The hook
The Public Land Survey System divides the western United States into a grid of 6-mile-by-6-mile townships, each cut into 36 sections of one square mile. The job of the modern surveyor isn't to lay out new sections — it's to perpetuate the original GLO corners that were set in the 1800s. Click through the township + section grid below to see how aliquot parts nest down to a single 40-acre tract.
Township (6 mi × 6 mi)
Sections numbered 1-36 in the boustrophedon order — start NE, snake west, drop south.
Section 14 (1 mi × 1 mi · 640 ac)
Aliquot description
Sec. 14, T2N R3W
≈ 640 acres
Try this: click section 14, then click the NW quarter of the section, then the SE quarter of THAT. You've just described SE¼ of NW¼ of Sec. 14, T2N R3W — a 40-acre parcel. That's how the PLSS lets a single line of text uniquely identify any 40-acre tract in the country.
Memorize these
Concepts that show up on the exam
Township
6 mi × 6 mi block of land. Identified by the township & range from the principal meridian and baseline (e.g., T3N R5W). Contains 36 sections.
Section
1 sq mi (640 acres). Numbered 1-36 in the boustrophedon ("ox-plowing") order: 1 in NE corner, snake west, drop south, snake back east.
Aliquot parts
Quarters and quarter-quarters of a section. NE¼ = 160 ac. SE¼ of NE¼ = 40 ac. Smallest aliquot is the quarter-quarter.
Lot
A parcel along the north or west boundary of a township that doesn't come out to a clean aliquot because of curvature/correction line. Numbered consecutively.
Original / dependent / independent resurvey
Original = the first GLO survey. Dependent resurvey = re-establish original corners using best available evidence. Independent = wipe and resurvey (rare; only when original is destroyed AND title hasn't vested).
Existent / obliterated / lost corner
Existent = found, original. Obliterated = position certain from collateral evidence (deeds, fences, witness trees). Lost = position not recoverable; restored by proportionate measurement.
| Corner status | Definition | How you re-establish |
|---|---|---|
| Existent | Found in place; recoverable physical evidence agreeing with the original record. | Use as is. No restoration required. |
| Obliterated | Original monument is gone, but its position is recoverable from collateral evidence (witness trees, accessories, fences, deeds, parol). | Restore to the original position from the collateral evidence. |
| Lost | Position cannot be determined from any acceptable evidence. | Restored by proportionate measurement between the two nearest existent or obliterated corners. |
Keep these in muscle memory
Formulas to know cold
Single proportionate measurement
d₁_new = (D_orig_to_lost / D_orig_total) · D_meas_totalD_orig = original record distanceD_meas = today's remeasured distance
Double proportionate measurement
Apply single proportion in BOTH N-S and E-W directions, then take intersection.Used for interior section corners that have control on all four sides.
Try it before you peek
Worked example
The problem
Original record between two existent corners shows 5,280 ft. Re-measurement today gives 5,295 ft. The lost corner was originally 2,640 ft from the south corner. Where is its proportional position?
Don't fall for these
What trips people up
Calling a corner "lost" too quickly
Lost is a last resort. Witness trees, original bearings, parol from neighbors, line trees, fence lines — all are collateral evidence that can pull a corner from "lost" to "obliterated." Once you call it lost, you forfeit the right to use the original measurements.
Resurvey vs. retracement
A retracement follows in the footsteps of the original surveyor — it does NOT change boundaries. A resurvey can change them but requires authority (BLM for federal lands; rarely available to private surveyors).
Order of operations on a section
BLM Manual: corners are restored in a specific order. Section corners on the township boundary FIRST (single proportion). Then interior section corners (double proportion). Finally, quarter corners. Don't reverse this — it changes answers.
Test yourself
How well did it stick?
A quick 5-question check on Perpetuation of the U.S. PLSS. See where you stand and what to review.