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Measurement

2.1Measurement: The Basics

2.1.1Uniformity, Reliability, and Accuracy

We do not measure things. Rather, we measure properties ofthings. For example, we cannot measure a box, but we can measure its properties such as its mass, length, and temperature.

To properly compare and analyze the things in our universe, weneed to compare and analyze their properties. Because people all around the world are making measurements, we must ensure there isagreement on all the various types ofmeasurements used. Difficulties arise because measurements have both quantitative and qualitative aspects. The fact that the two lines onthe international prototype platinum-iridium bar inFrance are one meter apart isquantitative; how you measure other objects with that baris qualitative. The ability to match uptwo lines may seem simple, but, depending the desired accuracy, such simple operations are in fact difficult. This difficulty is why using measuring equipment is a qualitative art.

No one uses the prototype meter as anactual measuring tool; rather, copiesare made from the original prototype, and these copies are used as masters to make further copies. By thetime you purchase a meter stick, it is a fardistant cousin from the original meter prototype. However, despite the length of the progeny line, you hope that the copy you have is asgood as the original. Depending on the expertise of theengineers andmachinists involved, it should be very close.To obtain that quality, theengineers andmachinists were guided by three factors; uniformity, reliability, and accuracy. Without these basic tenets, the quality of the meter stick you usewould be in doubt. Likewise, thequality of the use of the meter stick isalso dependent on the same three factors, without which all readings made would be indoubt.

Uniformity requires that all people use the same measurement system (i.e., metric vs. English) and that all users intend that a given unit ofmeasurement represents thesame amount andis based on thesame measurement standard used

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66 Measurement

everywhere else. It is theuser's responsibility to select equipment that provides measurements that agree with everyone else.

Reliability requires theability to consistently read a given measurement device and also requires a given measurement device to perform equally well, test after test. It is the user's responsibility toknow how to achieve repeatable data from the equipment being used.

Accuracy refers tohow well a measurement device is calibrated and how many significant figures onecanreliably expect. It is theuser's responsibility to know how to read hisequipment andnotinterpolate data to be anymore accurate (i.e., significant figures) than they reallyare.

Laboratory research is dependent onreliable quality measurements andthe use of uniformity, reliability, and accuracy to achieve this goal and this cannot be emphasized enough. Poor or inaccurate measurements can only lead to poor or inaccurate conclusions. A good theory can be lost if the experimental data are misread.

Commerce is equally dependent onuniformity, reliability, and accuracy of measurement systems. The potential economic liabilities of mismeasurements and misunderstanding areeasy to understand. In fact, it was theeconomic advantages of uniformity that ledto themetric system's expansion after the Napoleonic wars. What canupset and/or confuse consumers and businesses is when thesame word (which may have varying meanings) is applied to different weights. Westill confuse the weight value of a ton and the volume of a gallon: In theUnited States,the ton is equal to 2000 lb; however, in Great Britain it is equal to 2240 lb. Similarly, in the United States, the gallon is established as 231cubic inches; however, in Great Britain it is 277.42 cubic inches. If you areaware of these differences, you can make theappropriate mathematical corrections. But realistically, it should not be a problem to be dealt with. Rather, theproblem of different measurement systems should be avoided in the first place. That is specifically was what themetric system was designed to do.

2.1.2 History of the Metric System

Overcoming the incongruities of inconsistent measurement systems on an international basis wasconsidered for centuries. Thebasics of the metric system were first proposed by Gabriel Mouton of Lyon, France, in 1670. This vicar (of St. Paul's Church) proposed three major criteria for a universal measurement system: decimalization, rational prefixes, andusing parts of the earth as a basis of measurement (length was to be based on the arc of one minute of the earth's longitude). There wasalso a desire to find a relationship between thefoot and gallon (i.e., a cubic foot would equal one gallon). Unfortunately, these measurement units were already in use, andbecause there was nobasis for these measurements

Measurement: The Basics 2.1

 

67

Table 2.1 Base SI Units*

 

Quantity

Unit

Symbol

length

meter

m

mass

kilogram

kg

time

second

s

electric current

ampere

A

thermodynamic temperature

kelvin

K

amount of substance

mole

mol

luminous intensity

candela

cd

* From the ASTM document E380-86, Table 1. With permission.

to have any easy mathematical agreement, they did not. No simple whole number could be used to correct the discrepancy.

Gabriel Mouton's ideas were discussed, amended, changed, and altered for over 120 years. Eventually, a member of the French assembly, Charles Maurice Talley- rand-Perigord, requested the French Academy of Sciences to formalize a report. The French Academy of Sciences decided to start from scratch and develop all new units. They defined the meter as one ten-millionth of the distance from the North Pole to the equator. They also decided that the unit for weight would be based on the weight of a cubic meter of water in its most dense state (at 4°C). This plan allowed the interlinking of mass and length measurement units for the first time. In addition, they proposed prefixes for multiples and submultiples of length and mass measurements, eliminating the use of different names for smaller and larger units (i.e., inch/foot or pint/quart units).

On the eve of the French Revolution, June 19, 1791, King Louis XVI of France gave his approval of the system. The next day, Louis tried to escape France but was arrested and jailed. A year later from his jail cell, Louis directed two engineers to make the measurements necessary to implement the metric system. Because of the French Revolution, it took six years to complete the required measurements. Finally, in June 1799 the "Commission sur l'unite de poids du Systeme Metrique decimal" met and adopted the metric system. It was based on the gram as the unit of weight and the meter as the unit of length. All other measurements were to be derived from these units. The metric system was adopted "For all people, for all time."

The metric system sought to establish simple numerical relationships between the various units of measurement. To accomplish this goal, the Commission took a cubic decimeter* of water at its most dense state (4°C), designated this volume as one "liter," and designated its mass (weight) as one "kilogram." In so doing, the commission successfully unified mass, length, and volume into a correlated mea-

For a description of how the meter was derived, see Sec. 2.1.3.

68 Measurement

surement system for the first time. Official prototypes of the meter and kilogram were made and stored in Paris.

Because of Napoleon's conquests, the metric system spread rapidly throughout Europe. However, it was not in common usage in many areas (even in France) until international commerce took advantage of its simplicity and practicality. By the mid-1800s, it was the primary measurement system in most of Europe. In 1875 the International Bureau of Weights and Measures was established near Paris, France. It formed a new international committee, called the General Conference on Weights and Measures (CGPM), whose goal was to handle international matters concerning the metric system. The CGPM meets every six years to compare data and establish new standards. Every member country of this committee* receives a copy of the meter and kilogram prototype with which to standardize their own country's measurement system.

Over the years there has been ongoing fine-tuning of the measurement system because the greater the precision with which our measurement units can be ascertained, the better we can define our universe. A new era in the measurement system came in 1960, at the 11th meeting of the CGPM, when the International System of Units (SI) was established. This system established four base units: the meter, kilogram, second, and ampere. They are collectively known as the MKSA system. Later, three more base units were added: kelvin (for temperature), candela (for luminous intensity), and mole (for the amount of substance) (see Table 2.1). In addition, two supplementary base units (which are dimensionless) were added: radian (plane angles) and steradian (solid angles) (see Table 2.2).

From the nine base units, over 58 further units have been derived and are known as derived units. There are two types of derived units: those that have special names (see Table 2.3) and those that have no special names (see Table 2.4). An example of a derived unit with a special name is force, which has the unit newton (the symbol N) and is calculated by the formula "N = kg-^s2." An example of a derived unit that does not have a special name is volume, which has the unit of cubic meter (no special symbol) and is calculated by the formula "volume = m3."

Table 2.2 Supplementary SI Units"

Quantity

Unit

Symbol

Plane angle

radian

rad

Solid angle

steradian

sr

" From the ASTM document E380-86, Table 2, with permission.

"The National Institute of Standards and Technology (formally the National Bureau of Standards) represents the United States at the CGPM. They store the United States' copies of the original measurement prototypes.

Measurement: The Basics 2.1

69

Table 2.3 Derived SI Units with Special Names*

Quantity

Unit

Symbol

Formula

Frequency (of a periodic phenomenon)

hertz

Hz

1/s

Force

newton

N

kg-m/s2

Pressure, stress

pascal

Pa

N/m2

Energy, work, quantity of heat

joule

J

N-m

Power, radiant flux

watt

W

J/s

Quantity of electricity, electric charge

coulomb

C

A-s

Electrical potential, potential difference, elec-

volt

V

W/A

tromotive force

 

 

 

Electric capacitance

farad

F

C/V

Electric resistance

ohm

a.

V/A

Electric conductance

Siemens

s

A/V

Magnetic flux

weber

V-s

Wb

Magnetic flux density

tesla

Wb/m2

T

Inductance

henry

H

Wb/A

Celsius temperature

degree

°C

Kc

Luminous flux

lumen

lm

cd-sr

Illuminance

lux

lx

lm/m2

Activity (of a radionuclide)

becquerel

Bq

1/s

Absorbed dose*

gray

Gy

J/kg

Dose equivalent

sievert

Sv

J/kg

° From theASTM document E380, Table 3, reprinted with permission.

h Related quantities using the same unit are:specific energy imparted, kerma, and absorbed dose index.

c Celcius temperature (t) is related to thermodynamic temperature (T) by the equation: t =T- To where To = t0 273.15 K by definition.

Table 2.4 Some Common Derived Units of SI

Quantity

Unit

Formula

Absorbed dose rate

gray per second

Gy/s

Acceleration

meter per second squared

m/s2

Angular acceleration

radian per second squared

rad/s2

Angular velocity

radian per second

rad/s

Area

square meter

m2

Concentration (of amount of

mole per cubic meter

mol/m2

substance)

 

 

Current density

ampere per square meter

A/m2

Density, mass

kilogram per cubic meter

kg/m2

70

Measurement

Table 2.4 Some Common Derived Units of SI (continued)

Quantity

Unit

Electric charge density

coulomb per cubic meter

Electric field strength

volt per meter

Electric flux density

coulomb per square meter

Energy density

joule per cubic meter

Entropy

joule per kelvin

Exposure

coulomb per kilogram

Heat capacity

joule per kelvin

Heat flux density

watt per square meter

Irradiance

 

Luminance

candela per square meter

Magnetic field strength

ampere per meter

Molar energy

joule per mole

Molar entropy

joule per mole kelvin

Molar heat capacity

joule per mole kelvin

Moment of force

newton meter

Permeability (magnetic)

henry per meter

Permittivity

farad per meter

Power density

watt per square meter

Radiance

watt per square meter steradian

Radiant intensity

watt per steradian

Specific heat capacity

joule per kilogram kelvin

Specific energy

joule per kilogram

Specific entropy

joule per kilogram kelvin

Specific volume

cubic meter per kilogram

Surface tension

newton per meter

Thermal conductivity

watt per meter kelvin

Velocity

meter per second

Viscosity, dynamic

pascal second

Viscosity, kinematic

square meter per second

Volume

cubic meter

Wave number

1 per meter

" From the ASTM document E380, Table 4, reprinted with permission.

Formula

C/m3

V/m

C/m2

J/m3

J/K

C/kg

J/K

W/m2

cd/m2

A/m

J/mol

J/(mol)K)

J/(mol)K) N-m

H/m

F/m

W/m2

W/(m2-sr)

W/sr

J/(kgK)

J/kg

J/(kg-K)

m3/kg

N/m

W/(mK)

m/s

Pas

m2/s

m3

1/m

Among the advantages of the International System of Units system is that there is one, and only one, unit for any given physical quantity. Power, for instance, will always have the same unit, whether it has electrical or mechanical origins.

In the United States, measurements made with metric units were not legally accepted in commerce until 1866. In 1875 the United States became a signatory to the Metric Convention, and by 1890 it received copies of the International Prototype meter and kilogram. However, rather than converting our measurement system to metric, in 1893 Congress decided that the International Prototype units

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