physical science...2 physical science: a historical approach in early england, units of measurement...

Physical Science: A Historical Approach

Edited by John Truedson

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PHYSICAL SCIENCEA HISTORICAL APPROACH

…

By John Truedson

Bemidji State University

Copyright © 2011 University Readers, Inc. All rights reserved. No part of this publication may be reprinted, reproduced, transmitted, or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfi lming, and recording, or in any information retrieval system without the written permission of University Readers, Inc.

First published in the United States of America in 2011 by Cognella, a division of University Readers, Inc.

Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identifi cation and explanation without intent to infringe.

15 14 13 12 11 1 2 3 4 5

Printed in the United States of America.

ISBN: 978-1-935551-66-9

CONTENTS

Chapter 1: Measurement 1

Chapter 2: Motion: Speed, Velocity, and Acceleration 23

Chapter 3: Force and Newton’s Law 45

Chapter 4: Work and Energy 63

Chapter 5: Introduction to Celestial Spheres and Astronomy Basics 97

Chapter 6: The Birth of Modern Astronomy 125

Chapter 7: Brahe, Kepler, Galileo, and Modern Astronomy 145

Chapter 8: The Power of the Sun, Classifi cations of Stars, 179and the H-R Diagram

Chapter 9: The Distances to Stars and Galaxies; Telescopes 201

Chapter 10: Minerals and Rocks 235

Chapter 11: Geology and the Age of Earth 259

Chapter 12: Volcanoes, Earthquakes, Tsunamis and the Movement of the Earth 279

Chapter 13: Plate Boundaries, Mountain Building, and Weathering 301

Chapter 14: Geology, Intelligent Design, and the Nature of Science 321

Chapter 15: Atmospheric Measurements 335

Chapter 16: Air Motion, Global Wind Patterns, and Clouds 355

Chapter 17: Weather Fronts, Thunderstorms, Tornadoes, and Hurricanes 381

Chapter 18: Climate Change and Global Warming 415

Chapter 19: Sound and Light Waves 449

Chapter 20: Electricity and Magnetism 487

Chapter 21: Atomic and Nuclear Physics 519

Chapter 22: An Introduction to Chemistry 561


Chapter 1: Measurement

A BRIEF HISTORY OF MEASUREMENT

The history of science begins with measurement, since it is necessary to conduct measurements of some sort if one is to do meaningful quantitative science. One of the earliest types of mea-surement concerned that of length. Th e fi rst documented example is the Royal Egyptian cubit,

which was based on the length of the arm from the elbow to the outstretched fi nger tips. By 2500 B.C., this unit had been standardized in a royal master cubit made of black marble (about 52 cm).

Many units of length or area originated from agriculture or were based on human characteristics. Some examples include the inch, which was the width of a man’s thumb or the length of three bar-leycorn ears, and the foot, which was the length of a man’s foot. Th e furlong, 220 yards long, comes from the word “furrowlong” and was the distance a yoke of oxen could pull steadily through heavy soil

before they had to rest for the day. Th e English unit for land, acre, was the amount of soil that could be ploughed by one ox team in a day—actually in a morning because the oxen would need to be rested in the afternoon. Th is land area was 220 yards by 22 yards. Th ere are references to the acre at least as early as the year 732. Th e word “acre” also meant “fi eld” in medieval England.

Figure 1-1. Royal Egyptian Cubit Papyrus (NCSL)

2 Physical Science: A Historical Approach

In early England, units of measurement were not properly standardized until the 13th Century with variations continuing long after that. For example, there were three diff erent gallons (ale, wine, and corn) up until 1824 when the gallon was standardized. Although it might be convenient to use corn kernels or a person’s thumb to measure objects, the variation from kernel to kernel or among people’s thumbs resulted in signifi cant inaccuracies. Other early units of length included the English foot and the French pied de roi, both based on the assumption that all kings have feet of roughly the same length. Today, people sometimes still pace off a fl oor’s dimensions with their feet since a man’s size 11 shoe is very close to one foot in length.

European systems of measurement were originally based on Roman mea-sures, which in turn were based on those of Greece. Th e Greeks used as their basic measure of length the breadth of a fi nger (about two cm), with 16 fi ngers in a foot, and 24 fi ngers in a Greek cubit. Th ese units of length, as were the Greek units of weight and volume, were derived originally from Egyptian and Babylonian units. Trade was the main reason why units of measurement were spread widely. Around 400 B.C., Athens was a center of trade for the known world. Most trade disputes would arise over the weights and measures of the goods being traded, and a standard set of measures were kept in order that such disputes might be settled fairly. Th e size of a container to measure nuts, dates, beans, and other such items, had been laid down by law and if a container was found which did not conform to the standard, its contents were confi scated and the container destroyed.

Th e Romans eventually adapted the Greek system. Th ey had as a basis the foot, which was divided into 12 inches. Th e inch is derived from the Latin word, unciae, meaning a twelfth part. Th e Romans did not use the cubit but rather the Roman mile perhaps because most of the longer measurements were derived from marching over the vast Roman Empire, which extended at its peak from Britain to Greece and required a much larger unit of measure than the cubit. A distance of 5000 feet represented a Roman mile, which is close to the modern mile used today. Th is Roman system was adopted, with local variations, throughout Europe as the Roman Empire spread.

A country like England, though, was invaded at diff erent times by many peoples bringing their own measures. Th e Angles, Saxons, and Jutes brought measurement units such as the perch and rod along with the furlong that we discussed earlier. In England and France, measurement systems developed in rather diff erent ways. Th e standardization of measures has always presented problems as we shall soon discuss. In the Early 13th Century England, a royal ordinance of Weights and Measures gave a long list of defi nitions of measurement to be used. Th is was the fi rst successful attempt to standardize units and it lasted for nearly 600 years. However, although some units had been standardized, no attempt had been made to rationalize them and Great Britain retained a bewildering array of measures which were defi ned by the ordinance as rather strange subdivisions of each other. Scientists had long seen the benefi ts of rationalizing measures. Th e great English architect Christopher Wren in the 1700s had proposed that the yard be defi ned as the length of a pendulum in the Tower of London that would have a swing time of one second.

However, people continued to use units of length based primarily on local standards. An example would be the mile. Today, a mile in New York is the same distance as a mile in Minnesota. Th is standard unit of length makes life easier for map makers and travelers. However, early map makers in Europe used a mile commonly referred to, nowadays, as the “Old English mile.” Various maps have been studied in the past to get an estimate of what this unit might have been. Th e examples below have been found in various publications:

Figure 1-2. A thumb is about 1 inch across


• William of Worcester’s Itineraries (1477–1480) had a mile was equal to about 1.5 modern miles.• On a Mercator map of England in 1564, a mile was equal to 1.18 modern miles.• A Saxton map of Hampshire, England, made in 1565, had a mile equal to 1.22 modern miles.

Th is was a very chaotic system of measurement and made it impossible for cartographers to develop accurate maps. Finally, in 1593, Queen Elizabeth I signed into law a proclamation (“An Acte againste newe Buyldinges;” Act 35 Elizabeth I cap 6 1592/93), that prohibited building work within three miles of the gates of the City of London and standardized the length of the mile as follows:

• One mile = eight furlongs• One furlong = 40 rods• One rod = 16½ feet

Th is local ordinance had wider infl uence, and the “statute” mile spread slowly throughout England and wider. It only became universal in the country with the all encompassing act for weights and measures.

In France, on the other hand, there was no standardization, and as late as 1788, Arthur Young wrote in “Travels during the years 1787, 1788, 1789” (published in 1793): “In France the infi nite perplexity of the measures exceeds all comprehension. Th ey diff er not only in every province, but in every district and almost every town.” In fact, it has been estimated that France had about 800 diff erent names for mea-sures at this time, and taking into account their diff erent values in diff erent towns, around 250,000 diff erently sized units. It was not until France developed the metric system of units that the use of the chaotic system of units eventually came to an end. We will discuss later the standardization of units in modern times with the metric system.

Builders and architects have always relied on precise measurements. Th e Pyramids in Egypt were built to a fi ne precision even by today’s standards. Th e base of the Great Pyramid of Khufu like the other pyramids in the area is almost a perfect square. Th e sides of the bases are 230.25 meters for the north side, 230.44 m for the south side, 230.38 m for the east side, and 230.35 m for the west side. Each side varies no more than 0.10 m (10 cm) in length from the other sides. In addition, the sides of the Great Pyramid line up exactly parallel with the directions of the compass: North, South, East, and West. It is one of the great mysteries as to how the Egyptians were able to build these enormous structures with such precision. We will discuss the alignment of the Great Pyramids in more detail in Chapter 8.

Although they are not nearly as celebrated as the Egyptian pyramids and have not received com-parable scholarly attention, the extraordinary Mayan pyramids and temples, such as the Temple of Kukulcan (El Castillo) constructed by the Mayan in what is now southern Mexico and Central America are signifi cant from archaeological, historical, architectural, and engineering perspectives. Like the ancient Egyptians, the Maya, whose civilization dates from at least 3000 B.C. and fl ourished from the Fourth to the Ninth Century A.D. produced extraordinary structures, had a superb command

Figure 1-3. Th e Great Sphinx and the Pyramid of Khufe in Egypt


of mathematics, developed highly accurate calendars as well as an elaborate system of hieroglyphic writing, and established sophisticated and complex social and political orders.

In order to build the structures that still stand today, the Maya had to develop an accurate system of measurement as well as the ability to survey. However, little has been discovered on how they calcu-lated measurements or what their units of measurement were. Scientists have collected measurements of principal dimensions from ten buildings at three ancient Mayan sites, including Chichén Itzá. It has been speculated that a standard unit of measurement, the zapal, was about 1.5 m in length and divided into 16 smaller units, kab, and that each kab was divided into nine even smaller units, the xóot. Th us, 144 xóot make up a zapal, the xóot being equivalent to about 1 cm. Researchers believe that zapal is the Mayan term for the distance between extended arms. Even today, Guatemalan Indians from Mayan areas use a measure called a haah, which is the distance between outstretched hands. Th is is approximately 1.5 m for a person of moderate stature.

ANCIENT MEASUREMENTS OF TIME

Water was used for one of the earliest time-keeping devices. A device known as a clepsydra was used as a clock. One could defi ne the time by the amount of water required to empty a fi lled container with a hole in the bottom, or about four minutes for a three liter container. It is from this use of water for time keeping that we think of time “fl owing.”

Th e sundial is one of the oldest forms of time-keeping. Th e scaphe (Greek for “boat”) dial is a bowl-shaped cup within which lines are marked indicating hours of the day. At the time of summer solstice, the shadow is shortest and falls exactly on the bottom line. In the following months, the shadow grows again until it reaches the top line at the time of winter solstice as shown in the fi gure at the right.

Th e days themselves were divided into hours. Th e length of an hour was not fi xed; instead, the time between sunrise and sunset was divided into 12 intervals of equal length. For example, in Minnesota, the length of the day on the winter solstice (December 21) would have been about nine modern hours while the length of a day on the summer solstice (June 21) is about 15 hours. Th erefore, the length of a hour varied by almost a factor of two and would change on a daily basis. Th is situation created a nightmare for clock and watch makers. A need for a standard set of units was therefore necessary if time keeping was ever to achieve any high degree of accuracy.

Th e fi rst attempt to measure time with any real accuracy was the development of mechanical clocks. Th e fi rst mechanical

Figure 1-4. Th e temple of Kukulcan (El Castillo) in Mexico (Kyle Sim)

Figure 1-5. Sundial with Aramean Inscription, Sandstone, 1st. Cent. B.C. (Museum of the Ancient Orient)


clocks developed in the 14th Century were based on weights wrapped around a cylinder with a notched wheel. Th e ac-curacy of these clocks was not very good and could keep time to only about 15 minutes per day.

Th e next step in clock accuracy was the pendulum clock fi rst proposed by Galileo in the 1630s. Galileo realized that the pendulum could be used potentially to build a very accurate clock. Th e fi gure on the right shows a simple pendulum consisting of a ball attached to the end of a string that swings back and forth with consistent regular-ity. Unfortunately, Galileo did not advance beyond using a simple pendulum to conduct his experiments on motion and acceleration.

It took a Dutch scientist to develop a truly accurate pen-dulum clock. Christian Huygens built a pendulum clock in 1656 that was accurate to 10 seconds a day. Th is was truly a monumental advance in time-keeping.

A pendulum clock can be extremely accurate. However, the Earth’s surface is approximately 70% water. Sailors and navigators needed accurate time while sailing on the high seas for two reasons. First, they wanted to keep accurate time much like a person on land. Second, an accurate and reliable clock could be used to locate the ship’s position on the Earth’s surface. However, the only clocks available at the time were pendulum clocks and a pendulum clock will simply not work on a rocking ship. It was therefore necessary to develop an entirely new type of clock.

Th e next development in clock-making was the invention of the balanced wheel clock by Robert Hooke in 1675. Hooke was an English scientist and mathematician famous for “Hookes’ Law” that governs the properties of springs. Th e balanced wheel clock is based on a spiral spring. Modern me-chanical watches are based on the same principle. Th e Englishman, John Harrison, after many years and several false leads, developed a balanced spring watch that would keep very accurate time at sea. In 1764, one of Harrison’s watches, H4, while on a fi ve-month voyage to Jamaica gained only 54 seconds, or about one-third of a second per day. We will hear more about John Harrison’s fantastic clock in Chapter 6.

Th e next major leap in watch accuracy was the development of the quartz crystal mechanism in the 1960s. Th ese watches are based on the vibration of a quartz crystal embedded in the watch. Th ese watches produced using quartz crystal technology were accurate to one second in several years. Quartz clock operation is based on the piezoelectric property of quartz crystals. If you apply an electric fi eld to the crystal, it changes its shape, and if you squeeze or bend a crystal, it generates an electric fi eld. When put in a suitable electronic circuit, this interaction between mechanical stress and electric fi eld causes the crystal to vibrate and generate an electric signal of relatively constant frequency that can be used to operate an electronic clock display.

Since then extremely accurate clocks based on the vibrations of individual atoms such as cesium have been developed by the National Institute of Standards and Technology (NIST) in Boulder, Colorado. As of January, 2005, NIST’s latest primary cesium standard was capable of keeping time accurate to about 1 second in 60 million years. Called NIST-F1, it is the eighth of a series of cesium clocks built

Figure 1-6. A pendulum with path marked in red


by NIST and NIST’s fi rst to operate on the “fountain” principle, which we will discuss more about in the next section.

ANCIENT UNITS OF MASS AND WEIGHT

Units of weight are some of the oldest types of measurement dating back thousands of years. Th e oldest standard, the bega, can be traced to 7000–8000 B.C. in ancient Egypt. Weights seem to have been standardized in Egypt long before length. Th e bega was the smallest unit in a decimal system. Th e fi gure at the right shows a weight standard from the New Kingdom of ancient Egypt dating to about 1500 B.C. Other standards were developed over 5000 years ago in ancient Mesopotamia including the shekel. Th e shekel was used all over the world including Ireland. Ancient Mesopotamia was located in what is now Iraq and Turkey.

Th e ancient Mesopotamians did not have a money economy, so they developed a standard-ized system of weights to carry out their many commercial transactions. Th e original medium of exchange was barley. Th e smallest unit of weight was called a barleycorn, the approximate weight of one grain of barley. Other standard units of weight were the shekel, the mina, and the talent. Eventually, silver replaced barley as the medium of exchange, not as coinage but rather as small pieces that had the same weight as a shekel of barley.

Th e basic traditional unit of weight in the English system, the pound, originated as a Roman unit and was used throughout the Roman Empire. Th e Roman pound was divided into 12 ounces, but many European merchants preferred to use a larger pound of 16 ounces, perhaps because a 16-ounce pound is conveniently divided into halves, quarters, and eighths. During the Middle Ages, there were many diff erent pound standards in use. Th e use of these weight units naturally followed trade routes, since merchants trading along a certain route had to be familiar with the units used at both ends of the trip.

In traditional English law, the various pound weights are related by stating all of them as multiples of grain, which was originally the weight of a single barleycorn. Th us barleycorns are at the origin of both weight and distance units in the English system.

A grain is the same in the Troy (used for precious metals) and Avoirdupois systems. Th e troy system is believed to be named for the French market town of Troyes, where English merchants traded at least as early as the time of Charlemagne in the early Ninth Century). A troy pound is 5760 grains, or 12 ounces. An avoirdupois pound is larger at 7000 grains, or 16 ounces. Th e troy system was the basis of the old English monetary system, in which there were 12 pence (pennies) to the shilling and 20 shillings to the pound. Th e troy system quickly became highly specialized and is used only for precious metals and for pharmaceuticals, while the avoirdupois pound is the pound unit most commonly used today.

If the diff erence between the troy pound and avoirdupois pound is not confusing enough, the oldest standard of weight in England was the Saxon pound. It eventually became known as the Tower

Figure 1-7. Egyptian weight dated to about 1500 B.C. (Louvre Museum)


pound because it was kept in the Tower of London. Th e Saxon pound weighed 5400 grains. Henry VIII replaced it with the troy pound in 1527, ordering that a troy ounce be 480 grains. He made the new troy pound the offi cial standard for minting coins. Unfortunately, there is quite a bit of confusion between the troy pound and avoirdupois pound. Th e troy pound was abolished in 1878 to avoid any commercial confusion with the avoirdupois pound. Th e troy system is nearly obsolete today, but the prices of precious metals are still quoted by the troy ounce. Th e diagram above shows the confusing relationship between the classic Engish units of weight in use prior to the adoption of the metric system of units.

STANDARDIZATION OF UNITS

As you can see from the previous sections, the history of measurement has led to many diff erent unit systems being developed over the years. Although it has been long understood that there was a need for some sort of standardized units of measurement, the standards were somewhat arbitrary and dependent on the characteristics of specifi c objects as discussed previously.

Th e fi rst eff ort to develop a truly universal standard was the development of the metric system. In 1670, Gabriel Mouton, a French clergyman, proposed the creation of a new unit of length, the meter, equal to one 10-millionth of the distance from one of the earth’s poles to the equator. However, it was not until a century later that his proposal was fi nally implement during the French Revolution. A proposal for adopting the metric system was submitted to National Assembly in 1790 by the Bishop of Antun with the declared intent of being “For all people, for all time.” of offi cially approved in June 1799 Th is distance was calculated from a meridian drawn between the cities of Dunkirk, France, and Barcelona, Spain. Th e production of this standard required a very careful survey which took several years.

Figure 1-8. Diagram showing relation of classic English units of weight B.C. (Christoph Päper)


Two other units of measurement were derived from the meter. Th e liter is the volume enclosed by a cube with all edges 1/10th of a meter long. Th e kilogram is the mass of one liter of water. Th ese units, along with the second as the basic unit of time, became the basis of the early version of the metric system.

Th e seven basic unit standards of the International System of Units (S.I.) system are listed below:

Base quantity Name Symbol

Length meter mMass kilogram kgTime second sElectric current ampere ATemperature kelvin KAmount of substance mole molLuminous intensity candela cd

1. Length (meter): Originally defi ned as 1/10,000,000 the distance from the Equator to the North Pole ( one-quarter of the distance around the Earth). Originally, a standard meter was represented as the distance between two scratches inscribed on a metal bar kept under strictly controlled conditions in Paris, France; this was used to calibrate duplicate standard bars maintained in other countries. But this system, based on a manufactured artifact, was inherently inaccurate. Each time a bar was subjected to a small change in temperature or other disturbance, its length changed enough to introduce errors into extremely precise measurements. It was eventually realized that a single object, no matter how fi nely measured and marked, would not provide the needed accuracy in today’s highly technical world. Th e meter is now defi ned in terms of the distance light travels in 1/299,792,458 of a second. Th is corresponds to an accuracy of one centimeter in 3000 kilometers.

2. Time (second): Th e second was originally defi ned as 1/86,400 of a solar day. Th e solar day is defi ned as the time from the Sun’s peak altitude at noon local time to the next Sun’s peak latitude 24 hours later. Th eoretically, this is a potentially very accurate unit of time since the Earth’s rotational rate relative to the stars is extremely stable. However, the length of a solar day depends also on the Earth’s orbit around the Sun and varies over the course of a year. In fact, the time of the Sun’s peak altitude varies from noon local time as much as 15 minutes over the course of a year.

For early clock makers, the only method to accurately calibrate their clocks was to use the sidereal period of the Earth with respect to the stars. Th e sidereal day is the time for a star on the south meridian to return to the same spot the next day. Th is period is 23 hours, 56 minutes, 4 seconds long in modern units. Th e sidereal period is extremely accurate and consistent from day to day. However, the sidereal day is still an inconvenient unit for a unit of time Figure 1-9. Th e Atomic clock maintained by NIST (NIST)


due to its length and had the signifi cant limitation of a unit of time based on the Earth’s rotation relative to the stars. It was therefore decided to use the small rather than the big for the defi nition of the second.

Th e second is now defi ned as the duration for 9,192,631,770 cycles of a cesium atom vibration. Th e National Institute of Standards and Technology (NIST) built its latest atomic fountain clock, the NIST F-1, at its laboratory in Boulder, Colorado. Th is atomic clock is accurate to one second in 20,000,000 years. Th is clock is used to calibrate the timing of the Global Positioning Satellite (GPS) system, the most accurate navigation system ever created. Th e offi cial world-wide atomic clock time standard is Universal Coordinated Time (UTC). National laboratories around the world have atomic clocks synchronized to UTC. (Atomic clocks will be described at the end of this chapter.)

However, while atomic clocks enable scientists to determine time with extreme accuracy, our lives are connected to the Earth’s daily rotation. Th erefore, leap seconds are introduced at pre-defi ned intervals to compensate for variations in the Earth’s rotation. Leap seconds allows UTC time to closely match Universal Time (UT), which is synchronized to the Earth’s angular rotation rather than a uniform passage of time. UTC atomic clock time is also sometimes referred to as Zulu time.

3. Mass (kilogram): Th is standard is the kilogram based on objects kept in France. However, scientists of measurement are still frustrated by their failure to create a new kilogram measure that is independent of all artifacts, including the weight of a liter of water. Scientists hope that a new defi nition of the kilogram based on the mass of a single atom will someday be possible, but they are still short of the goal.

4. Th e remaining S.I. units are: Ampere (electric current), Kelvin (temperature), Mole (amount of substance), and Candela (luminous intensity of light). We will discuss these other units later in the text.

Th e National Bureau of Standards (NBS) was established by Congress on March 3, 1901, to take custody of the standards of physical measurement in the United States and to solve “problems which arise in connection with standards.” Although minor variations occurred in the name of the institution, it was known for most of the century as NBS until Congress mandated a major name change in 1988 to the National Institute of Standards and Technology, or NIST.

Th e nation’s need for standardization was strongly demonstrated in 1904, when a massive fi re swept across Baltimore, destroying more than 1500 buildings. Fire departments from cities as distant as New York were called in, but it was discovered too late that Baltimore’s fi re hose connectors were incompatible with those of other cities, so outsiders were unable to provide much help. In fact, at the time there were more than 600 diff erent sizes of fi re hose manufactured in the U.S. Clearly, a need for a consistent standard of measurement became obvious for this country’s manufacturers. Th e NBS led a successful eff ort to standardize fi re hoses across the nation. It went on to standardize thousands of other things, and today it sells about 35,000 “standard reference material” samples a year, with which manufacturers, laboratories, and other institutions can compare their own products.

A problem with measurement in this country that still exists today is the fact that our standard of measurement is still primarily based on English units, while the rest of the world uses the S.I. system. A campaign was mounted by the NBS in the late 1970s to wean the United States away from the traditional English system of measurement to the metric system. Unfortunately, the campaign was not successful.

Many American manufacturers have adapted by using the English system for products sold do-mestically and the metric system for products sold abroad. Th e United States stands almost alone as a non-metric country despite the consequent disadvantages. Even the National Aeronautics and Space


Administration (NASA), continues to use some non-metric specifi cations in the design of its spacecraft. A costly accident in 1999 was one of the results. On Sept. 23, 1999, NASA fi red rockets intended to nudge its Mars Climate Orbiter into a stable low-altitude orbit. But after the rockets fi red, NASA never heard from its expensive spacecraft again. Scientists later determined that it had either crashed on the Martian surface or escaped the planet completely. Scientists eventually concluded that the reason for the debacle was that the manufacturer had specifi ed the rocket thrust using the English units for force, the pound, while NASA assumed that the thrust had been specifi ed in the metric system unit for force, the newton. Th e result was the loss of a $125 million satellite. Until we fully adopt the metric

system of units in the United States problems like this are bound to occur in the future.Th e very word “measure” can glaze the eyes of people who feel uncomfortable with numbers. But

scientists everywhere, including those at NIST, regard measurement as the keystone of discovery. Lord Kelvin, the 19th Century English physicist who discovered the vital pillar of science known as the second law of thermodynamics, put it this way:

“When you can measure what you are speaking about and express it in numbers, you know some-thing about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.”

USEFUL CONVERSION FACTORS

Th e following list includes some useful conversion factors between SI (metric) and English units. Th e most important conversion factor is the defi nition of the inch as exactly equal to 2.54 centimeters. Although in an ideal world conversion factors would be unnecessary, the fact is that most people are more comfortable with certain sets of units than with others. For example, most people know that a long jump of 29 feet is a world-class jump. However, how many would realize the signifi cance of the same jump if it was reported as 8.90 meters? In 1968, at the Summer Olympics in Mexico City, U.S. Olympian Bob Beamon eclipsed the existing world record by almost two feet with his 29 foot jump. However, since measurements at the Olympics are in meters he did not know what he had done until a coach converted the metric measurement to feet and inches, at which time he fi nally realized enormity of his feat. We live in a world of mixed units requiring conversions and will for the foreseeable future.

Some common conversion factors between SI and English units are:

• 1 inch = 2.54 centimeters (cm)• 1 kilogram (kg) = 2.2 pounds (lb) • 1 pound = 454 grams (g)

Figure 1-10. Mars Climate Orbiter (NASA)

physical science...2 physical science: a historical approach in early england, units of measurement...

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