One of the better-known classes of maps are contour maps: maps covered with bunches of wavy lines (usually brown) depicting constant elevation. The lines allow the map reader to find (or mentally interpolate) the elevation of any given point. The closer the contour lines are in a given area, the steeper the slope. Because of this, map readers can also train themselves to read the contours in gestalt, giving them an idea of the shape of a land surface.

Cartographers making nautical charts turned it upside down, showing bottom depth below the water's surface. But they also realized the technique's great potential: the power to depict statistical surfaces generated by all sorts of geographic distributions. Meterorologists are quite fond of the latter, as witnessed by the large number of the weather forecast maps you see on TV.

Cartography seems to be a discipline which generates more terms of jargon than average, and this cartographic technique seems to be the silliest generator of jargon in the discipline. Over the years, cartographers making maps depicting various distributions have created a wide variety of terms for lines of constant value on a map:

and dozens of others too silly to list here. Making a budding young cartographer memorize these terms seems to be a favorite weed-out exercise for geography professors and graduate students forced to teach cartography to undergraduates. But to the person drawing the map, they all mean the same thing: A line on a map, connecting points of constant value.

To the rescue comes the term isarithm, the proper generic term for all such lines. Some cartographers think that the Greek ending is pretentious and use the horrible mixed term "isoline" instead.

An isarithmic map is one choice among many for depicting geographic distributions spread over areas (among them the choropleth and dasymetric techniques). As with all other techniques, it carries its own set of considerations and pitfalls. The most important consideration is picking the correct values for the isarithms (aka picking the "contour interval"), since bad choices will miss important important details (and add erroneous ones) to the map reader's picture of the statistical surface. Another consideration is symbolization: Some distributions are better depicted with the lines; others are better depicted by filling in shades or colors between the lines and omitting the lines themselves. As for the collection of data for isarithmic maps, and the construction of the isarithms themselves, a whole subfield of cartography is devoted to it.

As with choropleth maps, isarithmic maps cannot be made from volumetric values (although isopleth maps can be made by showing density values, just as with choropleth maps). With isarithmic maps, the reason seems to be clearer: You can't speak of the "population" of a point such as the location of the fire hydrant in front of your house. You can estimate the population density in the general vicinity of the hydrant, taking your whole neighborhood into account.

As academics do, they invent special terms for sub-concepts of larger concepts. For isarithmic maps, there are two such categories: isometric and isoplethic maps. The difference lies in the distribution being depicted.

An isometric map depicts a distribution you can actually go out and measure a value for in the field. The value you measure will correspond to the value you derive from the map. Thus, elevation and bathymetry maps are isometric, as are temperature maps, rainfall maps, relative humidity maps, and the ever-popular magnetic declination map. Isometric distributions are not limited to physical phenomena: the travel time map is isometric.

An isopleth map depicts a distribution you can't go out and measure. Thus, a contour map showing a population density or economic indicators such as income, poverty rate, as well as the cost of transporting goods.

A geographic distribution depicted with isopleths is a great deal more abstract than an isometric one. The value of an individual point isn't meaningful: Positional accuracy is germane to isometric maps, but not isoplethic ones. Also, you can't interpolate values for a point between isopleths, that is, you can't say "The povery rate over the manhole at the corner of Greenmount and 33rd is X" and expect anyone to take you seriously. You can say "The poverty rate in Waverly is X and decreases as you go north".

However, such shades of meaning (p.t.p.) are lost on most people, and many people consider all of the terms symonymous. But isarithmic maps are so widespread that you should be able to recognize one, even if you're not a cartographer and don't care about the niceties.

1Borden D. Dent, Principles of Thematic Map Design, 1985, Addison-Wesley, ISBN 0-201-11334-1

2Arthur H. Robinson, Principles of Cartography, various editions, Current edition ISBN 0-471-55579-7

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