Physical Science:
A Historical Approach
Edited by John Truedson
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PHYSICAL SCIENCE
A HISTORICAL APPROACH
…
By John Truedson
Bemidji State University
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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, Classifications of Stars,
and the H-R Diagram
179
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
he 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 measurement concerned that of length. The first documented example is the Royal Egyptian cubit,
which was based on the length of the arm from the elbow to the outstretched finger 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 barleycorn ears, and the foot, which was the length of a man’s foot. The furlong, 220 yards long, comes
from the word “furrowlong” and was the distance a yoke of oxen could pull steadily through heavy soil
T
Figure 1-1. Royal Egyptian Cubit Papyrus (NCSL)
before they had to rest for the day. The 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. This land area was 220 yards by 22 yards. There are references to the acre at least as
early as the year 732. The word “acre” also meant “field” in medieval England.
Chapter 1: Measurement
1
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 different 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 significant 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 floor’s dimensions with their Figure 1-2. A thumb is
feet since a man’s size 11 shoe is very close to one foot in length.
about 1 inch across
European systems of measurement were originally based on Roman measures, which in turn were based on those of Greece. The Greeks used as their basic measure of length
the breadth of a finger (about two cm), with 16 fingers in a foot, and 24 fingers in a Greek cubit. These
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. The 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 confiscated and the container destroyed.
The Romans eventually adapted the Greek system. They had as a basis the foot, which was divided
into 12 inches. The inch is derived from the Latin word, unciae, meaning a twelfth part. The 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. This Roman system was adopted, with
local variations, throughout Europe as the Roman Empire spread.
A country like England, though, was invaded at different times by many peoples bringing their own
measures. The 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 different ways. The 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 definitions of measurement to be used. This was the first 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 defined by the ordinance as rather strange subdivisions of each other. Scientists had long seen
the benefits of rationalizing measures. The great English architect Christopher Wren in the 1700s had
proposed that the yard be defined 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. This
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. The examples below have
been found in various publications:
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Physical Science: A Historical Approach
• 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.
This 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
This local ordinance had wider influence, 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 infinite perplexity
of the measures exceeds all comprehension. They differ not only in every province, but in every district and
almost every town.” In fact, it has been estimated that France had about 800 different names for measures at this time, and taking into account their different values in different towns, around 250,000
differently 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. The Pyramids in Egypt were
built to a fine precision even by today’s standards.
The base of the Great Pyramid of Khufu like the
other pyramids in the area is almost a perfect square.
The 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 Figure 1-3. The Great Sphinx and the Pyramid of
such precision. We will discuss the alignment of the Khufe in Egypt
Great Pyramids in more detail in Chapter 8.
Although they are not nearly as celebrated as the Egyptian pyramids and have not received comparable 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 significant from archaeological, historical, architectural, and engineering perspectives. Like the
ancient Egyptians, the Maya, whose civilization dates from at least 3000 B.C. and flourished from
the Fourth to the Ninth Century A.D. produced extraordinary structures, had a superb command
Chapter 1: Measurement
3
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 calculated 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. Thus, 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. This is
approximately 1.5 m for a person of moderate Figure 1-4. The temple of Kukulcan (El Castillo) in
Mexico (Kyle Sim)
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 define the time by the amount of water required to empty a filled 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 “flowing.”
The sundial is one of the oldest forms of time-keeping. The scaphe (Greek for “boat”) dial is a bowlshaped 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 figure at the right.
The days themselves were divided into hours. The length of an
hour was not fixed; 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. Therefore,
the length of a hour varied by almost a factor of two and would
change on a daily basis. This 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
Figure 1-5. Sundial with Aramean
accuracy.
The first attempt to measure time with any real accuracy was Inscription, Sandstone, 1st. Cent. B.C.
the development of mechanical clocks. The first mechanical (Museum of the Ancient Orient)
4
Physical Science: A Historical Approach
clocks developed in the 14th Century were based on weights
wrapped around a cylinder with a notched wheel. The accuracy of these clocks was not very good and could keep
time to only about 15 minutes per day.
The next step in clock accuracy was the pendulum clock
first proposed by Galileo in the 1630s. Galileo realized
that the pendulum could be used potentially to build a
very accurate clock. The figure 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 regularity. 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 pendulum clock. Christian Huygens built a pendulum clock in
1656 that was accurate to 10 seconds a day. This was truly
Figure 1-6. A pendulum with path marked
a monumental advance in time-keeping.
A pendulum clock can be extremely accurate. However, in red
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.
The 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. The balanced wheel clock is based on a spiral spring. Modern mechanical watches are based on the same principle. The 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 five-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.
The next major leap in watch accuracy was the development of the quartz crystal mechanism in
the 1960s. These watches are based on the vibration of a quartz crystal embedded in the watch. These
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 field
to the crystal, it changes its shape, and if you squeeze or bend a crystal, it generates an electric field.
When put in a suitable electronic circuit, this interaction between mechanical stress and electric field
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
Chapter 1: Measurement
5
by NIST and NIST’s first 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. The 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. The
bega was the smallest unit in a decimal system.
The figure 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. The shekel
was used all over the world including Ireland.
Ancient Mesopotamia was located in what is
now Iraq and Turkey.
The ancient Mesopotamians did not have a
money economy, so they developed a standardized system of weights to carry out their many Figure 1-7. Egyptian weight dated to about 1500 B.C.
commercial transactions. The original medium (Louvre Museum)
of exchange was barley. The 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.
The basic traditional unit of weight in the English system, the pound, originated as a Roman unit
and was used throughout the Roman Empire. The 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 different pound standards in use. The 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. Thus 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. The 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. The 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. The 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 difference 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
6
Physical Science: A Historical Approach
Figure 1-8. Diagram showing relation of classic
English units of weight B.C. (Christoph Päper)
pound because it was kept in the Tower of London. The 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 official standard for minting coins. Unfortunately, there is quite a bit of confusion
between the troy pound and avoirdupois pound. The troy pound was abolished in 1878 to avoid any
commercial confusion with the avoirdupois pound. The troy system is nearly obsolete today, but the
prices of precious metals are still quoted by the troy ounce. The 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 different
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 specific objects as discussed previously.
The first effort 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 finally 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 officially
approved in June 1799 This distance was calculated from a meridian drawn between the cities of
Dunkirk, France, and Barcelona, Spain. The production of this standard required a very careful
survey which took several years.
Chapter 1: Measurement
7
Two other units of measurement were derived from the meter. The liter is the volume enclosed by a
cube with all edges 1/10th of a meter long. The kilogram is the mass of one liter of water. These units,
along with the second as the basic unit of time, became the basis of the early version of the metric
system.
The seven basic unit standards of the International System of Units (S.I.) system are listed below:
Base quantity
Name
Symbol
Length
Mass
Time
Electric current
Temperature
Amount of substance
Luminous intensity
meter
kilogram
second
ampere
kelvin
mole
candela
m
kg
s
A
K
mol
cd
1. Length (meter): Originally defined 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
finely measured and marked, would not provide the needed accuracy in today’s highly technical world.
The meter is now defined in terms of the distance light travels in 1/299,792,458 of a second. This
corresponds to an accuracy of one centimeter in 3000 kilometers.
2. Time (second): The second was originally defined as 1/86,400 of a solar day. The solar day is
defined as the time from the Sun’s peak altitude at noon local time to the next Sun’s peak latitude 24
hours later. Theoretically, 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.
The sidereal day is the time for a
star on the south meridian to return
to the same spot the next day. This
period is 23 hours, 56 minutes, 4
seconds long in modern units. The
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. The Atomic clock maintained by NIST (NIST)
8
Physical Science: A Historical Approach
due to its length and had the significant 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 definition of
the second.
The second is now defined as the duration for 9,192,631,770 cycles of a cesium atom vibration.
The National Institute of Standards and Technology (NIST) built its latest atomic fountain clock,
the NIST F-1, at its laboratory in Boulder, Colorado. This atomic clock is accurate to one second in
20,000,000 years. This clock is used to calibrate the timing of the Global Positioning Satellite (GPS)
system, the most accurate navigation system ever created. The official 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. Therefore, leap seconds are introduced at pre-defined 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): This 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
definition of the kilogram based on the mass of a single atom will someday be possible, but they are
still short of the goal.
4. The 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.
The 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.
The nation’s need for standardization was strongly demonstrated in 1904, when a massive fire
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 fire 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 different sizes of fire hose manufactured in the U.S. Clearly, a need for
a consistent standard of measurement became obvious for this country’s manufacturers. The NBS led
a successful effort to standardize fire 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 domestically and the metric system for products sold abroad. The United States stands almost alone as a
non-metric country despite the consequent disadvantages. Even the National Aeronautics and Space
Chapter 1: Measurement
9
Administration (NASA), continues to use some
non-metric specifications in the design of its
spacecraft. A costly accident in 1999 was one
of the results. On Sept. 23, 1999, NASA fired
rockets intended to nudge its Mars Climate
Orbiter into a stable low-altitude orbit. But
after the rockets fired, 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 specified the rocket thrust
using the English units for force, the pound,
while NASA assumed that the thrust had been
specified in the metric system unit for force,
the newton. The result was the loss of a $125
Figure 1-10. Mars Climate Orbiter (NASA)
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.
The 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 something 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
The following list includes some useful conversion factors between SI (metric) and English units. The
most important conversion factor is the definition 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 significance 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 finally 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)
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Physical Science: A Historical Approach