Measurement is a basic skill that forms an essential part of our day to day activities

irrespective of what we do. You would definitely have observed that while cooking

food, measured quantities of ingredients are cooked for a measured amount of time.

When you go to buy fruits and vegetables, you take them in measured amounts. You

can identify which one of your friends runs fastest. This is possible by making them

run a known distance say from one end of a playground to the other and noting who

is first to reach the destination. In other words, you measure the time. Can you tell

by the above measurement how fast does your friend run? For this, you need to

precisely measure the distance run and the time taken. Science and technology help

us in making precise measurements for our daily life activities such as stitching,

cooking, sports, shopping, traveling, etc.


In this lesson, we would like to seek answers to several questions. What is the

measurement and why do we need it? How do we measure? How do we quantify

a measurement, so that it is understood by everyone in the same sense? What is

the currently accepted International System of units? We would also learn about

commonly used tools for measurements of physical quantities like length, mass,

time, area, and volume.


WHAT IS A MEASUREMENT?

Suppose you are asked to measure the length of the playground, what would you
do? Maybe you would walk from one end of the field to the other and count the
number of steps. The other possibility is that you may arrange for a measuring tape
or some scale, say a meter scale. Then again go from one end and count how many
times the meter scale was used to reach the other end. Let us take another example.
Suppose you need to weigh a carton full of books; you would use a weighing scale
and see how many kilogram weights you need to correctly weigh the carton- again
a kind of counting. Thus we may define measurement to be a counting of the
number of times a chosen scale is used.



Why do we need to make a measurement?

Suppose you go to the market to buy mangoes and they are priced at say Rs.50
per kilogram. What would you expect the shopkeeper to do? Would you be happy
if he/she gives you 4 or 5 small mangoes, which are surely less than a kilogram, and
asks for the price of one kilogram? Similarly, the shopkeeper will also not like to
give you more than a kilogram of mangoes for the price of a kilogram. An accurate
measurement is desirable for both buyer and the seller. The absence of a suitable
measurement may lead to conflicts between them. Measurement is an essential activity
in our everyday life. You may ask why it is essential. Can’t we do without it?

Have you ever wondered how space scientists make sure that the space shuttle
reaches the desired destination? Or when the shuttle comes back it comes at a
predetermined time and place. This is made possible by accurate measurement of
many parameters and extensive calculations. For measurement, we require a specific
scale which is called a unit.

What is a Unit?

Imagine a situation. Suppose you are blindfolded and handed a bunch of currency
notes. On counting them you find that they are 46 in number. Can you tell me how much
money is in your hand? For knowing the exact amount of money, you need to know
the denomination i.e., whether the notes are of Rs.10, Rs.50, Rs100, or of some other
denomination?

Similarly, if you are told that two trees are 100 away from each other. How would
you interpret it? Are the trees 100 cm, 100 ft, or 100 m or....away? These examples
suggest that the result of every measurement must be expressed in such a way that
it makes sense and has a unique meaning. For this, we need to know two things.
Firstly, what is the measuring standard used, say centimeter (cm), meter (m), or foot
(ft) in the above example and the number of times it is used.

The result of measurement of a physical quantity is expressed in terms of a value.
The value of the physical quantity is equal to the product of the number of times
the standard is used for the measurement and the quantity (the standard) defined for
making the measurement. This defined or standard quantity i.e., the scale used e.g.,
meter or the foot in the above case, is called a unit.

Value of physical quantity = numerical quantity x unit
A unit is a measure, device, or scale in terms of which we make the physical
measurement. The value of a physical quantity consists of two parts; a numerical
quantity and a unit and are equal to their product.

Thus, it is necessary to state the numerical quantity as well as the unit while expressing
the result of a measurement. So by now, we know that the measurements are essential
in every sphere of human activity and also that we need a unit or a standard in terms
of which we make the measurement and express the result of such a measurement.
Let us learn about the characteristics of such a unit. What qualities should a unit have?

Characteristics of a Unit
Can we measure the distance in kilograms? Obviously not; it is ridiculous to measure
distance in terms of the kilogram. It has no relevance for measuring distances. So to be
useful, a unit should be relevant for the quantity being measured. Further, the unit
used should be convenient also. Would it be convenient to express the distance
between two cities in inches? Don’t you think that kilometer would be a better unit?
In addition to being relevant and convenient, a unit should also be well defined i.e.
it should be well understood by other people. For example, we may express the
distance between my house and a nearby shop as 200 steps. To make some
sense, we need to define the step - whether it is my step or an adult and child. Is
it while walking slowly or while running fast? How long is the step? Thus, to be useful,
a unit must be:

1. Relevant
2. Convenient
3. Well defined

In today’s world, an accurate measurement is necessary. We have numerable
devices to make such measurements. You would be surprised to know that an atomic
clock is so accurate that it may make an error of just one second in about 15 million
years. Have you ever thought about how our ancestors made measurements? What were
the devices used and what the units of measurement? Let us try to learn about the
interesting way measurements were made and also the way the system of measurement
has evolved since then. However, why don’t you assess your understanding of the
meaning and need for measurement and about the units and their characteristics?

HOW DID OUR ANCESTORS MAKE MEASUREMENTS?

The need for measurement and measuring devices dates back to antiquity. When the
humans became civilized, started cultivating and living in communities they realized
that one cannot do everything and they need to be interdependent. This paved the
way for trade and then probably a need for a measure was felt. Various ways of
measurements were adopted. The system of measurement has evolved a lot since
then. Let us have a brief account of the interesting means of measurement used by our
forefathers.


The recorded history shows ample evidence that the different parts of the human
body were used as a point of reference while making measurements. Some of these
were digit: the width of a single finger; foot: the length of a foot; cubit: length of
an arm; hand span: the distance between the tip of the thumb and the tip of the
little finger when the hand is fully stretched out. similarly, fathom meant the distance between the ends of the hands of an Anglo-Saxon farmer when his arms were fully
outstretched. It is interesting to note that these are still used sometimes.

Certain historical units were based on the things around us, e. g., Romans used a
a unit called pace which was equal to the stride of their army contingent and they called
the distance traveled by it in 1000 paces to be equal to a mile. Similarly, the grain
was used as the unit of mass in the sixteenth century and was equal to the weight of
a wheat grain.

Need for a standard unit

As you would have concluded from the activity given above, the units based on parts
of the human body are arbitrary and inaccurate. The results of the measurements vary
from person to person because the size of the unit is different for a different person. For
example, the units like a cubit or a foot would depend on the person making
the measurement. This created problems in trade between different countries and
obviously in the day to day transactions. To overcome the limitations of body
parts as units, and to bring about uniformity in the measurement system, the need
for exact measurement was felt. For this, a standard of measurements had to be
developed which is acceptable to everybody.

The problem of measuring lengths accurately was first solved by the Egyptians as far
back as 3000 B.C. It was done by defining the standard cubit. It was defined
to be equal to the distance between the elbow and tip of the middle finger of the
Pharaoh ruling Egypt at that time. Measuring sticks of length exactly equal to that
of standard cubit were made. In this way, they made sure that the cubit was the same
length all over Egypt. Similar efforts were made by other rulers also. For example,
the British King Henry-I (1100-1137) decreed that a yard would exactly be equal
to the distance from the top of his nose to the end of his thumb on an outstretched arm.
Queen Elizabeth-I declared a mile to be exactly equal to eight furlongs. A furlong
(furrow long) was the distance a pair of oxen could plow in a field without stopping
to rest. It was found to be 220 yards.

These standards proved to be useful but were short-lived, as once a given ruler went
out of power or died, the system was not followed and a newer system came into
being. Further, since different countries and the different provinces in a given country
were governed by different rulers; they followed different systems of units. As a
consequence, by the eighteenth century, a large number of units for mass, length, area, and volume came to be in widespread use. Let us now learn about the systems of
units followed in India in different historical periods.

Indian measurement system

The measurement system in India also has evolved a great deal from ancient times.

1. Indian measurement system in the ancient period

In ancient periods in India, the lengths of the shadows of trees or other objects were
used to know the approximate time of the day. Long time durations were expressed in terms of the lunar cycles, which even now is the basis of some calendars. Excellent
examples of measurement practices in different historic periods are available. For
example, about 5000 years ago in the Mohenjodaro era, the size of bricks all over
the region was the same. The length, breadth, and width of bricks were always in the
ratio of 4:2:1 and taken as a standard.

Similarly around 2400 years ago during the Chandragupta Maurya period, there was
a well-defined system of weights and measures. The government at that time ensured
that everybody used the same weights and measures. According to this system, the
smallest unit of length was 1 Parmanu. Small lengths were measured in angels. For
long distances, Yojana was used. One Yojana is roughly equal to 10 kilometers.

Different units of measurements used in the period of 
Chandragupta Maurya


The Indian medicine system, Ayurveda, also had well-defined units for the measurement
of mass and volume. The measurement system was strongly followed to ensure
the proper quantity of medicine for a particular disease.

2. Indian measurement system in the medieval period

In the medieval period also the measurement system was in practice. As described
in Ain-i-Akbari by Abul Fazl-i-Allami, during the period of Moghul Emperor Akbar,
the gas was used as the unit of measuring length. Each gas was divided into 24 equal
parts and each part was called Tassuj. This system was extensively used to measure
land pieces, for the construction of buildings, houses, walls, gardens, and roads. You
should know that gas was widely used as a unit of length till the metric system
was introduced in 1956. Even today in many parts of our country, particularly in rural areas, gas is being used as a unit of length.

3. Indian measurement system during the British period

To bring about uniformity in the system of measurement and the weights used,
several efforts were made during the British period. The British rulers wanted
to connect Indian weights and measures to those being used in Great Britain at that
time. During this period the inch, foot, and yard were used to measure length whereas grain, ounce, pounds, etc. were used to measure mass. These units and weights were
used in India till the time of Independence in 1947. The essential units of mass used
in India included Ratti, Masha, Tola, Chhatank, Seer, and Maund. Ratti is a red
seed whose mass is approximately 120 mg. It was widely used by goldsmiths and
by practitioners of the traditional medicine system in India.

The relation between various units of mass used during the British period

8 Ratti                            =                           1 Masha
12 Masha                      =                           1 Tola
5 Tola                             =                           1 Chhatank
16 Chhatank                 =                           1 Seer
40 Seer                          =                           1 Maund
1 Maund                        =                           100 Pounds troy (exact)

THE MODERN MEASUREMENT SYSTEMS

Immediately after the French Revolution (1790) the French scientists took lead in
establishing a new system of weights and measures. They advocated the establishment
of national standards for the purpose and the use of a decimal arithmetic system. This
led to the birth of the metric system which like our Hindu-Arabic counting system is based
on the multiples and subdivisions often.

The meter was defined as one ten-millionth (1/107) of the distance between the north pole to the equator on the meridian running near Dunkirk in France and Barcelona in Spain.

After detailed deliberations, the basic unit of length and
mass were defined and their working standards were
prepared. The working standard for the meter was prepared
by marking two lines a meter apart, on platinum-
iridium bar. Similarly, the platinum-iridium cylinder was
constructed, equal to the mass of 1 cubic decimetre of
water, as the working standard for mass. These two
standards have been preserved at the International Bureau of Weights and Measures
at Serves near Paris. The copies of these were prepared and sent to different
countries. As regards the time, the concept of the hour, minute, and second based on the rotation of the earth was retained. An international treaty, called Metre Convention
was signed in 1875 to follow the metric system throughout the world for trade and
commerce.

In the course of the development of units, several systems were adopted. Two
systems that were extensively used were the cgs and mks systems. The cgs system
was based on centimeter, gram, and second as the units for length, mass, and time
while the mks system used meter, kilogram, and second for the same. In 1958 it was
realized that the units defined as standard needed to be redefined. Since 1983, it
is defined as the length of the path traveled by light in a vacuum in 1/299,792,458 of
a second. The new exercise of redefining the system of units led to the birth of the SI
system of units which is currently the system in use. Let us learn the SI system in
detail.