A rectangular survey with true-north boundaries cannot cover a curved earth. Meridians converge as they run north, so two range lines started six miles apart on a base line are less than six miles apart a day's walk to the north. Left alone, the error compounds until townships in the far north of a survey are visibly too narrow.
The PLSS solves this by refusing to run the grid indefinitely. At regular intervals the system stops, lays down a fresh correction line, and starts over with full-width townships. Those correction lines are the standard parallels running east and west, and the guide meridians running north and south. The visible result, familiar to anyone who has driven a straight section-line road in the plains, is a jog: the road runs true for miles and then steps sideways before continuing.
The geometry that forces the correction
Convergency is the angle between two meridians. It depends on how far apart they are and on the latitude, growing rapidly toward the poles because the meridians all have to meet there.
θ ≈ d · tan φ / R| Latitude | Convergency angle | Closure over 24 miles |
|---|---|---|
| 30° | about 3.0′ | about 111 ft (1.68 ch) |
| 35° | about 3.6′ | about 134 ft (2.04 ch) |
| 40° | about 4.4′ | about 161 ft (2.44 ch) |
| 45° | about 5.2′ | about 192 ft (2.91 ch) |
| 49° | about 6.0′ | about 221 ft (3.35 ch) |
These are spherical approximations, adequate for understanding the magnitude. The point they make is decisive: a hundred and fifty feet lost every twenty-four miles is far too much to ignore, and far too much to distribute quietly into the section measurements. The system therefore absorbs it in one place, deliberately, on a line established for that purpose.
Standard parallels
- Standard parallel
- An east-west correction line run as a true parallel of latitude at intervals of 24 miles north and south of the base line, from which the townships to the north are laid out anew with full width.
Standard parallels are numbered outward from the base line: the First Standard Parallel North lies 24 miles north of the base line, the Second Standard Parallel North 48 miles north, and so on, with the same pattern to the south. The base line itself functions as a standard parallel for the first block of townships north of it.
Each standard parallel is run as a true parallel of latitude, monumented with standard section and quarter-section corners at the usual half-mile spacing. Those corners control the townships to the north of the line. Townships to the south of the line were run northward from the previous standard parallel and close against it, so their range lines arrive at the parallel wherever convergency has taken them, generally not at a standard corner.
Guide meridians
- Guide meridian
- A north-south correction line run on a true meridian at intervals of 24 miles east and west of the principal meridian, from a standard parallel north to the next standard parallel, where it closes.
Guide meridians divide the survey into columns 24 miles wide, just as standard parallels divide it into rows 24 miles high. Each guide meridian is started at a standard corner on a standard parallel and run true north to the next standard parallel, where it closes and a closing corner is set. It is then abandoned: the next guide meridian north of that parallel is started fresh from a standard corner, not continued from the one below.
That restart is the whole mechanism. Because each 24-mile block begins from full-width standard corners on its own correction line, the convergency error can never accumulate beyond one block. Guide meridians are numbered outward from the principal meridian in the same way as standard parallels: First Guide Meridian East, Second Guide Meridian West, and so on.
The 24-mile block, and what came before it
The combination of standard parallels every 24 miles and guide meridians every 24 miles divides a survey into quadrangles roughly 24 miles square, each containing about sixteen townships. Within a quadrangle the townships are laid out from the southeast corner outward, and the accumulated discrepancy is carried to the north and west sides.
- Standard parallels are numbered north and south from the base line; guide meridians are numbered east and west from the principal meridian.
- Each is run as a true line: the parallel as a curve of constant latitude, the meridian as a true north line.
- Each guide meridian runs from one standard parallel to the next and stops.
- Townships north of a standard parallel take their width from the standard corners on that parallel, not from the townships below it.
What this means when you are retracing
Correction lines are where the geometry of the PLSS is deliberately broken, so they are also where naive assumptions break. Sections immediately south of a standard parallel are fractional in their north-south dimension and often carry government lots. Range lines from the south do not continue across the parallel. A closing corner falls on the standard parallel but its position along that parallel was determined by the line coming from the south, so it is not evidence of anything about the survey to the north.
In practical terms, treat a standard parallel as a wall. Control passes across it in one direction only, from the parallel northward. When a corner south of the line is lost, restore it from evidence south of the line and from the closing corner, not from the standard corners that happen to lie a few feet away.