Editing Public Land Survey System (section)

===Design===
The surveying of any regional area, such as a state or multiple states, is a multi-step process. First, two controlling survey lines are established: a baseline which runs east–west and a principal meridian which runs north–south.  The locations of the two are determined by a previously chosen [[Geodetic datum|initial point]], where they originate and thus intersect.  Next, at a defined distance interval, commonly 24 or {{convert|30|mi|km}} depending on the year and location, standard parallels of latitude are established parallel to the baseline.  The meridian, baseline and standard parallels thus established form a lattice upon which all further surveying is then based.  Subsequent work divides the land into [[survey township]]s of roughly {{convert|36|mi2}} or {{convert|6|mi}} on each side. This is done by the establishment of township and range lines. Township lines run parallel to the baseline (east-west), while range lines run north–south; each are established at 6-mile intervals.  Lastly, townships are subdivided into 36 [[section (United States land surveying)|sections]] of approximately {{convert|1|mi2|acre km2}} and sections into four quarter-sections of {{convert|0.25|mi2|acre km2}} each. The intersection of a township line (or baseline) with a range line (or principal meridian) constitutes a ''township corner'', of a section line with any other type of line a ''section corner'', and a point halfway between any two section corners a ''quarter corner''.  The federal government typically surveyed only to this quarter-section level, the subdivision of smaller parcels being carried out subsequently by private surveyors after original sale.

Because the survey design is two-dimensional (rectangular), while the actual Earth is three-dimensional (approximately spherical and topographically), adjustments to land areas must be made periodically to prevent error propagation; not all sections can be one square mile nor can all townships be exactly 36 square miles.  More specifically, all north–south running lines (all range lines and half of all section lines), as with the prime meridian, are always established with reference to true, geodetic north.  But it is a physical impossibility to meet this condition and still maintain a rectangular land grid, because such lines converge on the north pole.

These adjustments are done at two different scales.  At the small scale (within a township) it is done by starting the sectional surveys (township "subdivisions") in the southeast corner and moving progressively toward the northwest corner.  The algorithm used is to move northward to establish the six easternmost sections (and quarter-sections), then move west at one mile intervals, parallel to the eastern boundary of the township, repeating this process, until the western side of the township is reached.  The result of this is that the northernmost and westernmost tiers of sections—11 in all—are thus allowed to deviate from one square mile, but the other (southeasterly-most) 25 sections are not.  This method accommodates the curvature problem within a township and also allows for any errors made during the surveying—which were nearly unavoidable because of the physical difficulty of the work and the crude equipment used—without overly compromising the basic rectangular nature of the system as a whole.  At the larger multiple township scale, the standard parallels developed at the establishment of the baseline, so that townships widths do not continually decrease as the grid proceeds north (and is in fact the primary reason for their establishment).  Thus, corrections for [[curvature of the Earth]] exist at two separate spatial scales—a smaller scale within townships and a larger scale between multiple townships and within standard parallels.

[[File:Theoreticaltownshipmap.gif|thumb|left|200px|Figure 2. This [[United States General Land Office]] diagram shows the theoretical sectioning of a standard [[survey township]].]]

A specific and terse location descriptor is always used, in which the townships and sections are indexed based on (1) the township's position relative to the initial point, (2) the section's location within the designated township, and (3) the principal meridian reference.  Township, range, and section are abbreviated as T, R, and S, respectively, and [[Cardinal direction|cardinal bearings]] from the initial point by N, S, E, and W; each principal meridian also has its established abbreviation.  Thus, for example, the description "T1SR20E S13 MDM" reads as follows: Township 1 South, Range 20 East, Section 13, Mount Diablo Meridian.  That is, the 13th section in the first township south of the baseline (in this case, the Mount Diablo Baseline) and the 20th township east of the principal meridian (the Mount Diablo Meridian).  Since township and range lines are six miles apart, the "T1SR20E" part of the designation instantly places the location somewhere between zero and six miles south of the baseline, and 114 and 120 miles east of the principal meridian.  Knowing how sections are numbered within townships, section 13 is identified as therefore occupying the one square mile located 2 to 3 miles south, and 119 to 120 miles east, of the Mount Diablo initial point (in central California).  Note that the sections within a township are numbered in an unconventional, [[Boustrophedon]] pattern (Fig. 2), in which alternating rows are numbered in opposite directions, starting from section 1 in the northeast corner and ending with section 36 in the southeast corner, as per Figure 2. Therefore, section 13 is adjacent to the eastern range line of the designated township.  Numbering in this pattern ensures that numerically sequential sections within the same township are physically adjacent and share colinear boundaries.

[[File:Kent-1885-twp-co.jpg|thumb|left|Figure 3. [[Kent County, Michigan]] in 1885 as a PLSS example, showing 24 named townships and sectional subdivisions.]]