A Chronological History of the Modern Metric System (To 2008)
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Metric System Units of Length
Math 0300 METRIC SYSTEM UNITS OF LENGTH Þ To convert units of length in the metric system of measurement The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth. 1 centimeter=1 one-hundredth of a meter kilo- = 1000 1 kilometer (km) = 1000 meters (m) hecto- = 100 1 hectometer (hm) = 100 m deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m deci- = 0.1 1 decimeter (dm) = 0.1 m centi- = 0.01 1 centimeter (cm) = 0.01 m milli- = 0.001 1 millimeter (mm) = 0.001 m Conversion between units of length in the metric system involves moving the decimal point to the right or to the left. Listing the units in order from largest to smallest will indicate how many places to move the decimal point and in which direction. Example 1: To convert 4200 cm to meters, write the units in order from largest to smallest. km hm dam m dm cm mm Converting cm to m requires moving 4 2 . 0 0 2 positions to the left. Move the decimal point the same number of places and in the same direction (to the left). So 4200 cm = 42.00 m A metric measurement involving two units is customarily written in terms of one unit. Convert the smaller unit to the larger unit and then add. Example 2: To convert 8 km 32 m to kilometers First convert 32 m to kilometers. km hm dam m dm cm mm Converting m to km requires moving 0 . -
Varying Constants, Gravitation and Cosmology
Varying constants, Gravitation and Cosmology Jean-Philippe Uzan Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa). email: [email protected] http//www2.iap.fr/users/uzan/ September 29, 2010 Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to mat- ter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local posi- tion invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pul- sar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we arXiv:1009.5514v1 [astro-ph.CO] 28 Sep 2010 describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of differ- ent constants. -
Discovering the History of Measurement Through Words
CONTENT BASED TEACHING + PLURILINGUAL/CULTURAL AWARENESS CONBAT UNITS OF MEASUREMENT Gayane Hovhannisyan and Áine Furlong DISCOVERING THE HISTORY OF MEASUREMENT THROUGH WORDS WORKSHEET 4 Timing: 2 hours Material required: worksheet 3 Grouping: History of measurement From Wikipedia, the free encyclopedia 1.a. Find synonyms (similar words) or explanations for each word in bold print: Units of measurement were among the earliest tools invented by humans. Primitive societies needed measures for constructing dwellings of an appropriate size and shape, fashioning clothing, or exchanging food or raw materials. Earliest: Dwellings: Appropriate: Fashioning: Raw materials: 1.b. Something’s wrong! The spaces between the words have disappeared! Can you put a line between each word and re-write the sentences correctly? Theearliestsystemsofweightsandmeasuresseemtohavebeencreatedsometime betweenthe4thand3rdmillenniaBCbytheancientpeopleslivingbetweenEgyptand theIndusValley.Theeasternpeoplesachievedgreataccuracyinmeasuringlength,mass,andti me. 1.c. The weight units have been mixed up. Can you put them in the correct order? Check http://www.etymonline.com to discover the origin of the word ounce and why it is abbreviated as oz. The smallest division ever recorded on a scale of the Bronze Age was approximately 1.704mm. Weights were based on units of 100, 0.2, 500 , 20 , 2, 5, 10, 50 , 0.5 , 0.05, CONTENT BASED TEACHING + PLURILINGUAL/CULTURAL AWARENESS CONBAT UNITS OF MEASUREMENT Gayane Hovhannisyan and Áine Furlong 200, 1 and 0.1, with each unit weighing -
Weights and Measures Standards of the United States: a Brief History
1 .0 11 8 1.25 1.4 I 6_ DOCUMENT RESUME ED 142 418 SE 022 719 AUTHOE Judson, Lewis V. TITLE Weights and Measures Standards of the United States: A Brief History. Updated Edition. INSTITUTION National Bureau of Standards (DOC) ,Washington, D.C. REPORT NO NBS-SP-447 PUB DATE Mar 76 NOTE 42p.; Contains occasional small print; Photographs may not reproduce well AVAILABLE FROM Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Stock Number 003-0O3-01654-3, $1.00) EDRS PRICE MF-$0.83 HC-$2.06 Plus Postage. DESCRIPTORS Government Publications; History; *Mathematics Education; *Measurement; *Metric System; *Science History; *Standards ABSTRACT This document was published by the National Bureau of Standards to meet the current demand for information on the history of weights and measures in the United States. It includes an illustrated discussion of this history through 1962 followed by an addendum covering the period 1963-1975. Appendices provide a bibliography and photographic copies of eight documents important to the development of official standards of measurement. (SD) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every effort * * -to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality * * of the microfiche and hardcopy reproductions ERIC makes available * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original. *********************************************************************** U.S. DEPARTMENT OF HEALTH. -
Table of Contents
Division of Measurement Standards Department of Food and Agriculture FIELD REFERENCE MANUAL 2014 California Code of Regulation Title 4, Division 9 Chapter 1 National Uniformity, Exceptions and Additions Part 7: NIST Handbook 44 Appendices A through D CALIFORNIA DEPARTMENT OF FOOD AND AGRICULTURE DIVISION OF MEASUREMENT STANDARDS DISCLAIMER DISCLAIMER This document represents the Division of Measurement Standards’ field manual for enforcing regulations pertaining to weights and measures in California. This field manual is not to be considered as the official Code of Regulations, as published by Barclays Law Publishers. NOTE: Language in Handbook 44 that is not adopted is annotated “[NOT ADOPTED]” in this document. NOTE: Requirements are different than, or in addition to, the requirements of Handbook 44 are included in the appropriate section this document. They are shaded, bordered, and numbered in the 4002 series to differentiate them from the Handbook 44 requirements. To find the latest online version of the California Code of Regulations (CCR) Title 4, Division 9, visit the California Office of Administration Law at: http://ccr.oal.ca.gov/linkedslice/default.asp?SP=CCR-1000&Action=Welcome The CCR may also be accessed at http://oal.ca.gov/ by selecting the link Titled “California Code of Regulations” under the list of “Sponsored Links” in the left column on the OAL Home page. For information concerning the contents of this document, please contact the Division of Measurement Standards by e-mail at [email protected]. Links to NIST Handbook 44 (2014 Edition) - Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices as adopted by the 98th National Conference on Weights and Measures 2013 are available for viewing and downloading by simultaneously holding the “Ctrl” key and clicking the mouse on the desired format. -
Gravity and Coulomb's
Gravity operates by the inverse square law (source Hyperphysics) A main objective in this lesson is that you understand the basic notion of “inverse square” relationships. There are a small number (perhaps less than 25) general paradigms of nature that if you make them part of your basic view of nature they will help you greatly in your understanding of how nature operates. Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large-scale structure of galaxies, stars, etc. The gravitational force between two masses m1 and m2 is given by the relationship: This is often called the "universal law of gravitation" and G the universal gravitation constant. It is an example of an inverse square law force. The force is always attractive and acts along the line joining the centers of mass of the two masses. The forces on the two masses are equal in size but opposite in direction, obeying Newton's third law. You should notice that the universal gravitational constant is REALLY small so gravity is considered a very weak force. The gravity force has the same form as Coulomb's law for the forces between electric charges, i.e., it is an inverse square law force which depends upon the product of the two interacting sources. This led Einstein to start with the electromagnetic force and gravity as the first attempt to demonstrate the unification of the fundamental forces. It turns out that this was the wrong place to start, and that gravity will be the last of the forces to unify with the other three forces. -
A History of the National Bureau of Standards
APPENDIX A FERDINAND RUDOLPH HASSLER First Superintendent of the Coast Survey and of Weights and Measures When Professor Stratton arrived at the Office of Weights and Measures on B Street in Washington in the spring of 1898 to survey its equipment and operations, he found there in the person of Louis A. Fischer, the adjuster, a link with Ferdinand Rudolph Hassler, the first Superintendent of Weights and Measures in the Federal Government. It was in the atmosphere of the office over which Hassler had presided, Stratton said, with its sacred traditions concerning standards, its unsurpassed instrument shop, its world-known experts in the construction and comparison of standards, and especially in the most precise measurement of length and mass, that the boy Fischer, scarcely over 16, found himself when he entered the employ of Govern- ment in a minor capacity [about the year 18801. * * Scarcely 40 years had passed since the end of Hassler's services and the beginning of Fischer's. His first instructors were the direct disciples of Hassler and he knew and talked with those who had come in personal contact with the first superintendent.1 Fischer's reminiscences concerning the early historyof the Weights and Measures office, gathered from his association with the successors of Hassler, were never recorded, to Stratton's regret, and the only biography of Hassler, by Florian Cajori, professor of mathematics at the University of California, centers on his career in the Coast Survey gathered from his association with the successors of Hassler, were never recorded, to in the history of science in the Federal Government, is the principal source of the present sketch.2 1 Stratton, "Address Memorializing Louis Albert Fischer, 1864.—1921," 15th Annual Con. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Colorado Metric Conversion Manual
COLORADO OT . DEPARTMENT OF TRANSPORTATION METRIC CONVERSION MANUAL January 1994 This manual or any part thereof must not be reproduced in any form without the following disclaimer. The information presented in this publication haS been prepared in accordance with recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be used or relied upon for any specific application without competent professional examination and verification of its accuracy, suitability, and applicability by a competent licensed engineer or other licensed professional. Publication of the material contained herein is not intended as a representation or warranty on the part of the Colorado Department of Transportation (CDOT) , that this information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. Caution must be exercised when relying upon the specifications and codes developed by other bodies and incorporated herein, since such material may be modified or amended from time to time subsequent to the printing of this edition. COOT bears no responsibility for such material other than to incorporate it at the time of the initial publication of this edition, subject to the general comments set forth in the preceding paragraph. Table of Contents Preface ................................................... v Introduction . vii Chapter 1: Metric Units, Terms, Symbols, and Conversion Factors . ... 1-1 Basic Metric . 1-1 Length, Area, Volume and Temperature . 1-7 Civil and Structural Engineering . 1-10 Metric Project Definition ....................... .. 1-12 Chapter 2: Right-Of-Way ................................... -
Weights and Measures Standards of the United States—A Brief History (1963), by Lewis V
WEIGHTS and MEASURES STANDARDS OF THE UMIT a brief history U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS NBS Special Publication 447 WEIGHTS and MEASURES STANDARDS OF THE TP ii 2ri\ ii iEa <2 ^r/V C II llinCAM NBS Special Publication 447 Originally Issued October 1963 Updated March 1976 For sale by the Superintendent of Documents, U.S. Government Printing Office Wash., D.C. 20402. Price $1; (Add 25 percent additional for other than U.S. mailing). Stock No. 003-003-01654-3 Library of Congress Catalog Card Number: 76-600055 Foreword "Weights and Measures," said John Quincy Adams in 1821, "may be ranked among the necessaries of life to every individual of human society." That sentiment, so appropriate to the agrarian past, is even more appropriate to the technology and commerce of today. The order that we enjoy, the confidence we place in weighing and measuring, is in large part due to the measure- ment standards that have been established. This publication, a reprinting and updating of an earlier publication, provides detailed information on the origin of our standards for mass and length. Ernest Ambler Acting Director iii Preface to 1976 Edition Two publications of the National Bureau of Standards, now out of print, that deal with weights and measures have had widespread use and are still in demand. The publications are NBS Circular 593, The Federal Basis for Weights and Measures (1958), by Ralph W. Smith, and NBS Miscellaneous Publication 247, Weights and Measures Standards of the United States—a Brief History (1963), by Lewis V. -
Imperial Units
Imperial units From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the post-1824 measures used in the British Empire and countries in the British sphere of influence. For the units used in England before 1824, see English units. For the system of weight, see Avoirdupois. For United States customary units, see Customary units . Imperial units or the imperial system is a system of units, first defined in the British Weights and Measures Act of 1824, later refined (until 1959) and reduced. The system came into official use across the British Empire. By the late 20th century most nations of the former empire had officially adopted the metric system as their main system of measurement. The former Weights and Measures office in Seven Sisters, London. Contents [hide] • 1 Relation to other systems • 2 Units ○ 2.1 Length ○ 2.2 Area ○ 2.3 Volume 2.3.1 British apothecaries ' volume measures ○ 2.4 Mass • 3 Current use of imperial units ○ 3.1 United Kingdom ○ 3.2 Canada ○ 3.3 Australia ○ 3.4 Republic of Ireland ○ 3.5 Other countries • 4 See also • 5 References • 6 External links [edit] Relation to other systems The imperial system is one of many systems of English or foot-pound-second units, so named because of the base units of length, mass and time. Although most of the units are defined in more than one system, some subsidiary units were used to a much greater extent, or for different purposes, in one area rather than the other. The distinctions between these systems are often not drawn precisely. -
Napier's Ideal Construction of the Logarithms
Napier’s ideal construction of the logarithms Denis Roegel To cite this version: Denis Roegel. Napier’s ideal construction of the logarithms. [Research Report] 2010. inria-00543934 HAL Id: inria-00543934 https://hal.inria.fr/inria-00543934 Submitted on 6 Dec 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Napier’s ideal construction of the logarithms∗ Denis Roegel 6 December 2010 1 Introduction Today John Napier (1550–1617) is most renowned as the inventor of loga- rithms.1 He had conceived the general principles of logarithms in 1594 or be- fore and he spent the next twenty years in developing their theory [108, p. 63], [33, pp. 103–104]. His description of logarithms, Mirifici Logarithmorum Ca- nonis Descriptio, was published in Latin in Edinburgh in 1614 [131, 161] and was considered “one of the very greatest scientific discoveries that the world has seen” [83]. Several mathematicians had anticipated properties of the correspondence between an arithmetic and a geometric progression, but only Napier and Jost Bürgi (1552–1632) constructed tables for the purpose of simplifying the calculations. Bürgi’s work was however only published in incomplete form in 1620, six years after Napier published the Descriptio [26].2 Napier’s work was quickly translated in English by the mathematician and cartographer Edward Wright3 (1561–1615) [145, 179] and published posthu- mously in 1616 [132, 162].