Chapter 3: Scales and Direction
A survey sheet is spread flat on a table, held down at the corners. On it a river winds between low hills, a metalled road crosses the river at a causeway, and a scatter of small village squares sits along that road. Two students have been given one plain question: how far is it from the village to the causeway, and in which direction must a person walk to get there? Neither answer can be lifted off the paper directly. The river on the sheet is a few centimetres of blue ink, while on the ground it is kilometres of water. The road on the sheet is a thin line that bends five times, and a ruler laid straight across it measures the shortcut, not the walk. North on the sheet is a printed arrow, while north on the compass in the students’ hands is a needle that settles a little to one side of that arrow. So the sheet has to be translated. Every map is a shrunk copy of real ground, and the amount it has been shrunk by is its scale. Every map also fixes a direction, and the direction it fixes is not quite the one a compass finds. Handle both, and a flat sheet of paper begins to describe real country.
Diagram
Fig. 3.A1 Caption: A map answers two questions at once — how far, and which way. Brief: Draw a small map panel showing two marked points joined by a bending road; below it place a linear scale bar with primary divisions on the right of zero and secondary divisions on the left, and beside it a compass rose with the eight cardinal points labelled; label the panel ‘how far’ against the scale bar and ‘which way’ against the rose.
3.1 Scales
A map represents the features of the surface of the earth in a miniature form. The ground cannot be carried into a classroom, so it is shrunk until it fits on a sheet of paper. For that shrinking to be honest, every part of the map must be reduced by the same amount, and the map must therefore be drawn to scale.
The scale of a map denotes the proportion that the distance between any two points on a map bears to the distance between the same two points on the surface of the earth. It can also be defined as the ratio between the distance of any two points on the map and the actual distance of the same points on the ground. Expressed as a ratio, it is written as:
\[\text{Scale} = \frac{\text{Map distance between two points}}{\text{Ground distance between the same points}}\]
Here the map distance is measured on the paper, usually in centimetres or inches, and the ground distance is the real distance between the same two places, usually in kilometres or miles. The scale is the single number that ties the two together. Without it, a line on a map is only a line; with it, that line becomes a measured distance on real ground.
3.1.1 Types Of Scale
There are three main methods of representing the scale on a map. (a) A statement states the scale in words, so that the reader is simply told how much ground one unit of map length stands for. (b) A linear or graphic scale draws the scale as a straight line divided into equal parts, so that distances can be read off it directly. (c) A representative fraction writes the scale as a pure ratio of map distance to ground distance, with no units attached to it at all.
The three are three ways of saying the same thing, and a single map often prints more than one of them. Their differences lie in how easily they can be used, and in what happens to them when the map itself is copied at another size.
Flowchart
Fig. 3.A2 Caption: The same scale can be written in three ways, and each one is read differently. Nodes: Scale of a map → three methods of representing it → statement → written in words, such as 1 cm to 1 km → read by converting units; and → linear or graphic scale → drawn as a divided line, primary divisions right of zero and secondary divisions left of zero → read directly off the line; and → representative fraction → written as a ratio with the numerator one, such as 1:1,00,000 → read in any unit, provided both sides use the same unit
The Statement Scale
In the method the book calls ‘a statement’, the scale is stated in words, or we make a statement about it. Two examples of such a statement are 1 cm to 1 km, and 1 inch to 5 miles. The value on the left hand side usually represents the map distance, and the value on the right represents the matching distance on the ground.
This method is not suitable, for two reasons. The first is that we are required to know the units of measurement used in different countries, and a reader who does not work in inches and miles cannot use a statement written in them. The second is that when the map is reduced or enlarged from the original, the scale does not remain the same, while the printed words go on claiming that it does. This creates problems in measurement.
The Linear Or Graphic Scale
In this method, the scale is represented by a straight line divided into equal parts, primary and secondary, to show what these markings represent on the actual ground. The primary divisions are the major divisions on the scale, graduated from left to right from the zero mark. The secondary divisions are smaller units, graduated from right to left on one primary division, that is, on the single division placed to the left of the zero.
The two sets of markings work together. Whole units are read to the right of the zero using the primary divisions, and the leftover part of a distance is read to the left of the zero using the finer secondary divisions. This is why the zero of a linear scale is never at its extreme left end.
Figure 3.1 shows such a scale. The total length of this linear scale represents a distance of 25 kilometres. Each primary division denotes a distance of 5 kilometres, and each secondary division denotes a distance of one kilometre on the actual ground.
Diagram
Fig. 3.1 Caption: Scale represented by graphical method. Brief: Reproduce the printed linear scale bar labelled ‘Linear Scale - 1:1,00,000’, with primary divisions marked 0, 5, 10, 15, 20 and 25 to the right of zero and secondary divisions marked 5, 4, 3, 2, 1 to the left of zero, the two groups labelled ‘Secondary Divisions’ and ‘Primary Divisions’ with arrows as printed.
The Representative Fraction
In this method, the scale is represented as the ratio of the length of a line on the map and the corresponding actual distance on the earth’s surface. The numerator is always expressed as unity, that is, one unit of map distance is equivalent to a number of units of ground distance. This fraction is called the Representative Fraction, written in short as R.F.
\[\text{R.F.} = \frac{\text{Distance on the map}}{\text{Distance on the ground in the same unit}}\]
The most important point in a Representative Fraction is that the unit of measurement of distances in the numerator and the denominator is the same. A fraction whose top and bottom are measured in different units is not yet a Representative Fraction, and must be converted before it can be reduced.
For example, if the R.F. of a map is 1/1,00,000 or 1:1,00,000, it means that one unit on the map represents 1,00,000 units on the ground. If the unit of measurement is centimetre, we will say that 1 centimetre on the map represents 1,00,000 centimetres on the ground. If, however, the unit of measurement is inch, then we will say that 1 inch on the map represents 1,00,000 inches on the ground.
The main advantage of R.F. is that it is only a fraction, and is independent of any particular unit of measurement. It can be converted into any unit of measurement and has universal application. It is therefore also known as the International Scale or the Natural Scale.
Working With The Three Forms
Because the three forms describe the same relationship, any one of them can be turned into any other. The three worked examples that follow show the conversion running in each direction, and every one of them begins from the same fraction.
The result says that one centimetre of paper stands for ten lakh centimetres of ground. The units have cancelled out of the fraction, and that is exactly what makes it usable: a reader working in inches would read the same map as one inch to ten lakh inches, without a single line being redrawn. The linear scale built from it in Figure 3.2(a) puts the same relationship on a line, so that distances can be lifted off it with no arithmetic at all.
Diagram
Fig. 3.2(a) Caption: Linear scale for Example 1. Brief: Reproduce the printed scale bar with primary divisions marked 0, 10, 20, 30, 40 and 50 km to the right of zero, one primary division of 10 km to the left of zero marked 10, and that left-hand division subdivided and marked 8, 6, 4, 2.
Notice that the awkward mixture of inches and miles has disappeared from the answer. The statement scale needed a reader who knew both units and the conversion between them, while the fraction needs neither. This is the practical value of the R.F., and it is why a map meant to be read outside the country that drew it prints one.
Diagram
Fig. 3.2(b) Caption: Linear scale for Example 2. Brief: Reproduce the printed scale bar with 0 at the zero mark, primary divisions marked 4 miles and 8 miles to the right of zero, one primary division of 4 miles to the left of zero subdivided into smaller parts, and the left-hand subdivisions labelled in inches.
The conversion therefore runs both ways. A fraction can be read out in words for a local reader, and a statement can be reduced to a fraction for any reader at all. What decides which form a printed map carries is not accuracy, since all three are equally exact, but convenience of use.
Diagram
Fig. 3.2(c) Caption: Linear scale for Example 3. Brief: Reproduce the printed scale bar with primary divisions marked 0, 5, 10, 15, 20 and 25 km to the right of zero, one primary division of 5 km to the left of zero, and that left-hand division subdivided and marked 4, 3, 2, 1.
Why The Graphical Method Is Preferred
The book adds a note at this point, and it is worth taking slowly. The graphical method is preferred to represent the scale of a map for two reasons. The first is that it combines both the R.F. and the verbal statement, since the line carries the ratio while its markings say in plain figures how much ground each part stands for. The second is that it remains valid if the map is reduced, enlarged, or if only a small portion of it is used.
That second reason is the deciding one. A printed statement and a printed fraction are only words and numbers, and they do not change when the paper is shrunk in a copier, so they quietly begin to lie. A linear scale is a drawing on the same sheet as the map, so it shrinks or stretches by exactly the same amount as everything else on it, and goes on telling the truth.
3.2 Measurement Of Distances On A Map
A scale is only useful once it is put to work. Having fixed how much ground one centimetre of paper stands for, the next task is to take a real distance off the sheet, whether that distance runs straight, bends along a river, or spreads out over an area of country.
The following methods are used to measure distances on a map. Which one is chosen depends entirely on the shape of the thing being measured.
Flowchart
Fig. 3.A3 Caption: The shape of what is being measured decides the method used. Nodes: Measurement on a map → is it a line or an area? → line → is the line straight or curved? → straight → paper strip marked with a pencil, or a divider → transferred to the linear scale; and → curved → paper strip folded at every bend, or a thread laid along the course, or an opisometer wheel run along it → transferred to the linear scale; and → area → grid square method → complete squares counted, part squares estimated, and the counts added
3.2.1 To Measure Distance Along A Straight Line
A ruler cannot be laid on the map and read off in kilometres, because the ruler is marked in centimetres and the answer is wanted in ground units. The distance is therefore first transferred to a strip of paper, and then compared with the linear scale, which already speaks in ground units.
The method has three steps, taken in order. (a) Place the straight edge of a strip of paper along the required line, so that the edge runs exactly from the first point to the second. (b) Mark the limits of the distance on the strip by means of a sharp pencil, keeping the marks fine, because a thick pencil line on a map stands for a wide band of real ground. (c) Place the strip along the linear scale, and measure the distance, reading whole units from the primary divisions and the remainder from the secondary divisions.
A divider can also be used to measure straight distances. Its two points are opened to sit exactly on the two places on the map, and the opened divider is then carried across to the linear scale and read there, without the distance ever having to be written down as a number of centimetres.
The answer, 2.5 km, is a distance on the ground, not on the paper, and this is the whole point of the exercise. Note also what it is a distance along: a straight line drawn between the two places, which is what a survey sheet calls the direct distance. If A and B are joined by a road that curves, a person walking between them covers more than 2.5 km, and the map has not measured that walk at all.
Diagram
Fig. 3.3 Caption: Scale — straight distance method. Brief: Reproduce the printed figure showing a map panel with points A and B joined by a straight line and a strip of paper laid along it, the strip marked at both points, and the same strip shown below placed against a linear scale marked 0 to 6 km with the scale stated as 2 cm = 1 km; label the reading obtained as 2.5 km.
3.2.2 To Measure Distance Along Curves
A river or a winding road cannot be measured in one straight reading, because a straight edge laid across a bend measures the shortcut and not the course. The strip of paper is therefore made to follow the curve, a little at a time.
To measure distances like the course of a river or a winding road, a straight edge of a paper can be used. First you mark the starting point on the strip of paper, and at every bend you hold the paper in place and fold the paper, carrying on in this way until the end of the course is reached. Now, by using the graphical scale, the actual distance on the ground can be calculated in miles, yards or kilometres.
Two other methods do the same job. (a) A winding road or a river course can also be measured by placing a thread along its course, so that the thread takes the shape of every bend; the thread is then straightened and measured against the linear scale to calculate the actual distance. (b) An opisometer is an instrument used to measure a road, a rail line or a river, and it does the folding and the counting mechanically instead.
The opisometer is a small spiked wheel that moves along the curved surface. Its one revolution is graduated on a scale, so that the wheel turning once stands for a known length of map. The revolutions are recorded manually or on a calibrated dial, and thus the distance can be measured.
Diagram
Fig. 3.4 Caption: Opisometer. Brief: Reproduce the printed photograph of an opisometer with its calibrated dial resting on a topographical sheet, with the spiked measuring wheel clearly visible at the base of the instrument.
3.2.3 Area By The Grid Square Method
Distance answers how far; area answers how much country. A forest, a field of cultivation or a built-up settlement covers a patch of the sheet, and its size is found by counting the squares of the grid that the patch sits on.
On topographical maps, each grid square measures 2 cm × 2 cm on the sheet, or 1 km × 1 km on the ground, since 2 cm is equal to 1 km at this scale. Therefore, the area of each square is 1 sq. km, that is, the area of a square measuring one kilometre along each side. The grid does the arithmetic in advance: every whole square counted is one square kilometre added.
The difficulty is that a real patch of forest does not end tidily at a grid line. Its edge cuts across squares, leaving parts of squares to be accounted for, and these have to be estimated by eye.
To calculate a certain area on a topographical map, the following steps are involved. (a) Find out the number of complete grid squares within the area. (b) Note the number of remaining squares within the area which are not complete squares; if the squares covered are more than half, take them to be two-thirds squares, and if less than half, take them as one-third squares, and count them. (c) Add all the squares to get the area of the portion required.
In Figure 3.5, the forested area enclosed can be calculated in the following manner.
That last line matters more than the figure above it. The 4 sq. km of complete squares is exact, but everything after it rests on a judgement made by eye about how much of a square the forest fills. Another student working carefully on the same extract might reach 8 or 9 sq. km, and neither would be wrong. An area read off a grid is an estimate with a range around it, and it should be quoted as one.
Map
Fig. 3.5 Caption: Area by grid square method. Brief: Reproduce the printed topographical sheet extract covering eastings 67 to 71 and northings 24 to 28, ruled into grid squares of 2 cm each representing 1 sq. km, with the forested patch outlined; the complete squares numbered 1 to 4 and the part squares marked with their fractions must be legible, along with the labelled protected forest, the rocky knobs, the spot height 1425 and the water body named on the extract.
3.3 Direction
Direction forms an important element of a map. It helps us in locating a place, because a distance alone is never enough: a village 3 km away could lie anywhere on a circle drawn around you, and only a direction fixes which point on that circle it is.
Knowledge of directions is obtained from the rotation of the earth. The earth rotates on its axis, which is the imaginary line it spins about. The northern end of its axis is called the North Pole and its southern end is known as the South Pole. These two fixed points give the whole system its starting reference, and every direction on every map is measured from them.
Any two points lying on the line joining these poles are said to be in the north and south of each other. Any line at right angles to the north-south line indicates the east-west direction. Thus, we have four main directions, that is, North, South, East and West, and these four main directions are called Cardinal Points.
There is another set of four directions lying between these Cardinal Points. They include the following. (a) North-East (NE) lies between North and East. (b) South-West (SW) lies between South and West. (c) North-West (NW) lies between North and West. (d) South-East (SE) lies between South and East.
Together these make the eight points shown in Figure 3.7(b), which is the set used for marking directions between locations on a map.
Diagram
Fig. 3.7(a) Caption: Earth showing North Pole and South Pole. Brief: Reproduce the printed globe with the North Pole and South Pole labelled at the ends of the axis, the Equator marked across the middle, and the tilt of the axis marked 23.5° as printed.
Diagram
Fig. 3.7(b) Caption: Eight cardinal points. Brief: Reproduce the printed compass rose with N, NE, E, SE, S, SW, W and NW labelled around the ring and their angles marked as printed — N 360°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270° and NW 315° — with the star points radiating from the centre.
The direction of a line is described by the angle it makes with the North, measured in the clockwise direction. Thus, direction is a relative term: it is always the direction of one thing from another, and it changes the moment you change the point you are standing at. Direction can be found with the help of the following.
3.3.1 Bearing
Direction can be indicated by a system of angular bearing, which replaces the eight named points with a precise angle. Bearing is the horizontal angle between the North and the line joining the position of the observer and the object, measured in a clockwise direction.
In Figure 3.6, X is the position of the observer. The line XY connects the object Y with X and makes a clockwise angle of 75° with the north-south line, NS, passing through the observer. Thus, the bearing of the object Y with reference to the observer X is 75°.
Because a bearing is measured from one end of a line, the same line gives two different readings. The bearing from the observer to the object is called Forward Bearing, written FB. The bearing from the object to the observer is called Backward Bearing, written BB. Bearing of a line pointing towards East is 90° and that of a line pointing towards N.E. is 45°.
The two readings are linked by a simple rule, in which every quantity is an angle measured in degrees:
\[\text{BB} = \text{FB} + 180 \quad \text{(if FB} < 180) \qquad \text{BB} = 360 - \text{FB} \quad \text{(if FB} > 180)\]
We can locate any point on the map from a fixed point if its distance and bearing are known. This is what makes bearing worth the extra arithmetic: distance drawn a circle around the observer, and the bearing picks out the single point on that circle.
Diagram
Fig. 3.6 Caption: Bearing. Brief: Reproduce the printed figure with the observer at X, the north-south line NS drawn through X, the object Y to the right, the clockwise angle from North to XY marked 75° and labelled FB, and the return direction labelled BB, with all angle values shown exactly as printed.
Two kinds of bearing are distinguished by the north they are measured from. A bearing with reference to the magnetic north-south line is called magnetic bearing, and one with reference to the true, or geographic, north-south line is called true bearing. The difference between them is the subject of the next part of this chapter.
3.3.2 Magnetic North And True North
The Magnetic Compass is an instrument used to find directions. The north to which the compass needle points is called Magnetic North. When there are no magnetic substances near the magnetic compass, its needle points to the magnetic north, which is why a compass reading taken beside an iron gate or a parked vehicle cannot be trusted.
Magnetic North differs from the Geographic or True North. True North is the direction indicated by the North Star. On a globe, all the lines of meridian, which are the lines of longitude running from pole to pole, converge towards the True North. A map is drawn on the true north-south line; a compass needle answers to the magnetic one.
The angle between the true north-south line and the magnetic north-south line is known as Magnetic Declination. Magnetic North is not fixed but moves slowly from time to time, and this results in variation of the magnetic declination. Hence, it is also called magnetic variation.
The angular difference between Magnetic North and True North varies from place to place and from time to time. These variations are the same while travelling in a certain direction. Lines that are drawn joining the points of similar variations between the magnetic north and the true north are called Isotonic lines.
Hence, True North at a place can easily be found if the Magnetic North is found and the magnetic declination is known. The declination is simply added to or taken from the compass reading, and the correction turns a magnetic bearing into a true one.
The two numbers, 125° and 110°, describe exactly the same line on the ground. Only the north they are counted from has changed. This is why a walker who takes a bearing off a printed map and then follows it on a compass without correcting for declination will drift steadily off course, and the drift grows with every kilometre walked.
Diagram
Fig. 3.8 Caption: Magnetic bearing and true bearing. Brief: Reproduce the printed figure with the observer at X and the point Y to the right, MN drawn as the Magnetic North arrow and TN as the True North arrow, the angle from MN to XY marked 125° and the angle from TN to XY marked 110°, with both arrows springing from X.
Flowchart
Fig. 3.A4 Caption: A single line on the ground can be read against three different norths. Nodes: A line joining observer and object → measured from Magnetic North → magnetic bearing → apply the magnetic declination → measured from True North → true bearing → compare with the straightened meridians drawn on the map → measured from Grid North → grid variation
3.3.3 Grid North And Grid Variation
A third north appears the moment a curved earth is printed on a flat sheet. Semi-circular lines of longitude are assumed to be straight when they are represented in maps, because a flat page cannot hold lines that curve towards a point.
The North so represented is Grid North. It differs from True North due to the spherical shape of the earth, since straightening the meridians must tilt them slightly away from the direction in which they really converge. The variation between the Grid North and True North is called Grid Variation.
Diagram
Fig. 3.9 Caption: Grid North and True North. Brief: Reproduce the printed figure showing a shaded hemisphere with the curved meridians converging on TN at the top, the straight vertical grid lines marked GN across the sheet, and the key box reading ‘TN True North’ and ‘GN Grid North’ as printed.
Three norths therefore sit on one sheet of paper: the north the needle finds, the north the earth turns about, and the north the printed grid draws. They agree closely, but they do not agree exactly, and a direction is only fully stated once it is said which of the three it was measured from.
3.4 Summary
- A map represents the features of the surface of the earth in a miniature form, so it must be drawn to scale if it is to describe real ground.
- The scale of a map denotes the proportion that the distance between two points on the map bears to the distance between the same two points on the earth’s surface, and is written as map distance divided by ground distance.
- There are three main methods of representing the scale on a map.
- A statement gives the scale in words, such as 1 cm to 1 km or 1 inch to 5 miles, with the map distance usually on the left.
- A linear or graphic scale is a straight line divided into primary divisions, graduated left to right from zero, and secondary divisions, graduated right to left on one division placed left of zero.
- A Representative Fraction gives the scale as a ratio with the numerator always unity, and both numerator and denominator measured in the same unit.
- A statement scale is not suitable, because the reader must know the units used in different countries, and because the scale no longer holds when the map is reduced or enlarged.
- The main advantage of R.F. is that it is only a fraction and is independent of any particular unit of measurement, which is why it is also called the International Scale or the Natural Scale.
- The graphical method is preferred for two reasons.
- It combines both the R.F. and the verbal statement in a single device.
- It remains valid if the map is reduced, enlarged, or if only a small portion of it is used.
- A straight distance is measured by laying a paper strip along the line, marking its limits with a sharp pencil and reading the strip against the linear scale; a divider may be used instead.
- A curved distance, such as a river course or a winding road, is measured by folding a paper strip at every bend, by laying a thread along the course, or by running an opisometer wheel along it.
- On a topographical map each grid square measures 2 cm × 2 cm, or 1 km × 1 km on the ground, so each square has an area of 1 sq. km.
- Area by the grid square method is found in three steps, and the result is an approximation.
- Count the complete grid squares within the area.
- Count the incomplete squares, taking those more than half covered as two-thirds squares and those less than half covered as one-third squares.
- Add all the squares together to get the area of the portion required.
- Knowledge of direction comes from the rotation of the earth, whose axis ends at the North Pole and the South Pole, giving the four Cardinal Points of North, South, East and West.
- Between the Cardinal Points lie North-East, South-East, South-West and North-West, making the eight cardinal points used for marking directions on a map.
- The direction of a line is the angle it makes with the North, measured clockwise, so direction is a relative term that depends on where the observer stands.
- Bearing is the horizontal angle, measured clockwise, between the North and the line joining the observer to the object.
- The bearing from the observer to the object is the Forward Bearing, and from the object to the observer the Backward Bearing.
- BB = FB + 180 if FB is less than 180, and BB = 360 − FB if FB is greater than 180.
- Any point can be located from a fixed point once its distance and bearing are known.
- The magnetic compass needle points to Magnetic North, while True North is the direction indicated by the North Star, towards which all lines of meridian converge on a globe.
- The angle between the true and the magnetic north-south lines is the Magnetic Declination, also called magnetic variation, and lines joining places of equal variation are Isotonic lines.
- Magnetic North moves slowly over time, so the declination varies from place to place and from time to time; a magnetic bearing of 125° with a variation of 15° West gives a true bearing of 110°.
- Lines of longitude are drawn straight on a flat map, and the north so represented is Grid North; its difference from True North, caused by the spherical shape of the earth, is called Grid Variation.
Flowchart
Fig. 3.A5 Caption: A map answers two questions, and each is answered by its own chain of steps. Nodes: A map sheet → two questions → how far and how much? → read the scale, given as a statement or a linear scale or an R.F. → straight line → paper strip or divider against the linear scale; and curved line → folded strip, thread or opisometer against the linear scale; and area → grid squares counted, complete squares plus part squares → ground distance or area obtained; and → which way? → measure the angle clockwise from North → eight cardinal points, or an exact bearing in degrees → but from which North? → Magnetic North from the compass needle → apply the magnetic declination → True North from the North Star and the converging meridians → apply the grid variation → Grid North from the straightened meridians printed on the map
What This Chapter Cannot Tell You
A scale tells you how far, and nothing else. Two places 5 km apart on flat plain and 5 km apart across a steep ridge give the same reading, and the map’s linear scale has no way of saying which walk is harder or how long it will take.
An area read off the grid is an estimate, not a measurement. Only the complete squares are exact; everything after them rests on a judgement made by eye, which is why the chapter itself marks the total as an approximation.
A bearing fixes a direction, not a route. It tells you which way the object lies, but not whether a river, a wall or a forest stands between you and it. And because Magnetic North moves, a declination printed on a sheet is true for the year that sheet was drawn, and slowly stops being true afterwards. ## 3.5 Check Your Concepts
- Look at Figure 3.1. Each primary division stands for 5 km and each secondary division for 1 km.
- Explain why the zero of a linear scale is not placed at the extreme left end of the line.
- Describe how you would read a distance of 13 km off this scale, saying which side of the zero you would use for each part of the reading.
- In Figure 3.6 the forward bearing of the object Y from the observer X is 75°. Using the rule given in this chapter, work out the backward bearing of X from Y, and explain why the same straight line gives two different bearings.
- A winding river runs across a map. Describe, step by step, how you would find the true length of its course on the ground, and explain why a ruler laid straight between its two ends would give a smaller answer.
- The chapter works out the forested area in Figure 3.5 as 8.5 sq. km and then calls the answer an approximation.
- Which part of that calculation is exact, and which part is not?
- What would have to change about the map or the method for the answer to become more reliable?
- Explain magnetic declination with the help of a diagram.
- Why are ‘True North’ and ‘Grid North’ different?
3.6 Practice with Numericals
- Convert the following statements into R.F.
- 25 cm on the map = 5 km on ground.
- 2½ inches on the map = 5 miles on ground.
- 7 cm on the map = 63000 metres on ground.
- 5 cm = 500 metres.
- 15 cm = 6 km.
- On the map of India the cartographer forgot to draw the scale of the map. A student who knows the distance between Meerut and Delhi (70 km) was asked to complete the scale. How will the student draw the scale if the distance between Delhi and Meerut on the map measures 5 cm? Give the procedure, draw the scale and find out the R.F.
3.7 Case-Based Questions
- The map given in the chapter shows the houses of four friends A, B, C and D. Using the main road and the kutcha road, find the distances needed to answer the following.
- Which child would reach school first if A, B and C all leave their houses at the same time and walk at the same speed?
- Which child lives closest to the school, according to the road distance?
- How far must D walk to reach the village well?
- How far is B’s house from the bus depot?
- How much distance will C have to walk to reach the railway station?
- In what direction is C’s house from the school?
- Study the map extract given in the chapter and answer the following.
- Find the area in sq. km of the area enclosed within the Eastings 64 to 64 and Northings 32 to 35.
- Find the compass direction of the following.
- Gulabganj from Pithapura
- Pamera from Malgaon
- Moti Talao from Sirori
- Sirori from Pamera
- Find the direct distance of the metalled road from the Post Office at Pamera till it intersects with National Highway NH 168 in grid square 6432.