UNITS, MEASURES, &
DIMENSIONS
MEASUREMENTS
Measurement is the most useful form of description in science.
Often the most useful measurements are those that have a
number and a unit, such as 12.7 inches. Here '12.7' is the
number and 'inches' is the unit. This unit of inches in the
example is one of the common units in the dimension of length. A
number, then, is an expression in numerals. A unit is a
recognized
way to divide the essence of a dimension for measurement, and a
dimension is a measurable physical idea. Here is a bit of
advice you can overlook only at your peril: To become fluent in
the subject you should memorize the basic background of
information. The following units, dimensions, and measures are so
basic to the study of chemistry that you could always
help yourself by memorizing these. The real test of
whether you know this well enough is to recognize the dimensions
of any measurement and know its symbol and magnitude from the
unit alone.
Back to the beginning of Units and Measures.
DIMENSIONS, UNITS, AND SYMBOLS
Notice the symbols of the dimensions as they would be used in
formulas. The basic metric symbol or the symbol of the most
used metric unit is listed after the metric units.
DIMENSION
 SYMBOL
 METRIC UNITS
 SYMBOL
 'ENGLISH' UNITS

LENGTH  S, l, d, r  meter (+m.p.)  m  Ft, in,Yd, mi, etc. 
AREA  A  sq.meter,
etc,hectare  m^{2}  sq.Ft, etc., acre 
VOLUME  V  cu.meter,
etc., liter  m^{3}, L
 cu.Ft,cu.in,etc.,gal,Floz. 
TIME  t  sec
(+m.p.) sec,min,hr,day,yr,etc.(both metric & English) 
MASS  m  Kilogram (+
m.p.), AMU  kg
 (slug, rarely used) 
FORCE (weight)  F, Fw  Newton (+ m.p.)  N
 Pound (#), Oz, etc. 
VELOCITY  v  meter/sec,KPH,etc  m/sec  Ft/sec, MPH, etc.

ACCELERATION  a  meter/sec.sq., etc.
 m/sec2.  Ft/sec sq., etc.

PRESSURE  P  N/sq.m, atm.,Pa
 atm,Pa*  #/sq.in (PSI), inHg, etc. 
DENSITY  D  g/cc, Kg/liter, etc.
 g/cc  #/cu.Ft, #/gal, etc. 
TEMPERATURE  T  Celsius or Kelvin

°C or K  Fahrenheit or Rankine 
ENERGY  E  Joule (+ m.p.)
 J  footpound 
HEAT  Q  calorie (+
m.p.)  cal  BTU (British Thermal
Unit) 
CONCENTRATION  C**  gram/L, mol/L,
Molar  M  (#/gal or #/cu.ft, rare)

Abbreviations: Ft = foot, in = inch,
AMU = atomic mass unit, KPH = kilometers per hour, MPH = miles
per hour,
gal = gallon, PSI = pounds per square inch, cc = cubic
centimeter, inHg = inches of mercury, Pa = Pascal
m.p. = metric prefixes, cu. = cubic, sq. = square, atm = atmosphere.
*The unit Pa, for Pascal, is a unit of pressure that is the standard
unit for the SI system, the MKS system in the metric measurements. The unit
of Pascal, however, is rarely used in chemistry. Instead, the unit "atm,"
for "atmosphere," is still most used in chemistry.
**The symbol "B" is now the official symbol for concentration in the SI,
but there are still chemistry texts using the "C" as is shown here."
The table above lists almost all the dimensions you will need
in this course, the symbol for each dimension as it will be used
in common formulas, and the units of each dimension. Notice
Chemtutor has two systems of measurement displayed that
you should know. There are really two commonly used metric
subsystems. Most chemistry texts will use the MKS system
(meter, kilogram, second) rather than the lessused CGS
(centimeter, gram, second) system. A system is defined
by its
basic measure of distance, mass, and time.We will use the MKS
system, also called the S.I., or International System. The
symbol for only the basic unit of each dimension in the metric
system is on the list.
Back to the beginning of Units and Measures.
METRIC SYSTEM vs. "ENGLISH SYSTEM"
The metric system typically uses only one root word for any
basic dimension such as for length, the meter. All the metric
units of length use the root word 'meter' with the metric
prefixes in the next table. Our common system in the United
States
is not really a system, but is a throwntogether mess of
measurements with no overriding order. Chemtutor, as does most of
the United States, calls this group of measurements the "English" system. While calling it that is a
considerable slander on the English people, the United States
and Liberia are the only nations on earth to still cling to it.
Chemtutor thinks that the English system makes a fine learning
tool, along with being wonderfully poetic. You will want to know
how to relate the English System to the metric system.
Particularly notice the large number of units of length in the
English system. This is only a small number of the common ones.
We regularly use fathoms to measure depth in water and furlongs
to measure distance in horse racing. There are many
littleused English length units such as the barleycorn (one
third of an inch) that may be picturesque, but are not used
today. Notice that we define the barleycorn as a third of an
inch. The way to relate one English unit to another is by
definition. Length is the most common measurement. As a result,
it has not only the largest number of words to describe it,
but it also has the largest number of symbols to represent it in
formulas. The English language also uses distance, long, width,
height, radius, displacement, offset, and other words for length,
sometimes in specialized applications.
Here are some differences between the "English System" and the Metric System, or SI.
The Metric System (usually) uses only one root word for each basic dimension, such as "gram" for mass or "meter" for distance. Some dimensions have more than one root word, such as "liter" for volume instead of the cubic distance (such as "cubic centimeter"). The English System has a diffenent name for each measurement unit, such as inch, foot, yard, etc.
The Metric System uses metric prefixes before the root word to indicate the magnitude of the measurement, such as kilogram or microgram.
The Metric System units are arranged in powers of ten, according to their metric prefixes. One centimeter is equal to ten millimeters. The English System uses any traditional definition with any number. One foot equals twelve inches, or one yard equals three feet. Even More disturbing, the English System uses FRACTIONS of units, such as 3/8 inch or mixed units, such as pounds and ounces or feet and inches.
The Metric System uses the idea of MASS for measuring the amount of material rather than WEIGHT. The English System uses the POUND as a unit of weight, even though it is also a unit of force.
The great majority of the world uses the Metric System. The US is now SLOWLY beginning to convert to the Metric System. We see liters of drinks in the grocery stores. Our medicines are in grams or milligrams. Our food labels show Metric units.
Back to the beginning of Units and Measures.
LENGTH
A meter is a little longer than a yard, so a meterstick that
has inches on the back of it will has just a bit over thirtynine
inches
on the English side. Typically, on the English side, the inches
are broken into halves, fourths, eighths, and perhaps sixteenths.
On the metric side one meter breaks down into ten decimeters, one
hundred centimeters, and a thousand millimeters.
Back to the beginning of Units and Measures.
AREA
An area is a length multiplied by a length. (A= l l as in the
formula list.) An area is an amount of surface. Almost all area
units are length units squared, such as: square meter
(m^{2}), square centimeter (cm^{2}), square inch (in^{2}), etc. The acre and
hectare, units of land measurement, are the only units commonly
used that are not in the "distance squared" area unit
format. An acre is defined as 43,560 square feet, so in using the
unit 'acre' in dimensional analysis, the definition can be used
to relate the acre to other units. Notice the squaring of a unit
of length. A meter multiplied by a
meter is a square meter. A foot by a foot is a square foot,
etc.
Back to the beginning of Units and Measures.
VOLUME
Volume is length multiplied by length multiplied by length.
You may have heard that volume is length times height times
width, but it means the same thing. ( V= l l l ) You may think of
a volume as the space inside a rectangular (blockshaped)
fish tank. Volume is the measure of an amount of space in three
dimensions. Because volume is such a common type of
measurement, it is unique in that it has two types of commonly
used root word in both metric and English systems. The
metric roots are liter (L) and cubic meter (m^{3}). The English system also
uses cubic length, such as cubic feet (ft^{3}) and an extensive array of units that are not
in the cubed length format, such as teaspoons, tablespoons, cups, pints, quarts, and gallons. Again, analogously to area
measurements, a cubic meter is a meter multiplied by a meter
multiplied by a meter, and a cubic foot is a foot by a foot by a
foot.
Back to the beginning of Units and Measures.
TIME
Time is also a bit odd in its units. In both systems the units
of less than a second are in the metric style with prefixes
before the second, such as millisecond. Time units of more than a year are in a type
of metric configuration because they are in multiples of ten
(decades, centuries, millennia, etc). The dimension of time is
messy for good reason. The more commonly used time units
from day to year are all dependent upon the movement of the
earth. The unit of 'month,' particularly if it is directly
related to the moon, is useless as an accurate unit because it
does not come out even in anything. Having sixty seconds in an
hour and twentyfour hours in a day come about from the ease of
producing mechanical clocks. (Is it time to switch to metric
time? Consider ten hours in a day, one hundred
minutes in an hour, and one hundred seconds in a minute. It would
come out to almost the same length of second. I will let you do the math.)
Back to the beginning of Units and Measures.
MASS
Mass is an amount of matter. Mass has inertia, which is the
tendency of matter to stay where it is if it is not moving, or to
keep moving at the same rate and direction if it is already
moving. You could measure mass by an inertial massometer.
Visualize a metal strip held tightly on one end and "twanged," or given a push to make it vibrate on the
other end. It has a
natural pitch to vibrate. If you were to put a mass on the end of
that strip, you would change the pitch of the vibration. The
change of pitch would make it possible to calculate the mass of
the added object. This measurement of mass is completely
independent of gravity, the way we often weigh a mass by
comparing the push or force of the mass on a surface. Mass is a
more accurate way of thinking of amount of matter compared to
weight. The metric system is massbased whereas the
English system thinks in weight. Consider that an astronaut in
near earth orbit has no weight because the gravitational
attraction cancels inertia, but the mass of the astronaut remains
the same. The metric root word of mass measurement units is the gram. Notice
the difference between the "root word," gram, which is
the basis for adding metric prefixes, and the system base of
kilogram, the mass unit of the S.I. metric system.
Back to the beginning of Units and Measures.
FORCE
A force is a push or a pull. Those simple words are the best
definition of a force under our limited experience. A force cannot be seen or heard directly, so it is a bit of a difficult
concept beyond the simple definition. Having basic metric units
like 'kilogrammeter per second squared' make the idea of force
hard to think about using that tool also. It is shameful to give
you this in the same manner as a British sex
education, but until a better way comes about, that's all
there is to be said about it. The English unit of force is the pound, and the metric unit of force is the Newton.
Back to the beginning of Units and Measures.
WEIGHT
Weight is a downward force due to the mass of an object and
the acceleration of gravity. The English system can
conveniently use the idea of weight to measure amount of material
because there is very little difference in the acceleration of
gravity over the surface of the earth. There are certainly other
forces besides gravity. Magnetism produces a force. Electric
charge produces a force. Like the unit of force, the English unit of weight is the pound, and the metric unit of weight is the Newton.
Back to the beginning of Units and Measures.
VELOCITY
Velocity is a complex dimension. The unit of velocity is a
combination of more than one type of basic dimension. A velocity
is a distance per time. The word 'per' here means 'divided by,'
and distance divided by time is not only the definition of
velocity, but it is the easy way to remember the velocity
formula, v = d/t. Velocity also has the name of rate. You might
know the same formula as, "rate times time equals
distance." Here's where we could start complicating the
math by using
calculus, but we won't. If you are taking a course that
requires calculus, the math is only slightly different, but the
basic ideas
behind it are the same.
Back to the beginning of Units and Measures.
ACCELERATION
An acceleration is just another step down the same road as
velocity, that is, acceleration is a distance per time per time,
or,
another way to see it, distance per time squared. An acceleration
is a time rate of change of velocity. If something changes
its velocity, it has an acceleration. An acceleration causes an
increase or decrease in speed or a change in direction. Newton
and Einstein identified gravity as an acceleration. Gravity has a
fairly consistent amount of acceleration on the surface of the
earth, that is 32 ft./sec2 or 9.8 m/sec2. As you can see, the acceleration of gravity, "g," can substitute for the "a" of
acceleration in the formulas below when the acceleration is due
to gravity.
Back to the beginning of Units and Measures.
PRESSURE
A pressure is a force per area. You can almost see the
pressure of the wind on a sail. The pressure of the wind is the
same,
so the larger the area of the sail, the greater the force of the
wind on the ship. Pressure unit definitions that we need for this
course revolve around the unit "atmosphere" because
historically the pressure was first measured for weather.
Back to the beginning of Units and Measures.
DENSITY
Density is mass per volume, weight per volume, or specific
gravity, which is the density of a material per the density of
water. Metric system densities are usually in the units of mass
per volume, such as kg/_{L} (kilogram per liter) or g/_{cm}^{3} (gram per cubic centimeter). English
densities are usually in weight per volume, such as #/_{gal}.
(pounds per gallon) or #/_{ft}3 (pound per cubic
foot). Specific gravity has no units (!) because it is a
comparative measurement. Specific gravity is the density of a
material compared to the density of water. Expressing density as
specific gravity shows neither system.
We can have fun in a density demonstration by passing a
largegrapefruitsized ball of lead around the class. That size
of lead ball weighs about 35 pounds. People do not expect
something that compact to weigh so much. One way to think of
density is, "How much mass is packed into a volume."
Back to the beginning of Units and Measures.
TEMPERATURE
Temperature is a bit more subtle dimension. What we really
measure is the average velocity of the atoms or molecules in the
material. One way to measure it is by the expansion of a liquid
in a very small tube. This is the shape of a liquid (usually
mercury or alcohol) in a thermometer. The Fahrenheit scale is
still not a bad one for use with weather. Scientists are more
likely to use the Celsius or Centigrade scale. Gas law
calculations require the Kelvin scale because it is an absolute
scale.
The other absolute scale, Rankine (pronounced "rankin"), is useful for teaching purposes, but is not
in common use.
Back to the beginning of Units and Measures.
ENERGY
Energy is the ability to do work. A Joule, the metric unit of
energy is a kilogram meter square per second square. Both
of those ideas can be difficult to wrap your mind around. The
easier way to think of energy is perhaps by its various types.
You should have an intuitive feeling that a fifty pound rock held
above your head has more energy of position in a
gravitational field than the same fifty pound rock by your feet.
A rubber band pulled back has more spring energy than a lax
one. A speeding train has more energy of movement than a still
one. We usually value petroleum not for its beauty, but for
its chemical energy content. Energy is transferable from one type
to another, but is not lost or gained in changes.
Back to the beginning of Units and Measures.
HEAT
Heat is a form of energy. It is the energy of the motion of
molecules. Even though heat and energy are fundamentally the
same dimension, we measure and calculate them differently. We
define a calorie (note the lowercase 'c') as the amount of
heat that increases the temperature of a gram of liquid water one
degree C. The BTU, the English unit of heat, is the amount
of heat that increases the temperature of a pound of liquid water
one degree F. A food Calorie (note upper case 'C' ) is one
thousand heat calories of usable food energy. That is, the food
Calorie reflects the type of living thing eating AND USING
the energy. So the food Calorie depends on the type of (animal)
eating it. A cow or a termite could get much more food
value from a head of lettuce than a human being can, so what is a
Calorie for us would be different for them.
Back to the beginning of Units and Measures.
CONCENTRATION
Concentration is amount of material in a volume. In this
course, we will stay mostly with measuring the amount of solute
in a
solution. There is more on this in the chapter on solutions, and
we really need to explain the idea of mol or mole before a
thorough explanation of concentration can mean much.
Notice the formulas in the table below. Some of the simple
ones we use in this course only for practice with problemsolving
techniques and for defining the units and dimensions. There are a
few items in the formulas that have not been mentioned yet,
such as c, the specific heat; n, the number of mols; and R, the
universal gas constant. These we will consider in context as
we use them.
Back to the beginning of Units and Measures.
FORMULAS
A = l l  V = l l l  V = A l  v t = d  F
= m a ( Fw = m g) 
a = v/t  a = d/t^{2}  P = F/A  C V = n  D = m/V (D =Fw/V) 
P V = n R T  Q = m c T  Circle
Area, Ac = r^{2 . }Cylinder Volume
= Vc = Ac l =
r^{2}
l 
A formula is a relationship among dimensions. The symbols for
the dimensions in the formula list are in the dimension list.
Note the capitalization or lack of it in the symbols, for
instance, V = volume and v = velocity; C = concentration and c =
specific heat, etc. Also, there are some letters written after
and slightly under a symbol called a subscript. Subscripts
indicate
a special case of the symbol, as you see above with the area of a
circle being represented by the A for area and a subscript
c for circle.
Back to the beginning of Units and Measures.
DEFINITIONS TO CHANGE UNITS
There are three types of definitions you should know for
changing units, English system definitions, metric system
definitions,
and changeover definitions between the two systems.
There are a small number of English system definitions listed
below in Table C that you should know by rote. Notice that we
take the same approach here with one of the larger unit being
stated first and then some number greater than one of the
smaller unit. All of these English definitions are exact
definitions except for the cubic feettogallons relationship.
Take a look at any edition of the Chemical Rubber Company (CRC)
Handbook of Physics and Chemistry and you will see the incredible
number of nonmetric units and amazing amounts of other information.
CRC
Handbook available for sale from Amazon.
Don't be afraid to buy a used CRC handbook. I still use the one I bought in high school fifty or so years ago. There seems to be some information from the CRC Handbook available on line for free, but we cannot vouch for that.
Back to the beginning of Units and Measures.
ENGLISH SYSTEM DEFINITIONS YOU SHOULD KNOW BY
ROTE
1 ft. = 12 in.  1 mi. = 5280
ft.  1 cup = 8 Floz.  1 pint
= 2 cups  1 qt. = 2 pints 
1 gal. = 4 qts.  1 # = 16 Oz.
 1 ton = 2000 # 
1 acre = 43560 ft^{2} 
*1 ft^{3} = 7.48 gal. 
1 gal. = 231 in^{3} 
  
*Not an exact def. All others are exact. 
Back to the beginning of Units and Measures.
METRIC PREFIXES AS FACTORS OF TEN
FACTOR  PREFIX  SYMBOL 
+18  exa  E 
+15  peta  P 
+12  tera  T

+9  giga  G 
+6  mega  M 
+3  kilo  k 
+2  hecto  h 
+1 
deca  da 
0  *ROOT WORD ONLY* 
1  deci  d 
2  centi  c 
3  milli  m 
6  micro  ยต 
9  nano  n 
12  pico  p 
15  femto  f 
18  atto  a 
The above table includes only the commonly used metric prefixes. There
have been some metric prefixes suggested for some of the exponents of ten not
listed here, but they are not in common use, or are in use by only a small
number of people for limited use. The prefix "myria" (my or ma) as E4 is a
good example. The word "myriad" means tenthousand, so the prefix is well
documented in language. (Thanks to Van Isaac Anderson for the thought.)
A FEW ODD METRIC DEFINITIONS
1 metric tonne = E3 kg  1
mL. = 1 cc = 1 cm3 
 
1 Ångstrom = E10
m  1 cubic meter = 1000 L 
Back to the beginning of Units and Measures.
THE METRIC STAIRCASE
 peta +15        The
metric staircase below is a graphic way of showing how

 __           metric prefixes interact. It is the same thing
as the chart 
  __           above, but in a more
visual representation. Each step is 
    tera +12       a multiple of ten of the
lower step.
For instance, 'centi' 
    __           is on the next step above 'milli,' so a centimeter is 
     __           ten times larger than a
millimeter. Centigram is 
       giga +9        ten times larger than milligram. There are no 
       __           common metric prefixes for
some powers 
        __           of ten such
as +4,+5,7, etc. 
          mega +6      
          __                       
           __                      
   kilo +3                  
   hecto +2                
    deca
+1               
   
ROOT WORD           
    deci
1              
     centi 2            
    milli
3            
   __              
METRIC SYSTEM DEFINITIONS  __             
       micro 6       
Metric system
definitions are relationships      __           
between units with the
same rootword that,      __          
is, only the
prefix changes. The Metric Stair       nano 9    
case is just a way
to visualize the relationships      __        
among the metric
prefixes. We make a metric       __       
system definition in the
following way, using the        pico 12  
units kilometer and millimeter as an
example:
      __     
        __    
1.Pick the largest
metric prefix. Begin the metric definition with 
  femto15 
one of the larger units, e.g. 1
km = (some number of)
millimeters.    
_  
2. Count the number of 'steps' down the metric staircase
between the two metric prefixes. For instance, kilo to milli is
six steps.
3. The number of the smaller unit is ten to the power of the
number of steps between the metric prefixes. In our example
1 km = E6 mm. Another way to
think of it is that the number of zeros of the smaller unit is
the number of steps, so
1 km = 1,000,000 mm.
The reason for stating the metric system definitions this way
is to make calculations easier and make the sense of the
definition more obvious. It is easier to use 1 km = E6 mm than 1
mm = 1/1,000,000 km in math, even though they are
both correct.
Here is more information on the metric units, their origins and uses.
This chart emphasizes the point of view of computer
use.
There are some times you will need to convert between systems.
The following few conversion definitions are all you should
need to memorize to convert almost anything. Notice we show a "bridge" between the systems in length, volume, and
mass
to weight.
Back to the beginning of Units and Measures.
COMMONLY USED CONVERSIONS FROM METRIC TO ENGLISH
1 in. = 2.54 cm.  1 L = 1.06
qt 
 
 
1 kg = 2.2 # (at 'g')
or 1
# (at 'g') = 453.6 grams (Use either of these, depending upon the number of significant digits you need.) 
These three conversions are all you will need in this course.
The DA (dimensional analysis) system will use these to convert
more complex units. See the DA problems at the end of Numbers and Math for more understanding as
to how these conversion factors work. As you need them for
whatever you might do on a regular basis, you might need to find
conversions that are more useful to you. A cook might want a
conversion factor between cups and liters. A doctor or
pharmacist might want a conversion factor between grains and
grams. The conversion between inches and centimeters is an
exact one by definition, but the others are not. The conversion
from metric mass to English weight must be done assuming
the acceleration of gravity is one g.
Particularly in the section on gases you will need the
following pressure units:
1 atm = 760 mmHg = 33.9 ftH_{2}O =
14.7 PSI = 30 inHg
Abbreviations: atm = atmosphere, mmHg = millimeters
of
mercury, PSI = pounds per square inch, ftH_{2}O
= feet of water,
inHg = inches of mercury. The unit "feet of watet" iis
not common, but included because it can be useful. For every
hundred
feet below the surface of water the pressure increases about
three atmospheres. The running equation above (It just keeps going!)
shows the common pressure units. You can use it to change between any
two of the units, for example:
760 mmHg = 14.7 PSI.
The official SI unit of pressure, the Pascal, Pa, is not often used
in chemistry because it is such a small unit. One atmosphere is about
equal to 100,000 Pascals, or you could say that one atmosphere is
approximately equal to 100 kPa.
More exactly, 1 atm = 1.01325 E5 Pa = 101.325 kPa
ISLAND SYSTEMS
Here is one way to think of the metric and "English" systems.
The metric system is the metric island with an orderly set of
towns and an orderly and simple and fast road system. The
"English" island has every town connected as well as they can (by
definitions) to other neighboring towns. The "English" system of
transportation is not too efficient.
There only has to be one good solid bridge (changeover
definition) between the two islands. You can get anywhere from
one system to the other by first coming to the bridge town,
crossing, and then taking the new system to wherever you want to
go.
Back to the beginning of Units and Measures.
Metric prefix humor (?) exaray exarated petacat teradactyl
gigalow terabull piconose decimate terapieceofpaper
petagreed tararism picopeach decacards attomobile
microphone nanopudding millimouse millicent picocard
petagogue petaful piconick banano picolow centimental
exalint attomiser millitent picoboo attowhack terapin
kilobug decaration centifold teratorialism
THERE'S MORE *
1 million microphones = 1 megaphone
2000 mockingbirds = two kilomockingbirds
10 cards = 1 decacards
1 millionth of a fish = 1 microfiche
453.6 graham crackers = 1 pound cake
1 trillion pins = 1 terrapin
10 rations = 1 decoration
100 rations = 1 Cration
10 millipedes = 1 centipede
3 1/3 tridents = 1 decadent
AND EVEN MORE
2 monograms = 1 diagram
8 nickels = 2 paradigms
2 wharves = 1 paradox
* Thanks to Ellen Averill
email Chemtutor at info@chemtutor.com
to add to this nonsense.
Back to the beginning of Units and Measures.
Heuristics
Numbers and Math
Atomic Structure
Elements
Periodic Table
States of Matter
Compounds
Reactions
Mols, Stoichiometry, and Percents
Oxidation and Reduction Reactions
Gases
Solutions
Acids and bases
Kinetics
Thermochemistry
A BRITISH SEX EDUCATION
The father calls his tenyearold boy into his study. After
the boy sits down, the father, clearly uncomfortable, blurts,
"Young lad, do you know what the stags do in the Autumn?"
The young fellow feels as out of place as his father and,
wishing to please, mutters, "Yes, sir."
Whereupon the father, visibly relieved, says, "I thought you
did. That's all. Good afternoon."
Back to Force.

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