98 THe geOgRaPHiC anD
CaRTOgRaPHiC FRaMeWORK
“tiers” is the original term, common usage has become “townships and ranges”).
The 36-square-mile areas formed are called
townships (Figure 6.8). Each township
is divided into 36 one-square-mile areas called
sections that contain 640 acres, and
the sections can be further subdivided
into quarter sections, eighth sections, and
so forth so that any parcel of land has a unique one-line designation. For example,
NE1/4,SW1/4,SW1/4,NE1/4, sec. 23, T1SR3W, Mt. Diablo Meridian would describe
a 2 1/2-acre piece of land located in the first tier south of the base line, the third range
west of the Mt. Diablo principal meridian in the northeast quarter of the southwest
quarter of the southwest quarter of the northeast quarter of section 23.
The PLSS is a systematic cadastral survey, but in much of the world unsystematic
property surveys, which are also called
metes and bounds or
indiscriminate loca-
tion, have been used. For metes and bounds, property lines and boundary markers
are arbitrarily selected and are often natural features such as rocks, rivers, or trees.
A property
description might begin, “From the granite boulder at the river bank
N30°E, 500 yards to the oak tree, then S80°E 150 yards. . . .” These boundaries,
unlike the PLSS, were usually drawn after settlement
and the lots tend to form a
crazy-quilt pattern.
tRAnsfoRmIng the eARth’s gRAtIcUle: mAP PRojectIons
A projection is the transformation of the earth’s spherical graticule onto a plane sur-
face. The formal definition is
a systematic and orderly representation of the earth’s
grid upon a plane. Unlike some shapes, such as a cone, a sphere cannot be flattened
without some distortion. The projection is a foundation because it governs the posi-
tions of points on the map with respect to one another. The projection forms the
fIgURe 6.7.
Public Land Survey System. The original 13 colonies and Texas are not covered
by the PLSS.
The earth’s graticule and Projections 99
framework for the map, and therefore it is necessary to decide which projection will
be used early in the planning stages of the map. There are an infinite number of pro-
jections possible, and more than 400 projections available, although only a relative
few are employed regularly.
The key terms in the definition are “systematic” and “orderly.” One does not cre-
ate a “projection” simply by peeling the globe or tearing off pieces. The graticule is
transformed or projected in a systematic manner onto a flat surface, and the positions
of continents and seas then plotted onto the transformed graticule.
The shape of the earth was discussed in the preceding section. Here we will not
be involved with the geoid or spheroid, but will consider the earth to be a sphere for
ease in understanding.
Although for large-scale maps, such as topographic maps,
the exact shape of the earth must be taken into account, for most thematic maps the
earth can be considered a perfect sphere.
Before
analyzing projections, the properties of the globe should be reviewed:
1. All parallels are parallel.
2. Meridians are half great circles and converge at the poles.
3. The meridians are evenly spaced along any parallel.
4. Quadrilaterals formed by the same two parallels and having the same longi-
tudinal dimensions will have the same areas.
