Locating Points on Earth

To locate anything on a sphere you need a grid. Latitude measures distance north or south of the equator, from 0 degrees at the equator to 90 degrees at the poles. Longitude measures distance east or west of the prime meridian through Greenwich, England, from 0 to 180 degrees. A location needs both, each with a direction: New York State sits at roughly 41 to 45 degrees north, 72 to 80 degrees west.

In the Northern Hemisphere there is a shortcut for finding latitude. The altitude of Polaris, the North Star, above the horizon equals your latitude. Stand at the North Pole and Polaris is straight overhead at 90 degrees. Stand at the equator and it sits on the horizon at 0. From Pleasantville, at about 41 degrees north, Polaris is 41 degrees up. Longitude was historically found using time instead. Earth rotates 15 degrees per hour, so comparing local solar time to Greenwich time gives you your longitude.

Latitude uses Polaris. Longitude uses a clock. Earth rotates 360 degrees in 24 hours, which works out to 15 degrees per hour. So every 15 degrees of longitude means an hour's difference in solar time. That is why sailors carried precise chronometers set to Greenwich time. They compared local noon, the moment the sun stands highest, to the clock. Every hour of difference is 15 degrees of longitude east or west. It is also why time zones are roughly 15 degrees wide, and why the sun rises in Boston before it rises in Buffalo.

Work an example. Say it is noon where you stand and 3:00 p.m. at a place to your east. That place is three hours ahead, and three hours times 15 degrees gives 45 degrees of longitude between you. East is ahead because Earth rotates from west to east, so the sun rises there first. This is exactly how early navigators found their longitude at sea. They carried a clock set to a known reference meridian, compared it to local noon, and converted the time difference into degrees. That is why a reliable ship's clock was worth a fortune.

A field is any region where a quantity has a measurable value at every point. Elevation, temperature, air pressure, and pollution are all fields. Maps show fields with isolines, which are lines connecting points of equal value. Isolines for temperature are called isotherms, isolines for pressure are isobars, and isolines for elevation are contour lines.

All isolines follow the same rules. They connect equal values. They never cross, because one point cannot have two values. They close on themselves, either on the map or somewhere past its edge. Where they crowd together, the field is changing quickly. Where they spread apart, it changes slowly. Learn these rules once and you can read any field map in the course.

Isolines show you the value of a field everywhere. They also show you something just as useful, which is how fast that value is changing. That rate is called the gradient, and reading it is one of the most tested skills in the course. The rule is simple. Where isolines are packed close together, the field changes quickly and the gradient is high. Where they are spread far apart, the field changes slowly and the gradient is low. Steep mountainsides crowd their contour lines together. A flat plain spreads them out.

You can also put a number on it. The gradient is the change in field value divided by the distance over which that change happens. So a hillside that climbs 100 meters over 2 kilometers has a gradient of 50 meters per kilometer. The same formula works for any field. You can find degrees of temperature per kilometer between isotherms, or millibars of pressure per kilometer between isobars. Always read the change in value from the isolines and the distance from the map scale, then divide.

Point an imaginary sextant at Polaris. Set its altitude above the horizon and the lab reads off your latitude, because in the Northern Hemisphere the two are the same number. Find the setting that puts you in Pleasantville.

Latitude measures north and south of the equator. Longitude measures east and west of the prime meridian. Together the pair locates any point on Earth. In the Northern Hemisphere, the altitude of Polaris gives you your latitude directly, and Earth's steady 15-degrees-per-hour rotation lets a clock give you longitude. Fields have a value at every point, and isolines let you see those fields. Isolines connect equal values, never cross, and crowd together wherever the field changes fast. The next chapter applies all of this to the most important field in the course, which is the elevation of the land itself.

Ten Regents-style questions, one at a time in a focused view, each with an instant explanation. The set reshuffles when you reach the end, so you can keep practicing as long as you like.