Evidence and boundary law

On the third day of field work, Grant's crew finds five iron posts along the old canal right of way on the Haugen quarter. Four of them fit the 1958 plan to within a centimeter after a best-fit transformation. The fifth sits three-quarters of a meter away from where the others say it should be, beside a fence brace and a cattle trail. Is it the original post, knocked sideways by cattle and pushed back by a farmer? A replacement set by someone who measured from the wrong place? Or the true corner, with the other four slightly off? The answer is not in the coordinates alone. It depends on what the evidence shows and on the rules of law that tell a surveyor how to weigh it. This lesson sets out those rules.

Boundaries are questions of evidence

A property boundary is where the parties to the original conveyance or survey intended it to be, as shown by the best available evidence. It is not where a modern measurement would put it if the survey were done again, and it is not where the area or the theory says it ought to be. When a parcel was created by a survey, the boundaries are where that survey placed them on the ground, as marked by its monuments. When a parcel was created by a description without a survey, the boundaries are where the words, read in light of the circumstances at the time, put them. In both cases the surveyor's job is historical: to reconstruct what was done, from what survives.

Evidence comes in many forms. Physical evidence includes monuments, their remains, pits and mounds, bearing trees, fences, hedges, old roads and buildings. Documentary evidence includes plans and plats, field notes, deeds, titles, previous surveys, aerial photographs, and the correspondence and diaries of earlier surveyors. Testimony includes what landowners, neighbors and former workers remember about where corners were and when fences were built. Measurement evidence includes the distances and bearings between found monuments, compared with those of record. A surveyor collects all of it, judges each piece for reliability and relevance, and forms an opinion in which the pieces fit together.

The order of importance

Courts in both Canada and the United States have developed, over a long history of boundary cases, a general order in which conflicting elements of a description or survey are usually given weight. The order is a guide to intent, not a mechanical rule; where it would defeat the evident intention of the parties, it gives way. With that caution, the common order is: natural boundaries and original monuments first, then artificial monuments and the lines of adjoining parcels, then courses (bearings or directions), then distances, and last, area. The logic is that people are least likely to be mistaken about what they could see and touch, and most likely to be mistaken about numbers they wrote down.

An original monument is one set by the surveyor who created the boundary, in the course of that survey. If it can be identified and is undisturbed, it controls, even if the distances to it are wrong. A purchaser bought the land as marked on the ground, not as written in a field book, and the law protects that reliance. A monument set later, in a retracement, is evidence of where an earlier surveyor believed the original was, and it is only as good as that surveyor's work. Distinguishing original from later monuments is therefore one of the most important skills in boundary surveying, and it rests on knowing the instructions, materials and markings of each period.

US courts, and the BLM's Manual of Surveying Instructions, hold that an original PLSS corner, once found and identified, is conclusive of its position, whatever the record measurements say. The same principle applies to monuments set in original subdivision surveys under state law. Michigan's Justice Thomas Cooley, in an often-quoted 1881 essay, warned surveyors that their task in a retracement is to find where the original lines were run, not to correct them, and that a surveyor who re-measures and resets corners to fit the record destroys the very evidence the owners relied on.

Obliterated and lost corners

When the original monument cannot be found, the surveyor must decide whether its position can still be determined from other evidence. If acceptable evidence of the original position survives, such as witness marks, bearing trees, the remains of a pit and mound, a fence built to the original corner, or reliable testimony from someone who saw it, the corner is said to be obliterated, and the surveyor restores it at the position the evidence shows. Only when no such evidence exists is a corner truly lost, and then it is restored by measurement from other corners, usually by proportion as Lesson 4 explains. The distinction matters, because restoring by proportion a corner whose position was in fact known from other evidence moves the boundary.

The BLM's Manual defines these terms precisely. An existent corner is one whose position can be identified by the original monument or its accessories; an obliterated corner is one whose monument has vanished but whose position can be recovered from acceptable evidence or testimony; a lost corner is one whose position cannot be determined beyond reasonable doubt from either, and which can be restored only by reference to other corners. State law in Montana adopts the federal rules for restoring PLSS corners.

Occupation, fences and agreements

Fences, hedges and walls are not boundaries in themselves, but they can be strong evidence of where a boundary was believed to be, especially if they were built soon after the original survey, when the monuments were still visible. A fence built in 1920 to a post that has since vanished may be the best evidence of where that post stood. A fence built in 1990 by a farmer who guessed is weak evidence. The surveyor investigates: who built it, when, from what, and whether neighbors treated it as the line. That investigation often matters more than any measurement.

Sometimes neighbors who were unsure where their common boundary lay agreed on a line and lived by it for many years. Courts in both countries have recognized such conventional or agreed boundaries in some circumstances, binding the owners and their successors even if the line differs from the original survey. The requirements vary by jurisdiction and are usually strict: genuine uncertainty about the true line, an agreement, and conduct consistent with it over time. A surveyor who suspects a conventional boundary does not decide the question, but documents the evidence and flags the possibility for the client and their lawyer.

Adverse possession is a different doctrine: a person in actual, open, exclusive, hostile and continuous possession of land for a statutory period can acquire title against the record owner. Each state sets its own period and conditions. Montana's statutes require, among other things, a relatively short period of five years and the payment of the taxes on the land during that time, and Montana courts have applied the requirements strictly. Montana, like most western states, also recognizes prescriptive easements, acquired by open, continuous and adverse use, such as a road, for the statutory period. Land held by the federal or state government generally cannot be acquired by adverse possession, which matters for any canal right of way still held by the United States. For the district, a farmer's shed that has stood on a privately held canal strip since 1975 raises questions a lawyer must answer, while one on federally held land does not.

Weighing the posts on the Haugen quarter

Back to the five posts. Theo computes a best-fit similarity transformation from the 1958 plan coordinates to the field coordinates, first using all five posts, then leaving out the one that fits worst. A transformation with rotation, scale and shift allows for the old plan's own bearing reference and chaining scale, so that only real disagreements show up as misfits.

import math
# Record coordinates (1958 plan, local plan grid) and field coordinates of the found iron posts
record = {"A": (0.00, 0.00), "B": (402.34, 0.00), "C": (402.34, 201.17), "D": (0.00, 201.17), "E": (201.17, 201.17)}
found  = {"A": (5000.012, 2999.992), "B": (5402.347, 3000.157), "C": (5402.289, 3201.331),
          "D": (4999.917, 3201.172), "E": (5201.725, 3200.841)}

def fit(names):
    """Best-fit 2D similarity (rotation, scale, shift) from record to field, by least squares."""
    n = len(names)
    xr = sum(record[p][0] for p in names) / n; yr = sum(record[p][1] for p in names) / n
    xf = sum(found[p][0] for p in names) / n;  yf = sum(found[p][1] for p in names) / n
    sa = sb = ss = 0.0
    for p in names:
        x, y = record[p][0] - xr, record[p][1] - yr
        X, Y = found[p][0] - xf, found[p][1] - yf
        sa += x * X + y * Y; sb += x * Y - y * X; ss += x * x + y * y
    a, b = sa / ss, sb / ss
    def to_field(p):
        x, y = record[p][0] - xr, record[p][1] - yr
        return xf + a * x - b * y, yf + b * x + a * y
    return a, b, to_field

def report(names, label):
    a, b, to_field = fit(names)
    print(f"{label}: scale {(math.hypot(a, b)-1)*1e6:+.0f} ppm, rotation {math.degrees(math.atan2(b, a))*3600:+.1f} arc-seconds")
    worst = None; mis = {}
    for p in record:
        E, N = to_field(p)
        d = math.hypot(found[p][0] - E, found[p][1] - N)
        mis[p] = d
        print(f"   {p}: misfit {d:.3f} m" + ("" if p in names else "   (not used in the fit)"))
        if p in names and (worst is None or d > worst[1]): worst = (p, d)
    return worst, mis

worst, _ = report(list(record), "all five posts")
if worst[1] > 0.10:
    keep = [p for p in record if p != worst[0]]
    _, mis = report(keep, f"without post {worst[0]}")
    print(f"post {worst[0]} sits about {mis[worst[0]]:.2f} m from where the others say it should be: treat it as suspect, not as proof")

all five posts: scale -123 ppm, rotation +32.9 arc-seconds
   A: misfit 0.121 m
   B: misfit 0.136 m
   C: misfit 0.175 m
   D: misfit 0.189 m
   E: misfit 0.574 m
without post E: scale +34 ppm, rotation +82.1 arc-seconds
   A: misfit 0.008 m
   B: misfit 0.011 m
   C: misfit 0.011 m
   D: misfit 0.007 m
   E: misfit 0.747 m   (not used in the fit)
post E sits about 0.75 m from where the others say it should be: treat it as suspect, not as proof

With all five posts the misfits are spread over every post, from 0.12 m to 0.57 m, because the one bad post drags the fit. Without post E, the other four fit to within about a centimeter, and post E sits about 0.75 m from where they say it should be. The arithmetic shows that post E is inconsistent with the rest of the survey. It does not show that post E is wrong. Ines examines it: the post is the right type for 1958, but its stamp is worn and the ground around it is disturbed; the fence brace beside it was replaced in the 1990s, according to Mr. Haugen; and the 1958 field notes describe the post as set in undisturbed sod. Taken together, the evidence suggests the post was knocked out and reset by eye when the brace was built. Ines treats it as disturbed, restores the corner from the other four, records her reasons in her field notes and on the plan, and leaves the old post in place, noted, so that anyone who disagrees later can see the evidence for themselves.

The surveyor's role, and its limits

Boundary decisions are professional opinions. A surveyor forms one from the evidence, shows it on a plan, explains it in a report and stands behind it. A surveyor who finds conflicting evidence that cannot be reconciled, such as two sets of monuments for the same corner, each with some claim to be original, should show both, explain the conflict and advise the client that the matter may need to be settled by agreement or by a court. It is never the surveyor's role to resolve a genuine conflict by setting a third monument halfway between, or to move a boundary to suit a client. The surveyor serves the evidence, and through it the public's confidence in the cadastre.