Introduction to Earth Systems: Lesson 2 Measure and Scale   Reading Assignment: David Greenhood, Mapping, Chapter 3 NAVIGATION (To return, use back button) Reading Key Concepts Discussion More Links Exercises
Side Notes	Key Concepts	Links
Measure along Earth	These are the key concepts in this lesson. You should be able to define or describe them after you have read this lesson, finished the assigned reading and explored the links. You should also be able to do the exercises and answer the questions at the end of the lesson. distance area metric system English system area measure scale   Location While Earth is a three-dimensional object, its surface is two dimensional. Places are named by means of coordinate systems, e.g. latitude-longitude, that require two components to assign a unique name to a location. For example, the city hall of San Francisco, California is at approximately 37°46' North latitude and 122°25' West longitude. Measure on the surface of Earth is therefore one-dimensional or two-dimensional. Measurement in one dimension is length, or distance, and in two dimensions, area. Distance Paths along Earth's surface are generally not straight lines. As a nearly-spherical surface, the Earth is curved everywhere, and paths tend to deviate from constant direction anyway. So most distance measure on Earth is along curved paths. The units are linear units, i.e. the same as those used for measuring along straight paths.	Examples of maps and data
Definition of meter         Units of measure | | | | | | V	Metric system  In the metric system, the fundamental unit of distance is the meter. Historically, it was defined as one ten-millionth of the distance from the Equator to the North Pole as measured along the Greenwich Meridian, i.e. on a North-South path from the Equator to the North Pole through Greenwich, England. The current definition is as the distance that light travels, in a vacuum, in 1/(299,792,458) seconds. Other units are defined in terms of meters. The most commonly used metric units, with equivalents in terms of meters, are as follows: one nanometer = one billionth of a meter = .000000001 meter one micrometer = one millionth of a meter = .000001 meter one millimeter = one thousandth of a meter = .001 meter one centimeter = one hundredth of a meter = .01 meter one decimeter = one tenth of a meter = .1 meter one kilometer = one thousand meters = 1000 meters That is, 1 meter = 1,000,000,000 nanometers = 1,000,000 micrometers = 1,000 millimeters = 100 centimeters = 10 decimeters = .001 kilometers For examples,   235 centimeters = .235 meters = 2,350 millimeters = 2,350,000 micrometers and   3 kilometers = 3,000 meters = 3,000,000 millimeters = 3,000,000,000,000 nanometers	Description of the metric system.
Units of measure | | | | | | V                           Metric--English relationship                         Large distance units	English system  In the English system, definitions of units have colorful histories, most not based on Earth features, but on distances related to the human body, to lengths of strides, etc. Relating the English system to the metric system, the inch is defined as 2.54 centimeters. Other units are defined, ultimately, in terms of inches. Within the English system, we use in addition to inches, most commonly, feet, yards and miles. 1 foot = 12 inches 1 yard = 3 feet = 36 inches 1 mile = 5280 feet = 1760 yards And so, for examples, 5 miles = 5*5280 feet = 26,400 feet 11 feet = 11/3 yards = 3 2/3 yards Smaller distances, i.e. distances less than 1 inch, are often measured in terms of powers of 1/2, such as 1/4, 1/8, 1/16 , hence such measurements as one-half of an inch, three-eighths (3/8) of an inch, eleven- sixteenths (11/16) of an inch, etc. In certain contexts, small distances are in terms of decimal fractions of an inch, i.e. in terms of tenths, hundredths, thousandths, etc. Hence such measurements as three-tenths (0.3) of an inch, thirty-five hundredths (0.35) of an inch, fifteen thousandths (0.015) of an inch, etc. Since one inch is defined as 2.54 centimeters, conversion of measurements between the metric system and the English system is ultimately done through conversion between centimeters and inches. For example, to convert a distance two yards to meters, 2 yards = 2*3 feet = 2*3*12 inches = 72 inches = 72*2.54 centimeters = 182.88 centimeters = 1.8288 meters And 1 meter = 100 centimeters = 100/2.54 inches = 39.37 inches (approximately) Of course, the calculation is shorter through use of other conversion constants that can be built from the relationships given above. Nautical miles: A nautical mile is defined as the length along the equator of an arc whose arc measure is one minute. So, as we will see later when studying Earth geometry, a nautical mile is approximately 1.152 statute miles. Astronomical measure: Light travels at approximately 186,000 miles per second or, in metric measure, approximately 300,000 kilometers per second. A light year is the distance that light travels in one year. Thus,approximating a light year in terms of metric units, one light year = 300,000*60*60*24*365 meters = 9,460,800,000,000 meters = 9,460,800,000 kilometers In general, our distance from stars is measured in light years. The distance of Earth from the sun is approximately 93,000,000 miles, or approximately 150,000,000 kilometers, and is defined as one astronomical unit. Obviously, one astronomical unit is considerably shorter than one light year. Astronomical units are used in measuring long distances to objects that are closer than are the stars, e.g. distances among planets, and in comparing interplanetary distances with other distances.	Systems of measurement                                             Astronomical distance units.
	Area Just as distance can be represented by an interval, e.g. a line segment or an arc of a curve, the primitive units of area are squares. Units of area are squares whose sides are units of length. For example, one square inch is the area of a square whose sides have length one inch. Similarly area can be quoted in numbers of square centimeters, square yards, square meters, etc. For example, the area of a rectangle whose length is 15 centimeters and whose width is 8 centimeters is calculated as follows:, Area = length * width = 15*8 square centimeters = 120 square centimeters Metric System: In addition to the use of unit squares as area units, there are special, and specially named -- they are the "are" and "hectare" -- units in the metric system. By definition, 1 are = 100 square meters 1 hectare = 100 ares = 10000 square meters English System: Beyond the use of square inches, square feet and square miles, the most commonly used unit of area in the English system is the acre, which is defined as 43,560 square feet. Note that 1 square mile = 5,280*5,280 square feet = 27,878,400 square feet = 640*43,560 square feet = 640 acres Other units, e.g. the section, or square mile, and the township, or 36 square miles, are in use in special contexts. The section and township are actually entities of survey. A section has area one square mile and its shape is a square, or nearly so, one mile on a side. A township is approximately a square six miles on side. Conversion between the metric and English systems is ultimately through the relationship between the centimeter and the inch. Calculating in this manner shows that 1 hectare is approximately 2.471 acres	Practical formulas for calculations of some areas.
Distance on object vs. distance on map	Scale Most maps are smaller than their subjects. Accuracy in representing shapes requires that relationships among shape, distance and area on the map are the same as on its subject. This is possible if relationships among distances on the map are the same as relationships among distances on its subject. We achieve this by maintaining constant proportion between distances on the map and corresponding distances on the subject. Since a proportion is the equivalence of two ratios and the ratio is constant, the size relationship between a map and its subject is usually expressed with a ratio. This ratio is the scale of the map. For examples, A map using scale 1:24,000 is 1/24,000 as large as its subject. Each unit of distance measurement on the map corresponds to 24,000 of the same unit on the subject. Thus a length 2000 feet, i.e. 24,000 inches, would be represented as 1 inch on the map. A map using scale 1:12,000 represents a closer view than does a map using scale 1:24,000 because one unit on the map, e.g. one centimeter, one inch, etc., represents a smaller object using 1:12,000 than is the case with 1:24,000. One centimeter represents a length 12,000 centimeters rather than 24,000 centimeters. Other commonly used scales for maps, depending on the coordinate system, are 1:50,000 1:62,500 1:100,000 1:125,000 1:250,000 The representation of scale as described above does not depend on choice of distance units, hence applies to the metric system and the English system. With some maps, for reasons of tradition and ease of reading, the reader is shown a representation of scale that specifies units appropriate for the size of the map and for the size of the subject. For example, one inch to one foot: This specifies that one inch on the map corresponds to one foot on the subject. one centimeter to 2.5 kilometers: This specifies that one centimeter on the map corresponds to 2.5 kilometers on the subject. Frequently, scales, as well as many other ratios, are specified with 1 as one of the components, e.g. 1:12,000,   20:1,   1:1, etc. And so, as seen above, some specifications include a component that is not a whole number, e.g. 1:2.5, which is equivalent to 2:5	Representations of scale
	Links Metric-English equivalents       TOP   Discussion Exercises Describe a system for locating places on portions of Earth without using latitude and longitude.   Convert the distance 1,600 meters to feet and inches, to the nearest inch.   How many miles are there in a light year?   Given that the scale of a particular map is 1:1500, what are the dimensions of a map that represents a square whose sides are one mile long?   Given that the scale of a particular map is 1/16 inch : 1 mile, determine approximate dimensions for a map of California.   How many square kilometers are there in one square mile?   How many square miles are there in one hectare?   Approximately how much time is required for light to travel from the Sun to Earth?   to  ANSWER/HINT PAGE to  INDEX