Designing and Choosing symbols 171
sea level), and
isohypses, lines of equal elevation above sea level, also called
contour
lines (see Table 8.3).
If a horizontal plane is passed through the statistical surface, the line of inter-
section of the plane and the surface when projected downward is an isarithmic line
(Figure 8.33). We can see that every point along the intersecting
line is the same
distance from the datum. If a series of parallel planes intersects the surface, the lines
projected are isarithmic lines and the distance between the planes is called the
isarith-
mic interval.
Data Considerations
There are two major categories of isarithms,
isometric lines and
isoplethic lines, and
although the generic terms
isarithm or
isoline are more commonly used, it helps to
understand these symbols by considering the two categories.
These categories are
based on the nature of the
z-values and the form in which the data are collected. If
the data are collected for actual points, such as weather stations, or elevation control
points, for which values actually exist (true points), the type of line is an
isometric
line. The
z-values may be absolute values, such as temperature at a specific time, or
derived values, such as average temperature at that point.
But if the points for which the data are obtained are assumed or arbitrary (con-
ceptual points), such as the center of a distribution or the center of an enumeration
area like a county or census tract, the values refer to an area rather than a point, and
the
z-values are derived, that is, ratios, averages, and percentages. This type of line is
an
isopleth or
isoplethic line. Isopleths are often used to represent population densi-
ties and the like.
Understanding and interpreting isarithms
Although the methods of construction for these two kinds of isarithmic line are simi-
lar, the type of information that they portray and what the reader can extract from
the maps are different. An isometric line permits values to be determined by
interpo-
lating or estimating values between the lines.
Interpolation is the estimating of values by comparing the distance to all other
neighboring control points. The isarithmic method assumes an even gradient between
control points so the location of the 20-inch rainfall line on Figure 8.34 is midway
between 15 and 25 inches. When reading isarithmic maps, the reader interpolates or
“reads between the lines” to estimate the value of any point.
If the isarithmic interval is even, the rate of change is found from the spacing of
