Encyclopedia of Scientific Principles, Laws, and Theories Volume 2: L–Z Robert E. Krebs Illustrations by Rae Dejur Library of Congress Cataloging-in-Publication Data Krebs, Robert E., 1922– Encyclopedia of scientific principles, laws, and theories / Robert E. Krebs ; illustrations by Rae Dejur. p. cm. Includes bibliographical references and index. ISBN: 978-0-313-34005-5 (set : alk. paper) ISBN: 978-0-313-34006-2 (vol. 1 : alk. paper) ISBN: 978-0-313-34007-9 (vol. 2 : alk. paper) 1. Science—Encyclopedias. 2. Science—History—Encyclopedias. 3. Physical laws— Encyclopedias. I. Title. Q121.K74 2008 503—dc22 2008002345 British Library Cataloguing in Publication Data is available. Copyright C 2008 by Robert E. Krebs All rights reserved. No portion of this book may be reproduced, by any process or technique, without the express written consent of the publisher. Library of Congress Catalog Card Number: 2008002345 ISBN: 978-0-313-34005-5 (set) 978-0-313-34006-2 (vol. 1) 978-0-313-34007-9 (vol. 2) First published in 2008 Greenwood Press, 88 Post Road West, Westport, CT 06881 An imprint of Greenwood Publishing Group, Inc. www.greenwood.com Printed in the United States of America The paper used in this book complies with the Permanent Paper Standard issued by the National Information Standards Organization (Z39.48–1984). 10987654321 L LAGRANGE’S MATHEMATICAL THEOREMS: Mathematics: Comte Joseph-Louis Lagrange (1736–1813), France. Lagrange’s theory of algebraic equations: Cubic and quartic equations can be solved algebraically without using geometry. Lagrange was able to solve cubic and quartic (fourth power) equations without the aid of geometry, but not fifth-degree (quintic) equations. Fifth-degree equations were studied for the next few decades before they were proved insoluble by algebraic means. Lagrange’s work led to the theory of permutations and the concept that algebraic solu- tions for equations were related to group permutations (group theory). Lagrange’s theory of equations provided the information that Niels Abel and others used to de- velop group theory (see also Abel; Euler; Fermat). Lagrange’s mechanical theory of solids and fluids: Problems related to mechanics can be solved by nongeometric means. Before Lagrange, Newtonian mechanics were used to explain the way things worked, as well as to solve problems dealing with moving bodies and forces. By applying mathe- matical analyses to classical mechanics, Joseph-Louis Lagrange developed an analytical method for solving mechanical problems that used equations having a different form from Newton’s law (F ¼ ma), by which acceleration is proportional to the applied force to accelerate the mass. Lagrange’s equations, which can be shown to be equivalent to Newton’s law and can be derived from Hamilton’s formulation, are, like Hamilton’s formulation, very convenient for studying celestial mechanics. In fact, Lagrange himself applied his equations to the mechanical problems of the moon’s librations (oscillating rotational movement), as well as those dealing with celestial mechanics. For one exam- ple, he solved the three-body problem when he demonstrated by mechanical analysis that asteroids tend to oscillate around a central point—now referred to as the Lagran- gian point (see also Einstein; Newton). 326 Lagrange’s Mathematical Theorems Ancient people used the natural motions and cycles of the sun and moon, the seasons, and other natural observable phenomena to determine some of their measurements of time. Historically, many countries had their own system of weights and measurements that were arbitrarily based on someone’s idea of how much or how long something should be. Movement of people from region to region made communication and trade difficult when different systems of measurements as well as languages meshed. The introduction of the metric system is an example of the need for some standardization of units of weights and measurement. For instance, the metric system grew out of the Age of Reason in Europe and was spread widely across nations as the advances of Napoleon’s army introduced it. For example, this was the first time that kilometers rather than miles were used throughout Europe. It was natural for the United Sates to adopt the English systems of weights and measures since we were an English colony. Even so many enlightened leaders, such as Thomas Jefferson, Benjamin Franklin, John Quincy Adams, and others recognized the utility of the metric system (e.g., it is easy to convert weight to volume because 1 gram of water equals 1 milliliter or cubic centimeter of water). Jefferson developed his own decimal system that was somewhat like the metric system except he used his own terminology and units. For example, he based his system on a decimal system that did not equate different units. He declared that the foot was just 10 inches (somewhat shorter than the English foot); each inch was divided into ten lines, and each line into 10 points. Ten feet equaled a decade, 100 feet equaled a rod, 1,000 feet a furlong, and 10,000 feet equaled a mile (the present English mile is 5,280 feet long). But his decimal system of weights and volume was not based on some natural phenomena, as was the metric meter that was based on a fraction of the distance of the meridian that extended from the North Pole to the equator through a particular point in Paris, which was divided by 1/10,000,000. This distance was named meter after the Greek word for ‘‘measure.’’ Today the meter is defined as the length a path of light travels in one 299,792,458th on a second and is based on the speed of an electromagnetic light wave in a vacuum. The history of the acceptance of the metric system in the United States is not pretty. 1. 1800—was one the first times that the metric system was used in the United States when the U.S. Coast Guard used the French standard of meters and kilograms in its Geodetic Survey. 2. 1866—Congress authorized the use of the metric system and supplied each state with weights and measures standards. 3. 1875—The Bureau of Weights and Measures was established and signed the Treaty of the Meter to use this standard. 4. 1893—The United States adopted the metric standards for length, mass, foot, pound, quart, as well as other metric units. 5. 1960—The Treaty of the Meter of 1875 was modernized and called the International System of Units (SI) as the metric system is known today. 6. 1965—Great Britain begins conversion to the metric system so they could become a member of the European Common Market. 7. 1968—U.S. Congress passes the Metric Study Act of 1968 to determine the feasibility of adopting the SI system. 8. 1975—U.S. Congress passes the ‘‘Metric Conversion Act’’ to plan the voluntary conversion to the SI system. 9. 1981—The Metric Board reports to Congress that it lacks authority to require a national conversion. 10. 1982—The Metric Board is abolished due to doubts about the commitments of the United States to convert. 11. 1988—U.S. Congress has introduced ‘‘carrot’’ incentives to U.S. industries to convert, and by the end of 1992 all federal agencies were required to use the SI system for procurements of grants, and so forth. Lamarck’s Theories of Evolution 327 (Continued) Today, there are both metric and English systems placed on commercial products (e.g., ounces and grams), but there is much opposition to changing transportation (road) signs to kilometers from miles. It seems the American public, despite years of learning the metric system in schools, still does not recognize or accept the utility of the SI metric system, and stubbornly adheres to the use of the archaic English system of weights and measures. Lagrange’s concept for the metric system: A base ten system will standardize all mea- surements and further communications among nations. Historically, all nations devised and used their own system for measuring the size, weight, temperature, distance, and so forth of objects. As the countries of Europe developed and commerce among them became more common, it was obvious that the jumble of different measuring systems was not only annoying but limited prosperity. At about the time of the French Revolution, a commission was established to solve this problem. Lagrange, Lavoisier, and others were determined to find a natural, constant unit on which to base the system. They selected the distance from the North Pole to the equator as a line running through Paris. This distance was divided into equal lengths of 1/10,000,000, which they called a meter (‘‘measure’’ in Greek). A platinum metal bar of this length was preserved in France as the standard unit of length. Today, a meter is defined as the length of the path light travels in one 299,792,458th of a sec- ond and is based on the speed of electromagnetic waves (light) in a vacuum. Units for other measurements besides length were devised, using the base of ten to multiply or divide the selected unit. For instance, a unit of mass is defined as the mass accelerated one meter per second by a one-kilogram force. After several years of resistance, other countries recognized the utility of the metric system, which has since been adopted by all countries, except the United States, Liberia, and Myanmar (formerly Burma). Even so, international trade and commerce have forced the United States to use the metric system along with the archaic English system of measures. Despite several attempts to convert the United States to the metric system, the general public has refused to accept it. LAMARCK’S THEORIES OF EVOLUTION: Biology: Jean Baptiste Pierre Antoine de Monet, Chevalier de Lamarck (1744–1829), France.