 General Remarks ................................. 152 13.2 Description of the Several Parts ......................... 155 13.3 Examples of Observations and Measurements ................. 157 13.3.1 Measurement of the Absolute Declination ............... 157 13.3.2 Observation of the Variations of Declination .............. 161 13.3.3 Absolute Measure of the Intensity ................... 162 14 [W¨ohler and Weber, 1841] Composition of Galvanic Piles 183 15 [Weber, 1841a] Measurement of Strong Galvanic Currents with Low Re- sistance According to Absolute Measure 187 16 [Weber, 1841b] On the Electrochemical Equivalent of Water 195 17 [Weber, 1842] Measurement of Strong Galvanic Currents According to Absolute Measure 201 18 Gauss and Weber’s Absolute System of Units and Its Difference to the Modern “Gaussian” System of Units 207 18.1 The Absolute System of Units of Gauss and Weber .............. 207 18.2 The CGS System of Units ............................ 209 18.3 The Confusion Created by the so-called “Gaussian” System of Units .... 210 Bibliography 213 5 6 Chapter 1 General Introduction A. K. T. Assis1 Wilhelm Eduard Weber (1804-1891) was one of the main scientists of the XIXth century. From 1831 onwards he worked in close collaboration with Carl Friedrich Gauss (1777-1855). This book contains the English translation of his main works on electrodynamics. The main goal of these translations is to make Weber’s works known to a larger audience, especially those who can not read German. It is addressed to the students and scientists who wish to develop Weber’s electrodynamics and applications of his force law to gravitation. It is also intended for the readers willing to know more about the absolute system of units introduced by Gauss and Weber. Another goal is to allow a better appreciation