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Chapter 2: Geographic Grid: Latitudes and Longitudes

At half past five one morning, two cousins begin a phone call. One of them is in Assam, in the far east of India. Her window is already bright, the sun cleared the horizon a while ago, and the day has begun in the street below. The other is in Gujarat, in the far west. His window is still dark and the street lamps outside are on. Both are looking at exactly the same time on their phones. Neither clock is wrong, and neither of them has misread it. The sun is simply not overhead at the same moment in both places, because the earth turns from west to east, and the east meets the sun first. A second surprise is waiting for them further along the same idea. If the cousin in Assam could keep travelling east — past Japan, out across the Pacific — she would cross an invisible line drawn through open ocean, and on crossing it the date on her calendar would change, even though her journey had not paused for a night. Neither of these things is an accident of clocks or of calendars. Both follow from a framework of imaginary lines drawn across the globe, lines that let us say exactly where a place is, how far it lies from the Equator, and what the time is there at this moment.

Map

Map 2.A1 Caption: A single meridian at 82°30’E sets the clock for the whole of India, from Gujarat in the west to Assam in the east. Brief: Outline map of India showing the full extent of India as officially defined; draw the 82°30’E meridian as a bold north–south line; label Mirzapur near Allahabad (Prayagraj) where it crosses; label Gujarat in the west and Assam in the east; key to show the standard meridian only; no other longitudes, no state boundaries, no relief.

NoteCuriosity Corner

Q1. Why can two places in the same country see the sun rise hours apart and still keep exactly the same clock time? Q2. What is special about the line of longitude at 82°30’E, and why was that particular line chosen for India? Q3. Why does the date on the calendar change when a traveller crosses the 180° line in the Pacific? Q4. Every parallel of latitude is a full circle, so why is the Equator the only latitude that counts as a great circle? This chapter will answer all four.

2.1 The Geographic Grid

Why The Earth Needs Imaginary Lines

The earth’s surface is vast, and almost all of it looks the same from above — ocean, plain, forest, ice. A place carries no natural address of its own. Unless we use a mathematical method, it is impossible to say exactly where a place lies on this surface.

For this reason, imaginary lines are drawn on the globe. They exist on the globe and on the map, never on the ground. No traveller has ever walked over one of them, and yet every ship, aircraft and weather station depends on them.

The lines running east to west, parallel to the Equator, are called lines of latitude. The lines running north to south, passing through the poles, are called lines of longitude. Where a latitude and a longitude cross, they pinpoint a single place on the earth’s surface, and no other place shares that crossing point.

Q. Why do we need two sets of lines, and not one?

A. A single line such as 19°N carries thousands of places along its whole length. Only a second line crossing it narrows the answer to one point.

These criss-crossing lines together form a framework known as the Geographic Grid. Eratosthenes, the Greek philosopher who had for the first time calculated the circumference of the earth, devised lines of latitude and longitude in order to locate places on it.

The Grid And The Graph Page

This grid on the globe or on the map serves the same purpose as the system of coordinates on the x-axis and the y-axis of a graph paper. A coordinate pair is not a description of a point; it is an instruction for finding it. The earth’s grid works in exactly the same way. In this case the x-axis is represented by lines of latitude, which run horizontally, and the y-axis by lines of longitude, which run vertically. Fig. 2.1 shows the two sets of lines wrapped around the globe.

Diagram

Fig. 2.1 Caption: The Geographic Grid Brief: Globe showing latitude lines circling east to west and longitude lines running pole to pole; label the Prime Meridian at 0° at the base, mark East (+) to the right and West (−) to the left, and number the meridians 30, 60, 90, 120, 150 and 180 across the top.

Fig. 2.1 The numbers around the globe count degrees of longitude away from the Prime Meridian, marked 0°, running east as plus and west as minus. Notice how the meridians crowd together towards the top, near the pole. The figure shows only every thirtieth line, so it cannot show you how closely the full set of lines actually packs together.

2.2 Lines Of Latitude

The first half of the grid is the set of lines that run east to west. Five short statements fix what a latitude is, and each of them is worth reading slowly. (a) Lines of latitude are the imaginary lines joining all places having the same latitude towards north or south of the Equator. (b) A latitude is the angular distance of a place north or south of the Equator. (c) A latitude is marked in degrees, and the Equator itself is 0 degrees. (d) Latitudes are calculated according to the angle a place makes with the centre of the earth. (e) Since the lines of latitude are parallel to the Equator and to each other, they are called parallels of latitude. (f) Each parallel of latitude is a full circle, but only the Equator is a great circle.

The word ‘angular’ in point (b) is the one that does the work. To find the latitude of a place, draw a line from that place to the centre of the earth, and a second line from the centre out to the Equator. The angle between those two lines, measured in degrees, is the latitude of the place. This is why latitude is not measured in kilometres in the first place — it is an angle, and only afterwards is that angle turned into a distance. Fig. 2.2 (a) shows the measurement being taken from the Equator, north and south.

Diagram

Fig. 2.2 (a) Caption: Latitude degrees are measured from the Equator to its north or south Brief: Globe with the Equator marked 0°N as a dashed line and parallels drawn above it at 19°N and 30°N; label each parallel at the left edge; show the parallels as complete circles narrowing towards the top of the globe.

Lines That Shrink Towards The Poles

The parallels are drawn around a sphere, so they cannot all be the same size. The lines of latitude are not of equal length, and they become smaller as we move towards the poles. At 60° latitude, in each hemisphere, the length of the circle is half the length of the Equator.

Follow that shrinking to its end and the circle disappears altogether. At the poles these lines are just points or dots. A parallel drawn at 90° has no length at all, which is why the North Pole and the South Pole are places rather than lines.

2.2.1 Main Latitudes

There are 181 parallels of latitude at 1° interval. The count is easy to check: 90 parallels north of the Equator, 90 south of it, and the Equator itself, giving 181 in all. Seven of these carry names, because each one marks something the earth actually does. (a) The Equator is the longest line of latitude and it represents 0° latitude. (b) The North Pole (90° N) is located at an angular distance of 90° north of the Equator. (c) The South Pole (90° S) is located at an angular distance of 90° south of the Equator. (d) The Tropic of Cancer (23½°N) is a line of latitude located 23½° north of the Equator. (e) The Tropic of Capricorn (23½°S) is a line of latitude located 23½° south of the Equator. (f) The Arctic Circle represents 66½°N latitude, and it marks the limit of the north polar region surrounding the North Pole. (g) The Antarctic Circle represents 66½°S latitude, and it marks the limit of the south polar region around the South Pole.

2.2.2 Northern And Southern Hemisphere

The Equator runs midway between the poles, and in doing so it divides the earth into two equal halves. These two halves are known as the Northern Hemisphere and the Southern Hemisphere. Neither is larger than the other, because the dividing line is drawn exactly halfway.

The poles, the North Pole and the South Pole, are opposite to each other at the extreme ends of the sphere. They are each located at 90° angular distance north and south of the Equator, which is the largest angular distance any place on the earth can have.

The length of the Equator is equal to the circumference of the earth, or 40,075 km. Since the circumference of a circle is equal to 360°, the 1° angular distance is roughly equal to 111 km. That single figure is what allows an angle on a globe to be converted into a distance on the ground.

One Degree Is About 111 Kilometres Evidence: The Equator is the earth’s full circumference, measured at 40,075 km. Reasoning: A complete circle contains 360°, so one degree covers 40,075 km divided by 360, which is roughly 111 km. Limit: This holds along the Equator and along a meridian. It does not hold between two longitudes elsewhere, where the lines draw closer together.

2.2.3 Uses Of Latitudes

The lines of latitude form one of the two coordinates of the grid system, and they are put to three uses in this chapter. (a) To find the location of a place. Latitudes give us the location of a place north or south of the Equator, and such a location is known as an absolute location, because it does not depend on where the reader happens to be standing. (b) To measure the distance of a place. Distances are calculated with reference to the Equator at right angle to the place, so we can measure the distance of any place from the Equator based on its degree of latitude. (c) To divide the earth into heat zones. Besides helping us to locate places on maps and charts, the lines of latitude divide the earth into distinct heat belts.

Turning Degrees Into Kilometres

Use (b) rests on a single piece of arithmetic. Once the 111 km value is known, the distance of any place from the Equator follows directly from its latitude:

\[\text{Distance from the Equator} = \text{Latitude in degrees} \times 111 \text{ km}\]

Here the latitude is the angle in degrees north or south of the Equator, and 111 km is the ground distance covered by one degree of that angle. The chapter works this out for two Indian cities.

WC 2.1 — Distance Of Mumbai And New Delhi From The Equator The situation: The latitude of Mumbai is 19°N and that of New Delhi is 30°N, as given under the uses of latitudes in this chapter. The working: We know that 1° latitude = 111 km. For Mumbai, \(111 \times 19° = 2109\) km, so Mumbai is 2109 km away from the Equator. For New Delhi, \(111 \times 30° = 3{,}330\) km, so New Delhi is 3,330 km away from the Equator.

Read what these two numbers are, and what they are not. Each is a distance measured due north from the Equator, straight along the curve of the earth, at a right angle to the Equator. Neither tells you how far apart the two cities are, because that also depends on how far east or west each of them lies. Nor is either a travelling distance — no road or railway line runs along a parallel of latitude.

The Three Heat Zones

The lines of latitude indicate the general climate of the area by applying the principle of heat zones, or thermal zones, of the earth. Thus latitudes enable us to divide the whole earth into different climatic zones, and three kinds are named. (a) The Torrid or Tropical Zone is the area lying between the Tropic of Cancer (23½°N) and the Tropic of Capricorn (23½°S), which mark its limits. Torrid means very hot, and this is the hottest zone of the earth. (b) The Temperate Zones are set by two further lines based on temperature, the Arctic Circle (66½°N) and the Antarctic Circle (66½°S). Between the Arctic Circle and the Tropic of Cancer lies the North Temperate zone (23½°N to 66½°N), and between the Antarctic Circle and the Tropic of Capricorn lies the South Temperate zone (23½°S to 66½°S), where the climate is moderate, that is, neither too hot nor too cold. (c) The Frigid Zones lie between the Arctic Circle and the North Pole, and between the Antarctic Circle and the South Pole. These are the polar regions, they receive the sun’s slanting rays, and in these two zones very low temperatures are recorded.

Fig. 2.3 shows the five slices these boundaries cut, and Fig. 2.A1 sets out the same division as a branching classification.

Diagram

Fig. 2.3 Caption: Important Parallels of Latitudes Brief: Globe marked with 90°N, 66.5°N, 23.5°N, 0°, 23.5°S, 66.5°S and 90°S; label the Arctic Circle, Tropic of Cancer, Equator, Tropic of Capricorn and Antarctic Circle in place, with NP and SP at the poles; arrows on the right naming frigid, temperate, torrid, temperate and frigid zones from top to bottom.

Fig. 2.3 The globe is cut by five named parallels, running from 66.5°N down to 66.5°S, and the arrows on the right name the zone each slice makes. Read outwards from the Equator: torrid, then temperate, then frigid, in both hemispheres. The figure fixes these boundaries by latitude alone, so it cannot tell you how hot any single place inside a zone actually is.

Flowchart

Fig. 2.A1 Caption: Latitude alone sets the boundaries of the earth’s five heat zones. Nodes: parallels of latitude → heat zones of the earth → torrid zone, 23½°N to 23½°S, hottest / north temperate zone, 23½°N to 66½°N, moderate / south temperate zone, 23½°S to 66½°S, moderate / north frigid zone, 66½°N to 90°N, slanting rays / south frigid zone, 66½°S to 90°S, slanting rays

2.3 Lines Of Longitude

A longitude is the angular distance of a place east or west of the Prime Meridian. Latitude answers the question of how far north or south a place lies; longitude answers how far round the earth it lies, and the two together fix it exactly. Fig. 2.2 (b) shows the measurement being taken sideways from the Prime Meridian, east and west.

Diagram

Fig. 2.2 (b) Caption: Longitude degrees are measured from the Prime meridian to its east or west Brief: Globe with the Prime Meridian drawn as a bold vertical line and labelled; shade the band running from the Prime Meridian east to 78°E; mark 72°E and 78°E at the Equator with Mumbai and New Delhi labelled on them; show the Equator and the parallels 0°N, 19°N and 30°N at the left edge.

Four facts fix the system. (a) The Prime Meridian is the line of longitude whose angular distance is defined as 0°, and it passes through Greenwich, near London. (b) The lines to the west of Greenwich are suffixed with ‘W’ and those to the east of Greenwich are suffixed with ‘E’, so a line is written as 60°W or 60°E. (c) There are a total of 360 lines at 1° interval. (d) All meridians of longitude converge at the poles and are thus of equal length.

Point (a) is worth a second look. Nothing on the ground marks Greenwich out from the land on either side of it. The 0° line is defined, not discovered — someone had to choose it, and everyone else agreed to measure from there.

A Globe Without A Prime Meridian Remove: the agreed 0° line passing through Greenwich. Then: each map maker numbers the meridians from wherever they begin, the same place carries a different number on every map, and noon at a named meridian tells no one anything. Which tells us: the Prime Meridian adds no feature to the earth. Its entire job is to give every map and every clock one shared starting line.

Point (c) is also worth checking against the 181 parallels counted earlier. The longitudes come to a round 360 because the 0° line is counted once, the 180° line is counted once, and between them run 179 lines to the east and 179 to the west.

Why They Are Called Meridians

The lines of longitude are also called meridians of longitude. The word ‘meridian’ is derived from the Latin word ‘meridianum’, meaning noon. The sun crosses a meridian at noon, and all places on a particular meridian will therefore have noon at the same time.

That last sentence is the seed of everything in the next four sections. A meridian is not only a position line, it is a line of shared noon, and shared noon is what a clock is really keeping.

Pairs That Make A Full Circle

The Prime Meridian is numbered as 0°. The others are numbered between 0° and 180°E or W. The line 180°E and the line 180°W refer to the same meridian, because it is diametrically opposite to the 0° longitude, meaning it lies on the exact far side of the earth from it.

Q. Is 180°E a different line from 180°W?

A. No. Both names belong to the same single meridian, lying exactly opposite the Prime Meridian on the far side of the globe.

Thus the 0° and the 180° meridian together make a full circle round the earth. Proceeding at 1° interval from both East and West, other full circles will be 1° – 179°, 2° – 178°, 60° – 120° and so on. Of the two lines in any segment, one will be in the east and the other in the west, and the sum total of the two lines will always be 180°.

Individually, all lines of longitude are semicircles, because each one runs only from pole to pole, which is half way round. The two diametrically opposite lines make a full circle, also known as the Great Circle. Fig. 2.4 shows the meridians running down from the pole and spreading out across the Equator.

Diagram

Fig. 2.4 Caption: Lines of Longitude Brief: Globe seen with the North Pole near the top, showing meridians running from pole to pole and labelled 0°, 15°, 30°, 45°, 60° and 80°; mark the Prime Meridian in bold, label E to its east and W to its west, and mark the Equator as a horizontal line across the middle.

Fig. 2.4 Each curved line is one meridian, numbered by its angular distance east or west of the Prime Meridian, which is drawn in bold at 0°. Follow any two neighbouring lines from the Equator upwards and watch the gap between them close until they meet at the pole. The drawing shows the converging, but not the actual ground distance between the lines at any given latitude.

Spacing That Changes With Latitude

Because the meridians converge, the gap between two of them is not a fixed thing. The distance between two lines of longitude is maximum at the Equator, where it is 111 km, and it decreases gradually as one moves towards the poles.

Compare that with the parallels. One degree of latitude stands for about 111 km wherever you measure it, north or south. One degree of longitude stands for 111 km only at the Equator, and for steadily less as you travel away from it, until at the pole the two lines have closed together completely and the distance is nothing at all.

2.4 Longitude And Time

The lines of longitude, as stated earlier, are also known as the ‘Meridians’. At a particular moment of time, if it is 12 Noon at a given longitude, it must be 12 Noon at all places on this longitude. The rule holds however far apart those places are, because they all face the sun at the same instant. Fig. 2.5 makes the point with three places set far apart on one meridian.

Diagram

Fig. 2.5 Caption: Places on the same longitude have the same time — Places K, O and M have each 40° longitude. If it is 12 noon at K, it will also be 12 noon at O and M Brief: Globe with the Prime Meridian and the 40° Meridian drawn and labelled; mark points M in the north, O on the Equator and K in the south, all on the 40° Meridian; show the 40° angle at the centre for each of the three, with N and S at the poles and E and Q at the ends of the Equator.

Latitude And Longitude Side By Side

The two sets of lines have now both been described, and the chapter sets their differences out together in Table 2.1. Read it as a pair of columns that answer the same six questions.

Table 2.1 Caption: Difference between Lines of Latitude and Lines of Longitude | Latitude | Longitude | |—|—| | 1. A latitude is the angular distance of a place north or south of the Equator. | 1. A longitude is the angular distance of a place east or west of the Prime Meridian. | | 2. Lines of Latitude are parallel to the Equator and each other. | 2. All meridians of longitude converge at the poles. | | 3. Each parallel of latitude is a full circle. The lines of latitude are not of equal length and become smaller on moving towards the poles. | 3. Individually all lines of longitude are semicircles and of equal length. | | 4. Latitude degrees are measured from the Equator to its north or south. | 4. Longitude degrees are measured from the Prime meridian to its east or west. | | 5. The distance between two lines of latitude is approximately 111 km. | 5. The distance between two lines of longitude is maximum at the Equator, i.e., 111 km, but it goes on decreasing on moving towards the poles. It is 0° at the poles. | | 6. Lines of latitude are used to find the location of a place, to measure the distance of a place and to divide the whole earth into different heat or climatic zones. | 6. Lines of longitude are used to find the local and standard time of a place. Along with the lines of latitude, the longitudes are used to locate places on the globe or a map. |

Table 2.1 Read across a numbered row, not down a column, because each row sets one property against its opposite. Row 3 carries the shape difference, row 5 the spacing difference. The table lists how the two sets of lines differ, but it does not show how they work together, which is the one thing that actually fixes a place on the earth.

Turning Rotation Into Minutes

The Earth makes a complete circle on its axis, covering 360° longitudes in 24 hours. Dividing the turn by the time gives the rate at which the sun appears to move across the meridians:

\[\frac{360°}{24 \text{ hours}} = 15° \text{ per hour}, \qquad \frac{60 \text{ minutes}}{15°} = 4 \text{ minutes per degree}\]

That is to say, the earth covers every 15° longitudes in one hour, or 1° longitude every 4 minutes. Here the degrees are degrees of longitude, and the minutes are ordinary clock minutes.

Thus, if it is 12 Noon at 0° longitude, it must be 4 minutes past 12 Noon towards the east at the next 1°E longitude, and at 15°E longitude it must be 1 p.m. Towards the west, it will be 1 hour less, because the Earth rotates from West to East and the sun therefore first rises in the East.

Why Clocks In The East Run Ahead The earth rotates from west to east → an eastern meridian is carried into the sunlight first → noon arrives there earlier → its clock already reads later than a western one → 4 minutes are added for every 1° of longitude eastward.

The EGA-WLS Rule

For the purpose of memorising, the EGA-WLS formula is used. EGA stands for East-Gain-Add, and WLS means West-Lose-Subtract. In other words, for each 1° longitude towards the East, 4 minutes are to be added, and for each 1° longitude towards the West, 4 minutes are to be subtracted.

\[\text{Time difference in minutes} = \text{Difference of longitude in degrees} \times 4 \text{ minutes}\]

The difference of longitude is the number of degrees between the two places, and the answer is the number of minutes by which their times differ. Fig. 2.A2 sets out the two directions as a single decision.

Flowchart

Fig. 2.A2 Caption: Every time calculation in this chapter turns on one question — is the place east or west of the reference meridian? Nodes: two places, difference of longitude in degrees → multiply by 4 minutes → place lies east of the reference meridian? yes → gain, add the minutes → time is later; no, it lies west → lose, subtract the minutes → time is earlier

2.4.1 Eastern And Western Hemisphere

The Prime Meridian, together with the 180° longitude, usually divides the earth into the Eastern and Western Hemispheres. This division holds good practically for all purposes, and it is the one every atlas uses.

However, the split is not the only one possible. Any two diametrically opposite lines can also divide the earth into two equal hemispheres, because any such pair makes a full circle round the globe and cuts it into halves of the same size.

Q. If any opposite pair splits the earth equally, why use 0° and 180°?

A. Because the Prime Meridian is already the agreed starting line for numbering, so this split matches the ‘E’ and ‘W’ printed on every map.

2.5 Local Time

The local time of any place is obtained by the overhead sun at noon. When the sun reaches its highest point in the sky for that place, the clock there reads 12 noon, and every other hour of that day is counted from that moment. Local time is therefore not set by any authority. It is read off the sky.

Because the sun cannot be overhead at two longitudes at the same instant, the reading changes as you move east or west. For each degree of longitude, the local time varies by 4 minutes. The chapter works this out for two Indian cities that lie only a few degrees apart.

Finding Local Noon Evidence: The instant the sun stands at its highest for an observer, directly over that meridian. Reasoning: That instant is defined as 12 noon there, so the whole day is counted from it. Limit: It gives a separate noon for every longitude, so it cannot supply one shared time for a country or even for a state.

WC 2.2 — Local Time At New Delhi When It Is Noon At Mumbai The situation: The longitude of Mumbai is 73°E and that of New Delhi is 77°E. It is 12 Noon at Mumbai. The working: 77°E − 73°E = 4° longitude difference. Since 1° longitude = 4 minutes, 4° longitude = 16 minutes. The 16 minutes are to be added, because Delhi lies to the east of Mumbai. It must therefore be 16 minutes past 12 Noon at New Delhi at the same moment.

Sixteen minutes sounds like nothing, and that is exactly why it matters. Two cities that most people think of as far apart are separated by only 4° of longitude, so their suns are almost in step. The gap grows with the east–west distance, not with the distance travelled, so a long journey due north would change the local time not at all.

Q. Does local time change if you travel due north?

A. No. Local time depends only on longitude, so every place along one meridian keeps the same noon, however far north or south it lies.

One Country, Many Noons

Stretch the same reasoning across the whole country and the gap stops being trivial. This means that there will be a huge time difference between Gujarat in the west and Assam in the east, where the sun rises far earlier.

Taken strictly, every place at a different longitude will have its own local time. A town a single degree east of its neighbour has a noon four minutes earlier. That is an honest description of the sky, and an impossible way to run a railway timetable, which is the problem the next section solves.

2.6 Time Zones And Standard Time

Local time is honest but unworkable. A country needs one clock that everyone inside it agrees to keep, and the solution is to stop following the sun at every longitude and start following it in wide belts.

2.6.1 Time Zones

To overcome the confusion while allowing the interplay of natural forces to operate, the earth has been divided into 24 Time Zones, according to the number of hours in a day. Each zone covers 15° longitude, since 360 ÷ 24 = 15. The time for the whole zone is determined on the basis of the central meridian of that place, so every clock inside a zone reads the same, even though the sun does not.

Q. Why 24 zones, and not 12 or 30?

A. Because a day has 24 hours. Dividing 360° of longitude by 24 gives each zone 15°, which is exactly one hour of the earth’s turning.

The number of zones a country needs depends on how far it stretches from east to west. Countries with a smaller east–west extent, like India, have only one Standard Time Zone, while countries like Russia, Canada and the USA have more than one Time Zone. A country wide enough to span several 15° belts cannot serve them all with a single clock without the clock drifting badly away from the sun at its two ends.

2.6.2 Standard Time

The uniform time based on a central meridian is known as the Standard Time. It is the local time of one chosen meridian, borrowed by everybody else in the zone.

Standard time must always be divisible by 7½°. This allows time to be reckoned by a unit of half-an-hour and not smaller differences. The reason lies in the four-minute rule: 7½° multiplied by 4 minutes comes to exactly 30 minutes, so a meridian chosen this way always sets a clock a whole number of half-hours away from the next.

Q1. Why can two places in the same country see the sun rise hours apart and still keep exactly the same clock time?

A. Because clocks stop following local noon. The whole country borrows the local time of one central meridian, so every clock reads the same however early or late the sun actually rises.

2.6.3 Greenwich Mean Time

Further, while fixing the Time Zones, the time at Greenwich (0° longitude) has been selected as the mean time — the reference against which every other zone is counted. Thus, if it is 12 Noon at Greenwich, at 15°E longitude the time will be 1 pm, and at 30°E longitude the time will be 2 pm. Each 15° step east adds one full hour, exactly as the four-minute rule requires.

The time fixed with reference to Greenwich is called the Greenwich Mean Time, or GMT. Every calculation in the rest of this chapter passes through it, because two places anywhere on earth can always be compared by first bringing each of them back to Greenwich.

2.6.4 Indian Standard Time (IST)

In our country, 82°30’E is the central meridian. The notation needs unpacking: 30’ means 30 minutes of arc, and 60 minutes of arc make one degree, so 82°30’ is 82½°. It passes through Mirzapur near Allahabad (Prayagraj), in Uttar Pradesh, and it is known as the Standard Meridian of India.

While fixing the Indian Standard Time with respect to the Greenwich Mean Time, we have to add 82°30’ × 4 minutes = 330 minutes, or 5½ hours. This means that India is 5½ hours ahead of GMT. Thus if it is 9 AM at London, it must be 9 + 5.30, or 14.30 hrs, or 2.30 PM in India.

Q2. What is special about the line of longitude at 82°30’E, and why was that particular line chosen for India?

A. It is the central meridian of the country, passing through Mirzapur near Allahabad (Prayagraj), and it divides by 7½°, so India’s clock sits a neat 5½ hours ahead of GMT.

2.6.5 Worked Out Example For Calculating The Time At A Place

The chapter now puts every rule so far to work on a single question, and answers it twice by two different routes. The example is this: it is 5.30 p.m. in India when the Prime Minister’s radio broadcast made from Montreal in Canada was heard. What must have been the time at Montreal?

WC 2.3 — The Time At Montreal When It Is 5.30 p.m. In India The situation: A radio broadcast made from Montreal, in eastern Canada, is heard in India at 5.30 p.m. After consulting the atlas we find Montreal lies 74°W. The working: Solution 1 goes through Greenwich. Time in India = 1730 hrs (5:30 PM). Since India is ahead of GMT by 5 hrs 30 m, the time at Greenwich = 1200 hrs (noon). Montreal’s time difference with respect to GMT = 74 × 4 min. = 296 min. = 4 hours 56 minutes. Montreal is to the west of GMT, so its time = 12 hrs − 4 hours 56 min. = 7:04 a.m. The working: Solution 2 goes straight across. Standard Meridian of India = 82½°E and Standard Meridian of Montreal = 74°W, so the total meridians between them = 156½°. Since 1 meridian = 4 minutes, 156½° meridian = 156½ × 4 = 626 minutes = 10 hrs 26 minutes. Montreal is to the west of Delhi, therefore the time difference will be deducted: 1730 hrs − 1026 hrs = 7.04 a.m. in Montreal. The Prime Minister made his broadcast at 7.04 AM from Montreal, which was received at 5.30 p.m. in India.

The two solutions matter more than the answer they share. Solution 1 treats Greenwich as a meeting point, converting India’s time back to GMT and then out again to Montreal. Solution 2 ignores Greenwich and counts the whole angular gap in one step, adding 82½° and 74° because the two places lie on opposite sides of the Prime Meridian — one east, one west. Both routes rest on the same four minutes per degree, and when a calculation can be checked by two independent paths, a mistake in either one shows up at once.

2.7 International Date Line

The line of longitude 180° is one and the same for East or West of the Prime Meridian. Since it is diametrically opposite to the Greenwich Meridian, it causes a time difference of a full day on crossing the line. The time difference works out to 12 hours (180° × 4 min) from either side, and thus, on crossing the line, a day is gained or lost.

Q. If both sides are 12 hours from Greenwich, why is the gap a whole day?

A. One side runs 12 hours ahead of Greenwich and the other 12 hours behind. Put together, that is 24 hours, so the two sides carry different dates.

Twelve Hours On Each Side

When crossing from the east, time will be 12 hours ahead, and while crossing from the west, time will be 12 hours behind. The chapter fixes this with a dated example.

If it is 8 PM Monday, 25th December at Greenwich, it will be 8 AM Tuesday, 26th December on crossing the 180° line. But if one were to travel from the west, it will be 12 hours behind, or 8 AM Monday, 25th December.

When the time lost and the time gained are computed together, the difference works out to a full 24 hours at 180°E and W. In the example above, the difference between 8 AM Monday 25th December and 8 AM Tuesday 26th December is exactly 24 hours.

The Line And The Two Boats

The International Date Line (IDL) is the 180° line, and when crossing this date line the date changes. Fig. 2.6 shows two boats approaching it from opposite sides.

Diagram

Fig. 2.6 Caption: The International Date Line Brief: View of the globe from above the North Pole with the International Date Line drawn as a bold vertical band at 180°; label SUNDAY to its left and MONDAY to its right; show Boat 1 on the left with an arrow pointing right, or eastwards, and Boat 2 on the right with an arrow pointing left, or westwards; label North America, Asia, Europe, Japan, East Longitude and West Longitude.

The boat 1 on the left is sailing to the right, that is eastwards. When crossing the International Date Line, Sunday becomes Monday, so that a day is lost. When the boat 2 on the right, which is sailing westwards, crosses the International Date Line, Monday becomes Sunday, so that a day is gained. Fig. 2.A3 sets the two crossings out as one decision.

Flowchart

Fig. 2.A3 Caption: Which way you cross the 180° line decides whether the calendar jumps forward or back. Nodes: a ship reaches the International Date Line → which way is it sailing? eastwards → Sunday becomes Monday → a day is lost; westwards → Monday becomes Sunday → a day is gained

Q3. Why does the date on the calendar change when a traveller crosses the 180° line in the Pacific?

A. Because the two sides of that line are a full 24 hours apart. Without a change of date there, a traveller circling the earth would arrive home on the wrong day.

Why The Line Bends

The 180° meridian is a straight line on the globe, but the date line drawn on maps is not. To avoid the confusion of having different dates within the same country, the Date Line bends and goes zig-zag at the Bering Strait, between Siberia and Alaska, and at Fiji, Tonga, New Zealand and some other Islands.

The reason is practical rather than astronomical. A country cut in half by the line would keep two different dates at once, so the line is bent out into open water to leave each of these territories whole. Fig. 2.7 shows the finished line running down the Pacific with its bends in place, and the 24 time zones on either side of it.

Map

Fig. 2.7 Caption: International Date Line Brief: World map of the 24 time zones, showing the full extent of India as officially defined; number the zones along the top and bottom by their hours ahead of or behind GMT; mark the Prime Meridian, the Equator, the Tropic of Cancer and the Tropic of Capricorn; draw the International Date Line in red with its bends at the Bering Strait and near the Pacific islands, labelled; name the Arctic, Atlantic, Pacific and Indian Oceans; include the scale bar and projection note as printed.

Fig. 2.7 The numbers running along the top and bottom edges are hours ahead of or behind GMT, not longitudes. Follow one number down its column and you have a time zone. Notice how the zone boundaries bend around countries rather than following meridians exactly. The map fixes clock time only, so it cannot tell you when the sun actually rises at any place shown.

2.8 Locating Places

Everything the chapter has built so far comes together here. With the help of the grid, we can locate places on the globe or the map, if we know the latitude and longitude of those places. A latitude on its own narrows a place to one circle running right round the earth, and a longitude on its own narrows it to one line running pole to pole. Only the two together give a point.

2.8.1 Worked Out Examples

The latitude and longitude of three places is given below. The task is to pinpoint these places on the globe. (a) New York = Latitude 41°N and Longitude 74°W (b) New Delhi = 30°N and 77°E (c) Mumbai = 19°N and 73°E

First look at the data of New York. It is a common practice to write first the latitude and then the longitude of a place, so the first figure in each pair always answers how far north or south, and the second how far east or west.

Q. Does the order of the two figures matter?

A. Yes. Written the other way round, 19°N 73°E would become 73°N 19°E, which lands in an entirely different part of the world.

For locating the above, identify the relevant latitudes and longitudes. Where the two lines meet, or the point at which they cross each other, lies the place which is to be located.

WC 2.4 — Pinpointing New York On The Globe The situation: New York is given as Latitude 41°N and Longitude 74°W, the first of the three places listed in this section. The working: Read the pair in order. The first figure, 41°N, is a latitude, so find the parallel drawn 41° north of the Equator and trace it right round the globe. The second figure, 74°W, is a longitude, so find the meridian 74° west of the Prime Meridian, on the far side from Greenwich, and trace it from pole to pole. The two lines cross at exactly one point on the globe, and that point is New York.

Notice what the method does not need. Nobody has to know what New York looks like, how large it is, or what lies around it — the two numbers do all the work, and they would do it just as well for an unnamed rock in mid-ocean. This is what makes an absolute location so useful: it is a set of instructions any reader can follow on any globe, in any country, and arrive at the same point. The same two steps place New Delhi where 30°N crosses 77°E, and Mumbai where 19°N crosses 73°E, both of them east of the Prime Meridian.

Diagram

Fig. 2.A4 Caption: A latitude alone gives a circle and a longitude alone gives a line, and only their crossing gives a place. Brief: Globe ruled with faint parallels and meridians; draw the 41°N parallel in one colour running fully round the globe and the 74°W meridian in a second colour running pole to pole; mark and label the single point where they cross; label the Equator, the Prime Meridian and the two lines with their values.

Fig. 2.A4 The two bold lines are the only ones that matter here — one parallel, one meridian, each labelled with its value and its direction letter. Follow each line away from the marked point and see how much of the earth it covers on its own. The figure shows how the point is found, not what is actually at that point on the ground.

2.9 Great And Small Circles

A great circle is a circle that is drawn on the surface of a sphere, such as the earth, that has a radius equal to the radius of the sphere, and whose centre is also the sphere’s centre. Cut the earth exactly through the middle and the edge of that cut is a great circle. The Equator is the only latitude that is a great circle, and all longitudes are a part of a great circle.

Circles which do not pass through the centre of the earth are the small circles. All the parallels of latitudes other than the Equator are small circles, because each of them is drawn round a narrower part of the globe, above or below the centre. Arcs of great circles are the shortest route between two points on a sphere, which is the fact the whole of section 2.9.2 rests on. Fig. 2.8 shows the two kinds of cut side by side.

Diagram

Fig. 2.8 Caption: Great and Small Circles Brief: Sphere sliced by two flat planes drawn in yellow; the upper plane cuts a narrow circle well above the middle and is labelled Small Circle, the lower plane passes through the centre, marked with a dot, and is labelled Great Circle; show both cut circles as dashed ellipses on the sphere.

Fig. 2.8 The two yellow sheets are imaginary planes slicing the sphere, and each one leaves a circle where it meets the surface. Watch the dot at the centre: the lower plane goes through it, the upper plane misses it entirely. That single difference decides which circle is great and which is small. The figure shows the geometry, not any real line drawn on the earth.

Q4. Every parallel of latitude is a full circle, so why is the Equator the only latitude that counts as a great circle?

A. Because a great circle must be cut by a plane passing through the earth’s centre. Only the Equator is, so every other parallel is a smaller circle sitting above or below the middle.

2.9.1 Characteristics Of A Great Circle

Four statements pin the idea down. (a) A great circle is a theoretical circle formed by the intersection of the earth’s surface and an imaginary plane that passes through the centre of the earth and divides it into two equal parts. (b) All such circles must pass through or touch the centre of the circle. (c) An infinite number of circles that touch the two opposite ends of the sphere can be drawn on a sphere. (d) Intersecting great circles always bisect each other, so wherever two of them cross, each cuts the other exactly in half.

In respect of characteristic (a) above, the Equator is the largest possible circle among lines of the latitude. The Equator and all diametrically opposite longitudes touch the centre of a circle and therefore are Great Circles.

Characteristic (c) is what excludes all latitudes except the Equator. All the other parallels of latitudes are small circles, because no plane through them can also pass through the centre of the earth.

2.9.2 Uses Of Great Circles

Great circles are not only a matter of geometry. They are put to work in three ways. (a) Navigators use great circles to find the shortest distance between any two points on the earth’s surface. A Great Circle Route is the shortest distance between two places on the earth and lies on the arc of a great circle. (b) Great Circle routes are specially important for places that are on opposite sides of the globe, and most globes show great circle routes between distant ports across the Atlantic, the Pacific and the Indian Ocean. (c) Great circles are used by meteorologists, the scientists who study the weather, to determine climate and weather conditions in a region.

Using the hypothesis in point (a), the shortest route from New York to Moscow would be over the North Pole. On a flat map that path looks like a long detour to the north, and on a globe it is plainly the direct line. Fig. 2.9 shows such an arc drawn between two points.

Diagram

Fig. 2.9 Caption: Great Circle Route Brief: Sphere with two marked points A and B set apart on its surface; draw the arc joining them in red, labelled Great Circle, and continue the same circle round the sphere as a dashed line; show one or two other great circles crossing it, also dashed.

The shortest route on paper is not always the route flown. The great circle route does not take into account restrictions such as weather or political restrictions imposed by the countries concerned. It also does not take into account the lack of landing and take off facilities for aeroplanes along the way.

Q. If the great circle route is the shortest, why is it not always flown?

A. Because it is a purely geometric answer. Weather, political restrictions and the absence of places to land or take off can all rule the shortest arc out.

Geographic grid — A framework of lines of longitude and latitude on a globe or a map. Hemisphere — One of the halves into which the earth is divided. Tropic zone — The temperature zone of the earth between the Tropic of Cancer and Capricorn. It is the hottest region of the earth. Temperate zone — The mild temperature zone between the Tropic of Cancer and Arctic Circle or between the Tropic of Capricorn and Antarctic Circle. Frigid zone — Either of two cold zones of the earth between Arctic Circle and North Pole or between Antarctic Circle and South Pole.

2.10 Summary

  1. The earth’s surface is so vast that a place cannot be located on it without a mathematical method, so imaginary lines are drawn on the globe.
  2. The criss-crossing lines of latitude and longitude form the Geographic Grid, devised by Eratosthenes, and it works exactly as coordinates on graph paper do.
  3. A latitude is the angular distance of a place north or south of the Equator, calculated from the angle a place makes with the centre of the earth.
    1. The parallels of latitude are full circles, but they are not of equal length; at 60° the circle is half the Equator, and at the poles they are only points.
    2. There are 181 parallels at 1° interval, of which seven are named: the Equator, the North Pole, the South Pole, the Tropic of Cancer, the Tropic of Capricorn, the Arctic Circle and the Antarctic Circle.
  4. The Equator divides the earth into the Northern and Southern Hemispheres, and its length equals the earth’s circumference of 40,075 km, which makes 1° roughly 111 km.
  5. The lines of latitude are put to three uses.
    1. They give the absolute location of a place north or south of the Equator.
    2. They measure distance from the Equator, so Mumbai at 19°N is 2109 km away and New Delhi at 30°N is 3,330 km away.
    3. They divide the earth into heat zones — the torrid zone, the two temperate zones and the two frigid zones.
  6. A longitude is the angular distance of a place east or west of the Prime Meridian, which is defined as 0° and passes through Greenwich, near London.
    1. There are 360 meridians at 1° interval, all converging at the poles and therefore all of equal length.
    2. Each meridian is a semicircle, and two diametrically opposite meridians together make a full circle, or great circle, their values always adding to 180°.
    3. The distance between two meridians is 111 km at the Equator and decreases towards the poles, reaching nothing at all there.
  7. The earth covers 360° of longitude in 24 hours, that is 15° in one hour or 1° in 4 minutes, which is remembered as EGA-WLS: East-Gain-Add and West-Lose-Subtract.
  8. Local time is obtained from the overhead sun at noon, so every longitude has its own; when it is noon at Mumbai (73°E) it is already 16 minutes past noon at New Delhi (77°E).
  9. To end that confusion the earth is divided into 24 Time Zones of 15° each, and the uniform time of a central meridian is the Standard Time, which must always be divisible by 7½°.
    1. The time at Greenwich, 0° longitude, is the Greenwich Mean Time, against which every other zone is counted.
    2. India’s standard meridian is 82°30’E, passing through Mirzapur near Allahabad (Prayagraj), which puts Indian Standard Time 5½ hours ahead of GMT.
  10. The 180° meridian is the International Date Line, and crossing it changes the date — a day is lost sailing eastwards and gained sailing westwards — while the line zig-zags to keep countries and island groups on one date.
  11. A place is located at the point where its latitude and longitude cross, and the latitude is written first by common practice.
  12. A great circle is cut by a plane passing through the centre of the earth, so the Equator is the only latitude that qualifies and every other parallel is a small circle.
    1. Arcs of great circles are the shortest route between two points on a sphere, which is why navigators use Great Circle Routes.
    2. The route is geometric only, and takes no account of weather, political restrictions or landing and take off facilities.

Flowchart

Fig. 2.A5 Caption: One grid, two sets of lines, and everything this chapter does with them. Nodes: the geographic grid → parallels of latitude, angular distance north or south of the Equator → absolute location north or south / distance from the Equator at about 111 km per degree / heat zones: torrid, temperate, frigid; and → meridians of longitude, angular distance east or west of the Prime Meridian → local time at 4 minutes per degree → standard time of a central meridian → GMT at 0° and IST at 82°30’E → International Date Line at 180°, where the date changes; both sets of lines together → the crossing point fixes one place on the globe

What This Chapter Cannot Tell You

The grid fixes where a place is and nothing else. A pair of coordinates says whether a point lies in the torrid zone, but not whether it is desert, forest or open sea, and the heat zones themselves are drawn by latitude alone, so they describe a general climate rather than the temperature of any particular town.

The time system has a similar blind spot. Standard time is the true local time of one meridian only, so every clock away from that meridian is already out of step with its own sun, and the further east or west it sits, the wider that gap grows.

2.11 Check Your Concepts

  1. Look at rows 3 and 5 of Table 2.1. Explain in your own words why the distance between two lines of longitude changes as you move away from the Equator, while the distance between two lines of latitude stays roughly the same.

  2. The Tropic of Cancer lies at 23½°N.

    1. Using the value this chapter gives for 1° of latitude, calculate its distance from the Equator, showing every step of your working.
    2. State one thing this figure does not tell you about any place lying on the Tropic of Cancer.

  3. Fig. 2.5 shows the places K, O and M, all on the 40° meridian and far apart from north to south. Explain why noon occurs at the same moment for all three, and say what would change if one of them were moved a few degrees to the east.

  4. Standard time must always be divisible by 7½°. Using the rule that 1° of longitude equals 4 minutes, show by calculation why this condition makes the standard time of a country differ from GMT by a whole number of half-hours, and check your reasoning against the Indian Standard Meridian.

  5. What are the Great Circle Routes? State their importance.

  6. Give a geographical reason for each of the following:

    1. Lines of latitude are called parallels of latitude.
    2. Lines of latitude are not of equal length.
    3. Lines of latitude carve out the heat zones of the earth.

  7. Draw a well labelled diagram showing the different heat zones of the world.

  8. State the use of the lines of longitude in relation to distance and time.

  9. State with an example how time lost or gained is computed with reference to the International Date Line.

2.12 Practice with Numericals

  1. Calculate the time at Durban (longitude 30°E) when the time is 7:00 a.m. at New York (75°W).