Theories of Geography Part 2 – Geodesy and Structure of Earth

Geodesy: Latitudes and Longitudes

Eratosthenes was the first person to calculate the size of the earth. He realized that Earth could be located with a basic grid of lines called Longitudes and Latitudes.

Great Circle

When a sphere is divided exactly in half through its center, the circumference represents the largest circle that can be drawn on that sphere. The shortest distance between two points on a sphere is a great circle, or a circle whose plane passes through the center of sphere. In case of Earth, only equator is a great circle among latitudes and all longitudes are half great circles.


Latitude is the angle between the equatorial plane and the axis. Lines joining points of the same latitude are called parallels. Equator {0° parallel} itself is largest parallel and only circle of latitude which also is a great circle. Equator is also used as fundamental plane of all geographic coordinate systems. It’s worth noting that geostationary satellites are over the equator at a specific point on Earth, so their position related to Earth is expressed in longitude degrees only. Their latitude is always zero. There are 180° of latitudes and each degree of latitude spans around 111 kilometers or 69 miles or 60 Nautical miles. But this distance varies because Earth is not a perfect sphere.  From Equator to 40° towards both poles it is slightly less than 111 kilometers and from 41° towards both poles it is slightly more than 111 kilometers. The 90° North and 90° South are not circles but only reference points. Latitudes tell us the temperature and climatic position of a particular place.


Longitude is the angle east or west of a reference meridian between the two geographical poles to another meridian that passes through an arbitrary point. All meridians are halves of great circles, and are not parallel to each other. They converge only at the north and south poles. A line passing to the rear of the Royal Observatory, Greenwich (near London in the UK) has been chosen as the international zero-longitude reference line and is known as the Prime Meridian. Places to the east are in the eastern hemisphere, and places to the west are in the western hemisphere. The antipodal meridian of Greenwich serves as both 180°W and 180°E. There are 360° of the meridians and the longitude of prime meridian is 0°. Length of all meridians is equal. The distance between two meridians is farthest at the equator and it decreases as we move towards poles and becomes zero at poles.

Structure of Earth

Earth Basic Information

Earth is located in the Solar System, which is located in the Orion (or local) arm of Milky Way Galaxy, which is a part of Virgo Super cluster. As a part of the Milky Way Galaxy, the Earth is accelerating outward toward the outer regions of the universe. The Earth and the other members of the solar system are orbiting the galaxy at about 225 kilometers per hour. Earth is third planet from the Sun and Fifth largest planet.  It is largest among the Solar System’s four terrestrial planets (Mercury, Venus, Earth, and Mars). Earth is also the densest planet of the solar system.

Radius and Circumference of Earth

The Mean radius of Earth is 6,371.0 km. Equatorial radius is 6,378.1 km, while polar radius is 6356.8 kilometers. This means that Earth is not perfectly spherical; no single value serves as its natural radius. Even calling it Radius is factually incorrect because “radius” normally is a characteristic of perfect spheres.  Earth’s rotation causes it to be like an oblate spheroid with a bulge at the equator and flattening at the North and South Poles. So the equatorial radius is larger than the polar radius.

The farthest point from Earth’s centre is Chimborazo, an inactive volcano in the Andes mountains in Ecuador, in South America. Chimborazo is not the highest mountain by elevation above sea level, but its location along the equatorial bulge makes its summit the farthest point on the Earth’s surface from the Earth’s center. The Equatorial Circumference of Earth is 40,075.16 km, while the Meridional Circumference is 40,008.00 km.

Other Basic Data 

Surface area 510,072,000 km2
Land Area 148,940,000 km2 (29.2 %)
Water Area 361,132,000 km2 (70.8 %)
Volume 1.08321 × 1012 km3
Mass 5.9736 × 1024 kg
Mean density 5.515 g/cm3
Equatorial surface gravity 9.780327 m/s2
Escape velocity 11.186 km/s
Sidereal rotation period 23h 56m 4.100s
Equatorial rotation velocity 1,674.4 km/h
Axial tilt 23°26’21”.4119
Albedo 0.36
Surface temp Minimum  −89.4 °C Median=14 °C Maximum =58 °C
Surface pressure


101.325 kPa

Composition 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.038% carbon dioxide, approx. 1% water vapour.

Structure of Earth

The internal structure of earth is layered. The Earth is generally divided into four major layers: the crust, mantle, inner core, and outer core.

The following defines each division.


The Earth’s crust is the outermost layer and is the most familiar, since people live on the outer skin of the crust. It is rigid, brittle, and thin compared to the mantle, inner core, and outer core. Because of its varying characteristics, this outer layer is divided into the continental and oceanic crusts.


Earth’s mantle lies beneath the crust and above the outer core, averaging about 1,802 miles (2,900 kilometers) thick and representing 68.3 percent of the Earth’s mass and 84% of Earth’s volume. A transition zone divides this layer into the upper and lower mantles.

Outer core

The liquid outer core is a layer between 2,885 and 5,155 kilometers deep in the Earth’s interior. It is thought to move by convection (the transfer of heat through the circulating motion of materials), with the movement possibly contributing to the Earth’s magnetic field. The outer core represents about 29.3 percent of the Earth’s total mass.

Inner core

The inner core is thought to be roughly the size of the Earth’s Moon. It lies at a depth 5,150 to 6,370 kilometers beneath the Earth’s surface and generates heat close to temperatures on the sun’s surface. It represents about 1.7 percent of the Earth’s mass and is thought to be composed of a solid iron- nickel alloy suspended within the molten outer core.

Density of Various Earth Layers

The average density of Earth is 5,515 kg/m 3. Since the average density of surface material is only around 3,000 kg/m3, it can be concluded that denser materials exist within Earth’s core.  When we move from earth’s Crust to Core, the density increases. The following table shows the depth as well as the average density of various layers:

Depth (Sq. Kms) Layer Density gm per cubic cm.
0–60 Lithosphere 1.2-2.9
0–35 Crust 2.2–2.9
35–60 Upper mantle 3.4–4.4
35–2890 Mantle 3.4–5.6
100–700 Asthenosphere NA
2890–5100 Outer core 9.9–12.2
5100–6378 Inner core 12.8–13.1


Earth’s Crust

Earth’s crust is the outermost layer composed of various types of rocks. The boundary between the crust and mantle is generally called the Mohorovičić discontinuity.

Thickness of Continental and Oceanic Crust

It varies in thickness from around 5 to 100 kilometers. The continental crust is thicker in comparison to oceanic crust. The oceanic crust ranges from 5 to 10 kilometers {average 7 km} while continental crust ranges from 25 to 100 kilometers {average 30-35 km}. Thickest continental crust regions are under large mountain ranges.

Difference in composition and density

Oceanic crust is made of dark rocks having more of Iron and Magnesium and are more basaltic. Continental crust is made of lighter rocks, having more of Silica and are more felsic. The below table shows the key differences between Oceanic and continental rocks.

Lithosphere, Asthenosphere and Pedosphere

Lithos means rock. Lithium is an alkali metal and its name is also derived from Lithos. Lithosphere is the upper 80 Kilometers layer composed of both the crust and part of the upper mantle. However, overall, it is cool enough to be tough and elastic than the molten mantle. The Oceanic lithosphere is associated with Oceanic crust and exists in the ocean basins, while the Continental lithosphere is associated with Continental crust. The Oceanic lithosphere is denser than the continental lithosphere.

Lithosphere is obviously thinner under the oceans and volcanically active continental regions than the other landmasses. The entire lithosphere is physically broken up into the brittle, moving plates containing the world’s continents and oceans. These lithospheric plates appear to “float” and move around on the more ductile asthenosphere.

The asthenosphere is the relatively narrow, moving zone in the upper mantle located between 72 to 250 kilometers beneath the Earth’s surface. It is composed of a hot, semi-solid material that is soft and flowing after being subjected to high temperatures and pressures. The asthenosphere boundary is closer to the surface-within a few kilometers under oceans and near mid-ocean ridges than it is below the landmasses. The upper section of the asthenosphere is thought to be the area in which the lithospheric plates move, “carrying” the continental and oceanic plates also known as Tectonic Plates.

Further, the uppermost part of the Lithosphere that reacts with the atmosphere, biosphere and Hydrosphere is called as pedosphere. Pedos means soil. Pedospehere is composed of soil and it is the cradle of all the chemical and biogeochemical reactions which leads to soil development.

Composition of Earth Crust

Almost half of Earth’s crust is made of oxygen, while a quarter of it is made of silicon. Since silicon and Oxygen react to make silica, around 48.6% of Earth’s crust is made of silica. Major elements in Earth’s crust are Oxygen (47%), Silicon (28%), Aluminum (8%), Iron (5%), Calcium (3.5%), Sodium (2.5%), Potassium (2.5%), Magnesium (2.2%) and other elements such as Hydrogen, Carbon, Phosphorus, Sulphur etc. Major compounds in Earth’s crust are shown in below table.

Compound Formula Continental Oceanic
Silica SiO2 60.2% 48.6%
Alumina Al2O3 15.2% 16.5%
Lime CaO 5.5% 12.3%
Magnesia MgO 3.1% 6.8%
Iron(II) Oxide FeO 3.8% 6.2%
Sodium Oxide Na2O 3.0% 2.6%
Potassium Oxide K2O 2.8% 0.4%
Iron(III) Oxide Fe2O3 2.5% 2.3%
Water H2O 1.4% 1.1%
Carbon Dioxide CO2 1.2% 1.4%
Titanium Dioxide TiO2 0.7% 1.4%
Phosphorus Pentoxide P2O5 0.2% 0.3%

Thus, most of the rocks in Earth’s crust are all oxides. The principal oxides are silica, alumina, iron oxides, lime, magnesia & potash.  There are not many iron loving compounds in Earth Crust because they were depleted and relocated deeper. Further, more meteoritic content is found in Earth’s Crust.

Conrad Discontinuity

Conrad discontinuity (named after the seismologist Victor Conrad) is considered to be the border between the upper continental crust and the lower one. It is not as pronounced as the Mohorovičić discontinuity, and absent in some continental regions.

Earth’s Mantle

The mantle is a layer between the crust and the outer core. The boundary between highly viscous crust and mantle is called Mohorovičić discontinuity after the name of Croatian geologist Andrija Mohorovičić who proposed this.  No one has been able to physically drill into the mantle and there are no samples of the mantle with human beings as of now. Whatever information we have is based on indirect study, particularly of seismic waves.

Composition of the Earth’s Mantle

Similar to earth’s crust, Oxygen is most abundant element in Earth’s Mantle.  The following table shows the composition of earth’s mantle.

Element Amount Compound Amount
O 44.8
Si 21.5 SiO2 46
Mg 22.8 MgO 37.8
Fe 5.8 FeO 7.5
Al 2.2 Al2O3 4.2
Ca 2.3 CaO 3.2
Na 0.3 Na2O 0.4
K 0.03 K2O 0.04
Total 99.7 Total 99.1

Salient Features of Mantle

Earth’s mantle is a rocky shell about 2,890 Kms thick that constitutes about 84 percent of Earth’s volume. It is predominantly solid and encloses the iron-rich hot core, which occupies about 15 percent of Earth’s volume.  The mantle is divided into sections viz. The Upper Mantle, which starts from the Mohorovičić discontinuity around 7 to 35 km, downward to 410 km), The transition zone (410–660 km) The Lower Mantle (660–2891 km). The upper and lower mantle differentiate on the basis of seismic and chemical changes in the layer. These changes create different kinds of discontinuities in the mantle. For example: Hales Discontinuity is found in the upper mantle at depths of about 60 to 90 kilometers, a region in which seismic velocities change. Gutenberg Discontinuity or the core–mantle boundary (CMB) lies between the Earth’s silicate mantle and its liquid iron-nickel outer core. This boundary is located at approximately 2900 km depth beneath the Earth’s surface. The boundary is observed via the discontinuity in seismic wave velocities at that depth.

Circulation in Mantle

Due to the temperature difference between the Earth’s surface and outer core and the ability of the crystalline rocks at high pressure and temperature to undergo slow, creeping, viscous-like deformation over millions of years, there is a convective material circulation in the mantle. Hot material upwells, while cooler (and heavier) material sinks downward. Downward motion of material occurs at convergent plate boundaries called subduction zones.  The convection of the Earth’s mantle is a chaotic process, which is thought to be an integral part of the motion of plates. Here, we have to note that the Plate motion is different from the continental drift which applies purely to the movement of the crustal components of the continents.

Earth’s Core

Using the seismic data, the scientists had first postulated the existence of a fluid core. In 1915, Gutenberg published a measurement of the core’s radius. In 1936, Danish seismologist Inge Lehmann (l888-1993) presented a paper titled, “P’” (or P -Prime, after the seismic waves), which announced the discovery of Earth’s inner core. The division between the inner and outer core is now called the Lehmann discontinuity. The size of this core was calculated later in 1960s when an underground nuclear test was conducted in Nevada. Because the precise location and time of the explosion was known, echoes from seismic waves bounced off the inner core provided an accurate means of determining its size. These data revealed a radius of Earth’s Inner solid Core about 1,216 kilometers. The seismic P-waves passing though the inner core move faster than those going through the outer core-good evidence that the inner core is solid. The presence of high-density iron thought to make up the inner core also explains the high density of the Earth’s interior, which is about 13.5 times that of water.

Outer Core versus Inner Core

Earth’s core is divided into two parts viz. a solid inner core with a radius of about 1,216 km and a liquid outer core extending beyond it to a radius of ~3,400 km. The solid inner core is generally believed to be composed primarily of iron and some nickel. How it was formed? The major event which led to the formation of core was iron catastrophe. Earth was formed approximately 4500 million years ago. After accumulation of the Earth’s material into a spherical mass, the material was mostly uniform in composition. The collision of the material which formed the Earth was significant; heating from radioactive materials in this mass further increased the temperature until a critical condition was reached, when the material was molten enough to allow movement. At this point, the denser iron and nickel evenly distributed throughout the mass sank to the centre of the planet to form the core – an important process of planetary differentiation. The gravitational potential energy released by the sinking of the dense Ni-Fe globules increased the temperature of the protoplanet above the melting point resulting in a global silicate magma which accelerated the process. This event occurred at about 500 million years into the formation of the planet and is known as Iron catastrophe. Recent researches show that the innermost part of the core is enriched in gold, platinum and other Siderophile elements (Siderophile elements are those ‘Iron Loving” elements that tend to bond with metallic iron as per Goldschmidt classification).

The Goldschmidt classification, developed by Victor Goldschmidt (1888-1947), is a geochemical classification which groups the chemical elements within the Earth according to their preferred host phases into lithophile (rock-loving), siderophile(iron-loving), chalcophile (ore-loving or chalcogen-loving), and atmophile (gas-loving).


Earth’s Magnetic Field and Magnetosphere

Earth’s Magnetic Field

The Magnetic Field of the Earth is generated by the motion of molten iron alloys in the Earth’s outer core. The solid inner core is too hot to hold a permanent magnetic field, but the outer core gives rise to Earth’s magnetic field. The geomagnetic field extends from outer core to where it meets the solar wind. At the surface of Earth, the magnitude of Earth’s magnetic field ranges from 25 to 65 microteslas (0.25 to 0.65 gauss).

How magnetic field protects life on Earth?

The magnetic field deflects most of the charged particles emanating from the Sun in the form of solar winds. If there were no magnetic field, the particles of the solar wind would strip away the ozone layer, which protects the Earth from harmful ultraviolet rays. One of the reasons that there is no atmosphere at Mars is that its magnetic field is turned off which led to the loss of carbon dioxide due to scavenging of ions by the solar wind.

How it is formed?

The Earth’s magnetic field is believed to be caused by electric currents in the liquid outer core, which is composed of highly conductive molten iron. The motion of the fluid is sustained by convection, motion driven by buoyancy. At the core, the pressure is so great that the super hot iron crystallizes into a solid. The higher temperature of the fluid lower down makes it buoyant. This buoyancy is enhanced by chemical separation: As the core cools, some of the molten iron solidifies and is plated to the inner core. In the process, lighter elements are left behind in the fluid, making it lighter. This is called compositional convection.

The mechanism of formation of Earth’s Magnetic field has not yet been understood fully. The basic physics of electromagnetism can be used to somewhat explain the phenomena. Iron, whether liquid or solid, conducts electricity; when we move a flowing electric current, we generate a magnetic field at a right angle to the electric current direction (Ampère’s  law) . The molten outer core of our planet releases heat by convection, which then displaces the flowing electrical currents. This generates the magnetic field that is oriented around the axis of rotation of the Earth, mainly due to the rotational effects on the moving fluid.  However, it has not been explained how the charges, necessary for creation of electric field originate, which in turn give rise to the magnetic field.

This convection caused by heat radiating from the core, along with the rotation of the Earth (Coriolis force), causes the liquid iron to move in a rotational pattern. It is believed that these rotational forces in the liquid iron layer lead to weak magnetic forces around the axis of spin.  The role of the Coriolis Effect is that it causes overall planetary rotation, and tends to organize the flow into rolls aligned along the north-south polar axis.

Reversal of the fields

Based on data from ancient and new rocks, it has been observed that Earth’s north and south magnetic fields have reversed polarity many times. This is because the polarity of the Earth’s magnetic field is recorded in sedimentary rocks. The switching from north to south (an individual reversal event) seems to take around a couple thousand years to complete; once the reversal takes place, periods of stability seem to average about 200,000 years. Nobody has been able to explain why the poles reverse, but theories range from the changes in lower mantle temperatures to the imbalance of landmasses on our world (most of the continental landmass is in the Northern Hemisphere). The last magnetic reversal was 780,000 years ago, which gives us current northern and southern magnetic poles.  It is believed that geomagnetic field is slowing weakening, so Earth might be heading for a long-overdue magnetic reversal. Reversals tend to occur when there is a wide divergence between the magnetic poles and their geographic equivalent (as it is now).

Intensity gradient of the Geomagnetic Field

The intensity of the geomagnetic field is greatest near the poles and weaker near the Equator. A map of intensity contours of the geomagnetic field is called an isodynamic chart. Isodynamic chart for the Earth’s magnetic field shows that minimum intensity of the magnetic field is over South America while maximum is over northern Canada, Siberia, and the coast of Antarctica south of Australia.

Magnetic Dip

Magnetic dip or magnetic inclination is the angle made with the horizontal by the compass needle of a vertically held compass. This angle varies at different points on the Earth’s surface. In the northern hemisphere, the field points downwards. It is straight down at the North Magnetic Pole and rotates upwards as the latitude decreases until it is horizontal (0°) at the magnetic equator. It continues to rotate upwards until it is straight up at the South Magnetic Pole.

North Magnetic Pole on the surface of Earth’s Northern Hemisphere at which the planet’s magnetic field points vertically downwards. In 2001, it was in Canada, but now, it has moved out of Canada’s territory towards Russia. The south magnetic pole was off the coast of Wilkes Land — a part of Antarctica — about 2750 km from South Pole.

Geomagnetic Equator & Equatorial Electrojet

Contour lines along which the dip measured at the Earth’s surface is equal are referred to as isoclinic lines. The locus of the points having zero dip is called the magnetic equator or aclinic line. In the following graphics, the green line shows the magnetic equator, which runs very close the southern tip of our country. This is the important reason for the establishment of the Vikram Sarabhai Space Centre at Thumba, which is close to Geomagnetic Equator. The reason is that the magnetic equator differs significantly from the geographic equator. Directly above the magnetic equator, at altitudes of around 110 km in the atmosphere, a system of electric currents exists that flows from west to east along the magnetic equator. It is known as Equatorial Electrojet.

The closer we are to the magnetic equator, the better we are placed to study the Equatorial electrojet. In the early 1960s, there were very few places in the world close to the magnetic equator with adequate infrastructure to support research in this field. That is the reason that Thumba was chosen. Thumba is located in the outskirts of Thiruvananthapuram. Here, Thumba Equatorial Rocket Launching Station (TERLS) was launched in 1963. Eventually, TERLS have given birth to the Vikram Sarabhai Space Centre (VSSC) and to the Indian Space Research Organisation (ISRO).

Earth’s Magnetosphere

Earth is surrounded by a magnetosphere. The invisible geomagnetic lines stretch from one pole, curve far out into space, then go back to the opposite pole. The curved lines are further shaped by the electrically charged particles of the solar wind into a teardrop shape called the magnetosphere. The Magnetosphere is thus the magnetic field that prevents the solar winds, or highly energetic particles to reach Earth. Please note that the shape of magnetosphere of Earth is determined by the Earth’s internal magnetic field, the solar wind plasma, and the interplanetary magnetic field (IMF). This shape is not static but is dynamic.

Structure of the Magnetosphere

The complex structure of Earth’s magnetosphere is the result of the interplay between the charged particles originating in the upper layers of the terrestrial atmosphere, whose motion is guided by the Earth’s magnetic field, and the solar wind particles carrying the interplanetary magnetic field. The magnetosphere is basically a space filled primarily with particles from terrestrial origin.

The shape of magnetosphere keeps changing throughout the day and night, with Earth’s rotation, revolution and during solar storms and other such events which can affect it.

To understand its boundary, we take an example of a boat that moves through the sea. In front of the boat a bow wave is formed: that bow wave demarcates the region in which the boat disturbs the flow of the water. The water behind the bow wave is forced to flow smoothly around the boat’s hull. Behind the boat a wake is formed. The similar kind of interaction is the solar wind – magnetosphere interaction. The solar wind consists of particles that are mainly of solar origin. It is pervaded by the interplanetary magnetic field. A bow shock is formed in front of the Earth’s magnetosphere, which demarcates the region where the solar wind flow is impeded by the presence of the Earth. The solar wind in the magneto sheath, the region between the bow shock and the Earth’s magnetosphere, is forced to flow around the Earth’s magnetosphere and is compressed.

The impermeable outer surface of the magnetosphere, where the total pressure of the compressed solar wind precisely balances the total pressure inside the magnetosphere, is called the magnetopause. As shown in the accompanying figure, the magnetopause has a shape that is elongated and stretched out in the anti-solar direction, forming a long magnetotail, which is in a sense similar to the wake behind the boat. Due the complex interplay, the magnetosphere becomes roughly bullet shaped and extends on the night side in the “magnetotail” or “geotail” approaching a cylinder with a radius that is around 20-25 times of the Radius of Earth. The tail stretches to around 200 times the Radius of Earth. The day side tip or sub-solar point of the magnetopause is called “nose’ of the magnetopause. It is normally located at 10 RE (Earth radii) towards the Sun. There are two polar cusp regions above the “Geomagnetic Poles”. These are regions where solar wind can enter relatively easily into the magnetosphere. The inner magnetosphere is strongly connected to the Earth’s ionosphere. The inner region, called the plasmasphere, which consists of dense cold plasma largely of ionospheric origin, rotates more or less, along with the Earth.

Van Allen belts

In the inner region of the Earth’s magnetosphere, there are two distinct rings of electrically charged particles that encircle our planet. These are called Van Allen belts after their discoverer. The particles in these belts originate from different sources; some come from the solar wind, some from the Earth’s upper atmosphere, and some from cosmic rays originating in the distant Universe. The belts are shaped like fat doughnuts, widest above Earth’s equator and curving downward toward Earth’s surface near the Polar Regions.


These charged particles usually come toward Earth from outer space—often from the Sun—and are trapped within these two regions of Earth’s magnetosphere. Since the particles are charged, they spiral around and along the magnetosphere’s magnetic field lines. The lines lead away from Earth’s equator, and the particles shuffle back and forth between the two magnetic poles. The closer ring is about 3,000 kilometers from Earth’s surface, and the farther belt is about 15,000 kilometers away. The highly charged particles of the Van Allen belts pose a hazard to satellites, which must protect their sensitive components with adequate shielding if their orbit spends significant time in the radiation belts.

Magnetospheric storms

We have read above that the magnetosphere is not a static structure. Rather, it is constantly in motion, as the orientation of the Earth’s magnetic dipole varies with the Earth’s daily rotation and with its yearly revolution around the Sun, and as the solar wind is characterized by a strong time- variability on time scales ranging from seconds to years. As a consequence of this time-variability, the sizes and shapes of the regions may change with time. When material from a solar Coronal Mass Ejection travels through the interplanetary medium and hits the Earth, the dynamic pressure of the solar wind is strongly enhanced so that the bow shock and the magnetopause are pushed inward, producing a Magnetospheric storm.


The magnetosphere is an almost completely ionized collision less plasma. Nevertheless, a large cloud of neutral hydrogen surrounds the Earth, which is called the Geocorona. Since collisions are so rare, this neutral cloud can co-exist with the plasma in the inner regions of the magnetosphere with relatively little interference.

Other plantets with magnetosphere

Other planets with intrinsic magnetic fields viz. Mercury, Jupiter, Saturn, Uranus, and Neptune. Jupiter’s moon Ganymede also has a small magnetosphere, but it is situated entirely within the magnetosphere of Jupiter, leading to complex interactions.

January 11, 2018

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