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Map Intrepretation III
Projections and Survey Systems
Contents
A.
Projections
B.
Coordinate Systems
C.
Survey Systems
1. Background
You can't squash a grapefruit peel flat without
breaking it into many pieces (try it sometime). In the same
way, we cannot transfer the spherical surface of Earth to
a flat surface without distortion. We can create a logical
way to transfer coordinates from the sphere onto a flat map.
Such ways of transferring coordinates are known as projections,
after the original method of transferring by literally projecting
a light through a globe onto a surface. But no projection
can accomplish its task without some distortion. Fortunately,
we can choose to preserve certain qualities that a globe possesses.
But in the process we sacrifice other qualities.
Before we project the actual Earth onto a surface, we usually
simplify it. Earth isn't a perfect sphere. It's somewhat flattened
at the Poles, so an ellipsoid represents Earth better (an ellipsoid
is formed by rotating an ellipse around one of its axes). Actually,
the diameter at the equator is only about 42.8 km more than the
polar axis. But it is enough to throw off exacting measurements,
like property lines.
An ellipsoid is still not perfect; the geoid is an irregular,
but even closer, representation of Earth. It's the equivalent
of mean sea level all over the globe. Since gravity and Earth's
surface are irregular, the geoid is not a smooth surface, and
can't be represented with equations easily, so it's rarely used
for mapping.
A particular ellipsoid, with particular values for equatorial
and polar diameters, is often used in projecting and measuring
on Earth, particularly for highly accurate measuring such as in
surveying. A dozen ellipsoids are in common use around the world,
including:
- Clarke Spheroid of 1866, used in most of the North America.
It was revised earlier this century, with the results called
the North American Datum of 1927, or NAD27.
- Geodetic Reference System 1980, a new ellipsoid, is being
adopted in North America to correct inaccuracies in NAD27. The
resulting "datum" is called the North American Datum of 1983,
or NAD83.
- International Ellipsoid, from 1924, used in most of the rest
of the world (but developed in the US from US data!).
2. Methods of Projection
Many projections can be visualized as literally projecting a light
source through a transparent globe onto a surface. The light source
can be any number of places - at the center of the globe, at the
opposite side of Earth, or out in space, for instance (see figure
below for examples). The map surface onto which the projection is
made can be various shapes, and can also be at various places. In
all projections, the map surface touches the globe at at least one
point. This is because any map is most accurate where it touches
the globe; there is no distortion here. The contact point between
globe and map is called the point of tangency; if it is a line,
it's a line of tangency, standard line, or (if it is a parallel)
standard parallel. Away from the tangent locations, the map surface
gets further from the globe, and hence more distorted. Most all
projections nowadays are done by computer using equations that relate
lat/long to x/y coordinates on the map.
Projections may be made onto three basic shapes, with three types
of projections resulting:
a. Planar
Also called azimuthal. In this case, the globe is projected onto
a flat surface. The "light source" can be from several locations.
Usually, the flat surface touches the globe at a single point.
Most often planar projections are used for Polar regions, and
the tangent point is the North or South Pole.
b. Cylindrical
Here a cylinder is wrapped around the globe, usually with the
map surface touching the globe at a circle (a great circle, to
be exact -- a circle whose center coincides with the center of
Earth). Cylindrical projections are the only one of the three
main types that can show the entire globe, and so most world maps
are cylindrical.
The most famous cylindrical projection is the one named for Gerhardus
Mercator, who developed it in 1569. It was valuable for early
navigators, since straight lines on a Mercator map are also compass
headings. Unfortunately, it greatly distorts the sizes of areas
near the Poles (see section 3 below), so it should not be used
as a general--purpose world map!
c. Conical
The third type of projection is made onto a cone. Usually this
means contacting the globe along one of the parallels (lines of
latitude), i.e., a small circle. Although we cannot use conic
projections for a world map, they are excellent for continent--sized
areas in the mid--latitudes. Most maps of the United States are
made with conic projections.
Conic projections are usually made more accurate by "sinking"
the cone part way into the globe (remember, this is all done with
computers, not literally!). Then we have two lines of tangency,
or two standard parallels, along which the map is extremely accurate.
This two--line approach is also called the secant case, as opposed
to the simple tangent case. You may see maps of the US with a
statement on the bottom like: "Lambert Conformal Conic Projection,
48° and 33° Standard Parallels." The projection was
developed by J.H. Lambert (1728--1777), an important figure in
cartography.
d. Other
Some projections are not based on any of the above three shapes,
and cannot be visualized as literally being projected. Instead,
they simply have equations that tell where to plot each latitude/longitude
coordinate from the globe. Some examples are the Sinusoidal and
van der Grinten projections. World maps are often made with these
projections, since they may have less distortion than cylindrical
projections.
3. Qualities of Projections
The other major factor you need to know about a projection is
the qualities about the globe that the projection either preserves
or distorts. Most projections can preserve one or more of the
following qualities, but none can retain all of them. Note that
the projection method (planar, cylindrical, or conical) does not
necessarily mean any of these qualities below are preserved or
distorted. It all depends on how the projection is done.
a. Equal-Area
Some projections show all areas in true proportion to their real
areas on the globe. For example, a dime placed on the map would
cover the same area regardless of where placed. To show areas
truly, a map must distort most of the other qualities below, at
least subtlely. But if you need a general--purpose map of the
world or continental area, an equal--area map, or a map that is
very close to equal--area, is your best bet. Some examples: Sinusoidal,
Albers Conic Equal--Area, and Lambert Azimuthal Equal--Area.
b. True Shape, or Conformality
Another important characteristic of the globe that can be distorted
on a map is the shape of areas. This distortion problem is obvious
on a cylindrical map that is equal--area, because the higher latitudes
near the Poles have to be distorted to preserve areas. The Mercator
projection is conformal, but at the expense of area. The Mercator
shows Greenland almost as large as South America, when in reality
it is about 1/8 the continent's size. Some people have accused
developed nations (which are mostly in the higher northern latitudes)
of intentionally portraying their lands as larger than developing
countries (which are mostly in lower, tropical latitudes). One
projection, known as the Peters projection, has been promoted
as the "true" world map, since it shows countries with true areas.
Peters is indeed equal--area, but does a number on shape-as one
person put it, it makes the world look like it was hung on a laundry
line. Many other equal--area projections are available that do
a better job with shape.
c. True Scale
In no map can you use one scale accurately for the whole map.
Some distortion occurs, although it is slight in many maps. Some
projections can preserve true scale and distance along one or
more lines. These are may be called equidistant projections. A
popular planar projection for polar areas is known as the Azimuthal
Equidistant, which has true scale from the central tangent point-the
Pole-to any other point on the map. You could also use an Azimuthal
Equidistant map centered on your location to measure distances
accurately to any other place on the globe. Some map software
can draw such a map for you.
d. True Direction
The last major quality of maps is direction. Maps that preserve
it are called azimuthal. Most planar projections preserve true
direction away from the center of the map (usually the Pole) and
so azimuthal is nearly synonymous with planar projection.
e. Other Qualities
Some projections are designed to have specialized qualities.
The Mercator projection is one: all constant compass headings
(rhumb lines, or loxodromes) are straight lines. The Gnomonic
projection is another: all great circle routes are straight lines.
As you may know, great circle routes are the shortest distances
between points on the globe. For example, when you fly from San
Francisco to London, you don't fly along a parallel of latitude,
but over the polar route; this is along a great circle. If you're
flying or sailing, then, you can combine the gnomonic and Mercator
maps for navigating. First you draw your route on the gnomonic
map (a straight line connecting the two places), then transfer
the route to the Mercator map as a series of straight segments
that approximate the gnomonic line. This way, you can follow the
straight segments on the Mercator map with a compass, and turn
only when you need to follow the next segment. You may notice
this when you're flying and the pilot periodically turns to follow
these segments.
How can we describe locations on Earth? If someone asks you,
"where is Hawaii?", what do you tell them? You can give them directions
relative to your position ("swim 2000 miles south--southwest").
Other ways are also possible, but what if you needed to pinpoint
a location for people coming from many directions? Or if you wanted
to record a location for later reference? Or if you had no landmarks
to guide you? This is the purpose of coordinate systems. They
are ways of describing locations on Earth in reference to an established
grid. You have probably been exposed to the most common method,
latitude/longitude, but there are many other methods in use.
1. Latitude & Longitude
The latitude and longitude system is also called the geographical
grid. This grid exploits the fact that Earth is nearly a sphere,
and that it spins on an axis. Looking down on the globe from above
the North Pole, we can fit a circle to the rotating Earth. We
could assign each location along any circle that surrounds the
Pole a measurement in degrees. A circle has 360 degrees. We could
use this range of numbers, going from 0° to 360°. Alas,
early map--makers didn't do this, exactly. They wanted low numbers
on both sides of the Prime Meridian (the 0 line). As a result,
the globe is divided into hemispheres, each assigned longitude
between 0° and 180°, with the addition of East or West
to differentiate the halves. The lines of longitude are meridians.
To complement the east--west measurement, a north--south measurement
is necessary, so that we may pinpoint locations. Since we only
need to measure along one meridian, we only need to assign measures
to a half--circle, or 180 degrees. Once again, it's more complicated
than necessary. Rather than go from 0° at the North Pole
to 180° at the South Pole (or vice--versa), the system starts
with 0° at the halfway point (the Equator), and measures
north and south to 90° at the Poles. Each line of latitude
is a circle; these lines are called parallels (sensible, since
they are parallel to one another).
With this system we can pinpoint any location on Earth. Since
a degree of latitude spans about 111 km, each degree can be broken
down to get more exact. A degree is composed of 60 minutes (60'),
and a minute is composed of 60 seconds (60') -- just like a clock.
Based on this system, SSU lies at 38° 20' 46" N, 122°
40' 30" W. If you're uncomfortable with this system, you should
practice looking up locations on a globe or atlas.
Lat/long is cumbersome to use for at least two reasons. First,
notice that meridians converge at the Poles. A degree of longitude
decreases from about 111 km at the Equator to 0 at the Poles;
1° is about 88 km in Sonoma County. Convergence makes lat/long
poor for use as a rectangular grid, where we want simple x,y coordinates
for locations. Second, lat/long is not a decimal system. How far
is it from 114° 34' 54" to 116° 14' 33"? Not very far,
but you'd have trouble giving me the distance even in terms of
degrees/minutes/seconds. For these reasons, lat/long is usually
replaced by other coordinate systems, especially at the local
level, for most descriptions of location. Most of these systems,
including those below, use a projection of the globe onto a flat
surface, onto which we can then draw an x/y grid.
2. State Plane Coordinates (SPC)
The National Geodetic Survey developed the SPC system beginning
in 1933. Eventually every state was covered, with coordinates
identified both on maps and on the ground, so that surveyors and
cartographers could accurately identify and measure locations.
The key to this system is that rather than having one coordinate
system for the entire US, separate systems were assigned to smaller
zones. Each zone used its very own projection and coordinate center
and system. 120 zones cover the US. Within each zone, you are
never far from the standard line. This way, the coordinates would
be extremely accurate within each zone (less than 1 foot per 10,000
feet of measurement, in fact). The problem, of course, is that
coordinates between zones don't match up, so the SPC system is
not useful for small--scale (large--area) maps that include more
than one zone.
Nearly all states have multiple zones, but zones never cross
county lines. California has 7 zones, most extending as east--west
bands; Sonoma County's zone extends to Lake Tahoe. Los Angeles
County has its own zone (naturally). Each state uses either the
Lambert Conformal Conic or the Transverse Mercator projection
(California uses the first).
Within each zone, locations are identified by x,y coordinates
in feet. Any x,y coordinate system needs an origin, that is, where
the coordinates are (0,0). In order to keep all SPC numbers positive,
the origin for each zone is placed off to the southwest of the
actual zone covered. This origin is not the actual center of the
projection (that is, where the globe "touches" the sheet projected
onto). That actual center is in the middle of each SPC zone, so
that coordinates are most accurate there. In short, the actual
center is assigned an arbitrarily large coordinate (such as 2,000,000
feet East, 400,000 feet North), and all other coordinates are
measured from there. This puts the "false origin" off to the southwest.
SPC coordinates are shown on all USGS topographic maps. Usually
tick marks on the margins of the map show regular spacing of the
grid, and selected marks have the actual coordinates in feet.
By examining the topographic map for Cotati, we can find that
the SPCs for SSU are 1,806,500' E, 246,200' N. As mentioned above,
the SPC system is used widely in conducting local land surveying
and public works. It can be used by the cartographer and geographer
not only to identify coordinates of places, but to calculate distances
between locations by use of the Pythagorean Theorem, as described
in the next section.
3. Universal Transverse Mercator (UTM)
The UTM grid is similar to the SPC system, at least regarding
how you use it at the local level and in being marked on all USGS
topographic maps. The principal differences are that the coordinates
are given in meters, not feet, and that the zones are much larger.
UTM zones extend north--south, practically from Pole to Pole.
The UTM grid system covers the entire globe (well, almost - except
for very near the Poles).
You encountered the Mercator projection before. In the standard
Mercator, the cylinder is "wrapped" around the Equator, and areas
become very distorted toward the Poles. A transverse Mercator
projection turns the cylinder, so that the circle of contact with
the globe is around a pair of meridians. This way, the projection
is very accurate on a north--south zone near the standard line.
Of course, once again it distorts severely at large distances
away from the meridian.
The Universal Transverse Mercator grid gets around the distortion
problem by the same method as the SPC system. The UTM has many
zones, each with its own projection centered on a meridian. There
are 60 zones to be exact, each 6° wide (which covers Earth,
60 x 6° = 360° around). Within each zone, then, the
grid is very accurate in matching true Earth distance and direction.
As with the SPC system, going across zones is difficult, so the
UTM is meant primarily for local and regional measurement.The
UTM was adopted and thus popularized by the Army in 1947. The
Army included the UTM grid on its topographic maps; later the
USGS added UTM coordinates to most of its maps and photoquads.
The Army numbered each 6°--wide zone around the globe from
1 to 60, starting at 180° W and going east; northern California
is in zone 10. They also lettered north--south segments of each
zone from A (south) to Z (north). The north--south segments aren't
necessary, and so are rarely used outside the military.
Within each UTM zone, x,y coordinates can be given in meters.
Like SPCs, an origin is needed, and is placed outside the zone
off the southwest corner. The north--south center of the zone
is arbitrarily designated as 500,000 meters east (that is, east
of a false origin off to the west). "Eastings" (x--coordinates)
for locations east of the center are higher than this, up to about
850,000 m E; westward the coordinates decrease, down to about
150,000 m E; the zone doesn't extend all the way to the false
origin. The "northing," or north--south (y) coordinate, depends
on which hemisphere you're in. For the Northern Hemisphere part
of each zone, the measurement starts at the Equator with 0 and
measures the number of meters north (up to about 8,800,000 m N
at 80° N). In the Southern Hemisphere, the Equator is designated
arbitrarily as 10,000,000 m N, and coordinates decrease as you
go south toward the South Pole.
Examples: A location with coordinates 334,400 m E, 4,203,600
m N would be 334,400 meters east of the false origin, or (500,000
-- 334,400 =) 165,600 meters west of the central line. It would
be 4,203,600 meters, or 4,203.6 km, north of the Equator. The
UTM coordinates for SSU are: 4,243,540 m E, 528,390 m N (these
are actually close to the coordinates for Stevenson 3065).
The UTM grid is shown on all recent USGS topographic maps. The
latest topographic maps draw in the grid as thin black lines.
All topos with the UTM have tick marks along the margin, along
with values for eastings or northings next to most ticks. Except
for a few values near the corners, the easting or northing value
is abbreviated . For example, instead of printing "3,445,000 m
N", the tick would be labeled 3445, with the thousands and meters--north
assumed from the context.
The UTM grid, even if drawn in on the map, may not give us the
exact coordinates for a given location. Even on 7 1/2--minute
quads, the grid is only every 1,000 meters (1 km). How can you
determine coordinates more precisely? The answer is called a roamer.
This is simply a sheet of paper, plastic or other material that
has finer distance intervals marked off that match the scale of
the map. Starting from the nearest grid lines, you can measure
over to the location and come close (at least within 100 m) to
the actual easting and northing coordinates.
Another big advantage of the UTM (or SPC) grid is that once you
have coordinates for two locations within the same zone, calculating
the distance between them is simple. Just apply the Pythagorean
Theorem. If the two locations are at the coordinates (x1, y1)
and (x2, y2), then the distance (D) between them is:
For example, say you find coordinates for two cities: Springfield
at 294,100 m E, 3,428,900 m N, and Garden City at 292,400 m E,
3,428,100 m N. The distance between them is then:
that is, the distance is 1880 meters, or 1.88 kilometers.
As you can see, the UTM grid is a very useful system for tracking
Earth locations. It is used extensively in remote sensing, computerized
mapping, and geographic information systems. It is worth your
while to familiarize yourself with it.
A related topic to coordinate systems is how we describe the
boundaries of parcels of land. SPC or UTM coordinates are great
for giving locations of points, but less so for describing area.
You can describe a parcel by going from point to point--this is
the first method below. But other methods are easier in some circumstances.
This section covers land-description methods used in the US. An
important fact about survey systems is that once land is surveyed
under a given system, that's it--the description of the land stays
with it permanently. Land within old Spanish Land Grants in California
still retain their descriptions based on the original survey.
1. Metes-and-Bounds
Early settlers in the Thirteen Colonies used the same method
for dividing and describing land as they had in the Old World
(especially England). This system is known as metes__-and-bounds.
The idea is very simple: a land parcel is described based on going
from one point to another, in a polygon that encompasses the parcel.
For example, a legal description might read:
"Commencing from a point one-half mile upstream from
Smith Bridge on Jones Creek, proceed northeast 500 feet to Spring
Hill, then northwest to the large oak tree, then southwest to
the large rock in the middle of Jones Creek, then along Jones
Creek to the origin."
The first settlers in an area naturally claimed the best land, and
set up boundaries that encompassed that land. Most of the time,
this worked alright, and in a sense it shapes human use of the land
according to the landscape itself, rather than imposing an artificial
pattern on the land.
But metes-and-bounds surveys are liable to create problems. Since
surveys were done as land was claimed, overlapping claims often
resulted--with lengthy court battles ensuing. Even today, land
titles are more difficult to verify in areas surveyed by metes-&-bounds.
A bigger problem is that the boundary markers (oak tree, big rock)
eventually are obliterated, with the boundaries becoming ambiguous.
One measure to help has been to replace landmarks with exact compass
directions and distances (also known as "Coordinate Geometry").
The description above might be replaced with:
"Commencing from a point one-half mile upstream from
Smith Bridge on Jones Creek, proceed N 45° E 500 feet, then
N 50° W 324 feet, then S 35° W to Jones Creek, then
along Jones Creek to the origin."
A final problem with metes-&-bounds was that the US government wanted
to sell off land in the West quickly, in order to raise cash (no
income taxes back then). A system was needed that could quickly
and rationally divide up the land, allowing for sales without a
lot of legal wrangling. The US Public Land Survey, described below,
became the US answer to the problem.
2. Spanish Land Grants
The Spanish, and later Mexicans, ruled California and much of
the Southwest for about 300 years. They too parceled out land
for use by colonists (with little regard to Native occupation,
of course). The methods of description were very similar to metes-and-bounds.
Much of the land was given or sold to large landowners for ranchos
as Spanish Land Grants. These land grants usually focused on water
resources, which are scarce in the West; sometimes the system
is called Spanish Riparian (riparian means relating to watercourses).
Much of the better land in California ended up in one of these
land grants. Remember, once allocated, land continues to be described
under its original survey, permanently. Even after California
became part of the US, and land grant claims were honored (though
sometimes exchanging hands under questionable deals). The land
grants have be subdivided since then, but evidence still can be
found in property descriptions, and on USGS topographic maps.
For instance, some land grants in Sonoma County were Rancho Cabeza
de Santa Rosa, Petaluma Rancho, and Rancho Cotate. These labels,
along with their boundaries, can be found on topos for Sonoma
County.
3. Other Irregular Surveys
Other survey methods were used in certain parts of the US. In
Louisiana and other areas settled by the French, long-lots were
used. The land along important lanes of commerce, usually rivers,
was divided into narrow strips extending back into the interior.
This resulted in a series of long but narrow plots of land that
are still evident on topo sheets of Louisiana, coastal Texas,
and Mississippi River towns, even as far upstream as Wisconsin.
4. The US Public Land Survey (PLS)
The majority of the land in the US is described under the US
Public Land Survey (PLS) System. After independence, the US wanted
to dispose quickly of lands in the West (at that time, land between
the 13 Colonies and the Mississippi River). Some form of logical,
orderly system was inevitable, but the exact form took time to
shape. Thomas Jefferson and others eventually worked out a rational,
rectangular (squarish) survey, called the Public Land Survey (PLS)
system, which was enacted under the Northwest Land Ordinance of
1785 (with later revisions).
The PLS starts out by establishing an x,y coordinate system for
a given area. The north-south line is called a principal meridian,
and the east-west line a baseline. Each baseline is given a unique
name, so that each land parcel can be identified by that name.
The area described based on a principal meridian/baseline pair
varies from a small part of a state (e.g., eastern Ohio, northwestern
California), to several states (e.g., the Fifth Principal Meridian
covers most of Arkansas, Missouri, Iowa, Minnesota, and most of
the Dakotas).
California has three principal meridian/baseline pairs: the San
Bernardino Meridian (southern California), Mt. Diablo Meridian
(most of northern California), and the Humboldt Meridian (northwestern
corner of the state).
The initial point is the intersection of the principal meridian
and baseline. From this point, townships are marked off east/west
and north/south. Each township is 6 miles on a side, or 36 square
miles. Townships are designated on the east-west direction as
being a certain number of Ranges east or west of the principal
meridian. The township is also a certain number of Townships north
or south of the baseline (note the dual use of the term township,
as an area and as a coordinate). For example, the township that
is just on the northeast corner of the initial point is Township
1 North, Range 1 East, usually abbreviated T. 1 N, R. 1 E. Or
T. 3 S, R. 2 W would be the third township south of the baseline
and two townships to the west.
Each township had to be divided, since few people could afford
36 mi2. The division was into 36 sections, one square mile each.
Rather than using an x,y system here, the sections were simply
numbered consecutively from 1 to 36, starting in the northeast
corner and snaking around the rows, with 36 at the southeast corner.
Most land purchases were for less than one section; the Homestead
Act of 1863 allowed people to receive one-quarter section if lived
on by the claimant. Sections can be broken down into halves or
quarters, each part designated by a compass direction. If divided
in half, we have either east/west halves, or north/south halves.
If divided into quarters, we have the NE, NW, SW, and SE quarters.
Quarters can be broken down further if necessary, for example
we might have the NE quarter of the SE quarter.
A square mile contains 640 acres, so a quarter section has 160
acres, a quarter-quarter 40 acres, and so on. The typical Midwestern
farm used to be a quarter section, or 160 acres. Farms have been
consolidated over the past several decades, so the typical farm
occupies closer to a square mile, especially in California.
A complete property description must include all of these breakdowns
into township, section, and fraction of section (if less than
an entire section). A typical property description in a PLS area
might read:
E 1/2 of SE 1/4, Sect. 22, T. 87 N, R. 34 E, 6th Principal
Meridian
USGS topographic maps indicate PLS townships and ranges along the
margins. Section and township lines are shown on the map itself
with red lines, and sections are numbered in red. You will no doubt
notice on some topos that the PLS townships and sections end abruptly
in some part of the map. This is common around Santa Rosa. This
is because these non-PLS lands were in Land Grants before 1846,
when California became part of the US. Remember, once surveyed,
never again.
The PLS has had a dramatic impact on the American landscape.
Since all land is divided into squares, the landscape itself looks
very square. You'll notice this when flying over the middle part
of the US, where topography does not interfere with its effects
as much. It also contributed to the isolation of farm families
in the 19th Century, who lived on their own square farms far from
neighbors. Contrast this to French surveyed-lands, where people
live much closer together. Our survey system no doubt contributed
to the ideal of American individualism.
A final note about the PLS--it's far from a perfect system. There
are many irregularities, which are especially noticeable in certain
regions. Section and township lines are not always exactly north/south
and east/west, and sections are sometimes less than a full square
mile (they're then called government lots, or fractional lots).
The irregularities derive from several sources:
- Meridians converge to the north, so as surveyors moved north,
townships didn't match up with those further south. Often east-west
correction lines were set up, along which townships were re-aligned.
You'll notice this effect when driving north or south along
a country road and you have to take a sudden turn right or left,
then turn north/south again after a short distance.
- Surveying in wet or mountainous terrain is difficult, and
lines often went astray. Once set up, however, the errors were
kept, and lines remained askew.
- Surveyors were paid by the number of sections surveyed, so
hurried surveyors weren't always careful surveyors.
- Some surveyors simply weren't careful, or were even staggering-drunk
on the job.
Because of these irregularities, the PLS is not a great system
for computerized map coordinates when you want a regular x,y grid.
Use the UTM or SPC grid instead.
5. Other Rectangular Surveys
Some states weren't touched at all by the PLS: the original 13
Colonies (and subsequent split-offs: West Virginia, Vermont, Maine),
Tennessee, Kentucky, and Texas. Some New England towns used a
modified rectangular survey when settled. Some of the states had
considerable land left to dispose of in the 19th Century, and
developed their own rectangular survey for these lands. Texas,
in particular, used several variations on a rectangular survey,
some of which used Spanish units. These rectangularly-surveyed
areas look like PLS areas as you travel over them, even though
officially they're not.
  
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