The History of Surveying Parts 2 & 3

What, Exactly, Are You Buying?

(. . . and, where, exactly, is it located?)

Part II

         When we left the story in the last post, a hypothetical wealthy man in Baltimore – and it was almost exclusively men at the end of the Revolutionary War who owned property – found himself in possession of the idea of 3,500 acres of potentially rich farmland beyond the Appalachian Mountains.  Where was it?  What can he do with it?  Who would like to buy it?  What was a reasonable price for it?  Question after question.  A quick bit of mathematics revealed that 3,500 acres (1.0 acre = 43,560 ft2) is equivalent to 152,460,000 ft2.  Taking the square root of that number yields 12,347.5 ft.  To the average person, that means nothing.  Let us switch units to miles.  12,347.5 ft. is equivalent to 2.34 miles.  That means our hypothetical Baltimore grandee owns a tract of land this is 2.34 miles x 2.34 miles or about 5.5 square miles of potentially rich farmland or craggy mountaintops or lakes – who knew?   The process for the hypothetical wealthy man from Baltimore acquiring this asset was to seize an opportunity to transfer some of his real wealth into a risky commodity – ‘Continentals’.  Then he had to hold the ‘Continentals’ in a secure place while General Washington, et. al. prevailed against the nation with the greatest Navy and Army the world had ever seen.  The man from Baltimore then had to hold his breath (and/or lobby among his friends in government) while the intrinsic value of the ‘Continentals’ was defined by the nascent government.  Through taking advantage of the new government’s desire for security and funding, our Baltimore man is able to convert something of little value (‘Continentals’) to something of great potential value – land west of the Appalachian Mountains.  The new government of the United States of America found itself with a treasury of $4.0 million and debts outstanding of more than $40 million.  What to do?  Sell land west of the Appalachian Mountains.  Sitting in Baltimore, our man is no better off than he was before, although he no longer has to maintain secure storage for a mountain of ‘Continentals’.  Two more steps are required for him to convert his holdings to portable wealth (solid currency) or tangible wealth (a fine house in Baltimore).  He must secure and define his land west of the Appalachian Mountains and he must find a willing buyer for it.  Without those two steps, he is just in possession of the idea of farmland.  The keystone of the arch he must build to cross from the idea of land to portable or tangible wealth is an accurate survey of the land, which allows anyone to, 1) locate it on the face of the earth, 2) describe it in legal documents recognized by the system of courts in the new nation, and 3) establish its size and extent.    These three items of information allows the transfer of the property in exchange for consideration of a type acceptable to the owner.   

One of the major deficiencies of the population of the new nation was a ready supply of people with a sufficient knowledge of mathematics (particularly, plane geometry, solid geometry, plane trigonometry, and spherical trigonometry) to be able to conduct a survey measurement of a plot of land.  There is a schoolchild riddle that illustrates the problem:  A hunter awakes one morning and sets out to stalk some game.  He travels due south for 1.5 miles.  Finding nothing, he travels due west for 1.5 miles.  Again, finding nothing, he travels due north for 1.5 miles.  There he sees a bear rummaging through his equipment and shoots it.  What color was the bear?  The answer is, the bear was white because the only place his camp could be in this story is the North Pole.  His route was a triangle with the three interior angles being 90º + 90º + 57.3º = 237.3º, not the 180º we all learned in plane trigonometry.  Looked at another way, his route was a trapezoid with the shorter top side having a length of 0.0 miles, all the other sides having lengths of 1.5 miles (i.e., an equilateral triangle).  That is the problem with surveying large tracts of land.  If one is at the equator, four sides of a closed figure closely (but not exactly) approximate a rectangle.  The closer one gets to the pole, the closer the four sides approximate a triangle (a trapezoid with the short side, closest to the pole).  Using a little bit of 3rd grade arithmetic and a little bit of calculus reveals that the difference in area circumscribed by the hunter’s morning walk is about 94.5 acres – depending on calculating the area from the surface of a plane or the surface of a sphere.  That is the potential error, for a plot of land with a perimeter of 4.5 miles.  Our mythical man from Baltimore may have a plot with a perimeter of 9.36 miles.  Enter Rufus Putnam[1].

Rufus Putnam was an orphan who taught himself how to survey and practiced his trade during the French and Indian wars when he was a military engineer.  After a successful career in the Natchez area he relocated to the Ohio territory, got himself appointed Surveyor General to the United States with responsibility for the Northwest Territory (Ohio).  On behalf of the government, Rufus Putnam began employing a team of surveyors to layout the territory in ‘perfect’ squares, with the subdivision thereof left to the purchasers.  The investors in the Ohio Company bought land for $0.12 per acre in 1785.  In 1793, the same acreage had risen to $2.50 per acre.  In 1795, the price hit $15.00 per acre.  Could it be that our man from Baltimore has converted his investment of $420 (@$0.12 / acre) to $52,500 (@$15.00/acre)?

Even though the instructions to Rufus Putnam stated that the meridians (N-S lines) were to be laid out using true north, doing so required siting the pole star (true north) at night and resolving the deviation with the compass (magnetic north) during the day.  This required way too much time for people wanting to occupy the $15.00 per acre land, subdivide it, and sell it for $20.00 per acre.  Consequently, a hodgepodge of townships (6 miles x 6 miles) surveyed by the Putnam teams - some using true north, some using magnetic north and some using ‘estimated’ north - were occupied and the subdividing was left to the owners and occupiers.  Virtually nothing lined up and disputes on the borders arose. The names of the new landed gentry included all the ‘movers and shakers’ of the new nation – Washington, Supreme Court justices, Senators, Congressmen, etc.  States joined the new federal government in monetizing their vast land holdings that had just been made official by the new national government.  Rufus Putnam and his counterparts rushed to establish some kind of organization with a survey and a companion map of the new land.  The national land rush was in full swing.



Part 2 of a 3 Part Article by Gilbert C. F. Brunnhoeffer, III  PhD, P.E., Ret.

Roger Williams University, Bristol, Rhode Island


Many thanks to our friend and guest blogger for this scholarly work.

Part 3 to Follow


[1] Measuring America, by Andro Linklater, Walker Publishing Company, 2002, p.51.

What, Exactly, Are You Buying?

(. . . and, where, exactly, is it located?)

Part III

         The great land rush was impeded by the haphazard manner of the ‘surveyors’ of the time.  While Rufus Putnam had a reputation of getting things done, his casual approach caused problems as soon as the land was occupied.  Real money was involved.  Problems arose.  Thomas Jefferson, an architect (and a surveyor by necessity) by avocation, became President of the new nation.  Albert Gallatin, the Swiss-born Secretary of the Treasury fired Putnam in 1803 and replaced him with Jared Mansfield, former Professor of Mathematics at West Point (which was to become the first school of engineering in the United States later).  The 3.5 million acres of the Western Reserve (northern Ohio), equivalent to a square of 74 miles x 74 miles. needed to be surveyed and readied for speculation and habitation.  Time to engage rational professionals.

First, a little bit of spherical geometry.  There are 360º in a circle, 60’ in a degree, and 60” in a minute.  That makes 360º x 60 ‘/º x 60 “/’ = 1,296,000 “in a circle.  The radius of the earth is 3,958.8 miles.  Therefore, a measurement error of 1.0” will result in a distance error of RƟ = 3958.8 mi x (2π/1,296,000 radians) = 0.0192 miles or 101 ft. 4 in.  This leads to the question of where, exactly, does your boundary line begin?  Suppose your driveway was located 100 ft. over on your neighbor’s property?    

Yes, we have GPS today and, for a price, we can measure our position on the earth (latitude and longitude) to the nearest foot.  However, to accomplish a survey, one has to start from a point established by someone in the eighteenth century using a method that may or may not have been flawed.

         Registered Land Surveyors have ‘work around’ solutions for this problem.  More about that in a moment.  Back to our ‘soon to be wealthy Baltimore land owner’.  His problem is to find someone competent – really a team – to travel 360 miles, live mostly off the land, defend themselves from animals, Indians, Frenchmen, British soldiers, and teams representing other land speculators, locate and measure the land holding, draw a map, file the land claim in the local court, if any exists, and return to Baltimore with the information.  This idea of buying up worthless ‘Continentals’ and converting them to something of value is looking harder and harder.

         The first problem is where to start?  Typically, in the southern states, the use of ‘metes-and-bounds’ was favored.  The dictionary definition of metes-and-bounds explains that natural features (rivers, mountains, trees, etc.) and manmade features (bridges, buildings, roads, etc.) are used as reference points in a survey.  The quick fix after the Revolutionary War was to use a system of ‘metes-and-bounds’.  There were at least two potential problems with this – 1) land features change (river courses change, trees die, rocks move in earthquakes, buildings are razed) and 2) the magnetic north pole moves (during your lifetime the magnetic north pole has moved from the Hudson Bay to close to Siberia – the magnetic north and south poles have reversed at least four times in the last million years and we are ‘overdue’ for another reversal).  An example would be:

 “Beginning at a point from which the north quarter corner of Section 4, T. 1 N (township 1 north), R. 70 W (range 70 west) of the 6th PM (the sixth principal meridian, a north–south reference line) in Boulder County, Colorado, bears N 45° W 1,320 feet, at which point of beginning an iron stake has been placed; thence south 600 feet to a point also marked by an iron stake; thence N 45° W 700 feet to a large oak tree; thence northeasterly to the point of beginning.”

Once this is deciphered, an experienced surveyor could trace the outline it describes.  You will find that it converts to 148,492 ft2 (3.4 + ac).  The trick(s) is (are); 1) are the iron stakes still there? 2) has the oak tree disappeared? 3) what is the relationship of true north to magnetic north (then and now)? 4) did the original surveyor use true north or magnetic north or something else? 5) when was the original survey performed?  The description includes distances to the nearest foot.  Was the original survey done with a surveyor’s steel tape (100 ft. graduated in 0.01  ft)  or a Gunter’s chain (66 ft. – 100 links)?  If magnetic north was used, when was the survey performed?  The magnetic north pole has moved from the Hudson Bay area to closer to Siberia in the lifetime of most of the readers of this blog.  If true north was used, how was true north determined?  When one is worrying about 3.4 + acres, what difference does a foot make, either way?  Probably none unless you have a property line dispute with your neighbor.  Then a foot can be an expensive dispute if it means relocating a hedge or a fence. 

About ten years ago, a relatively expensive dream house was built on the coast of Rhode Island.  After construction was completed, it was discovered that the house was built on the wrong lot!  Pay a good surveyor to locate your property and its legal boundaries. 







$1.8 million Beach House Built on Wrong Lot

The house shown above was built in 2008 for $1.8 million, on the shoreline of Narragansett, Rhode Island – on the wrong lot. (  The builder just got it wrong and the courts found in favor of the landowner – The Rose Nulman Park Foundation.  Under provisions of the foundation trust, if any structure was built on the land an amount of $1.5 million was owed to the local Presbyterian Hospital.   At the time of the judgement, the owner of the structure estimated that it would cost $300,000 to move the house to an adjacent lot.  The plan to move the structure to an adjacent lot prompted an environmental group, Save the Bay, to sue to prevent the relocation – and you think a driveway location is a headache. 

An underlying theme in some of William Faulkner’s works is families that are ‘bound to the land’.  Yes, they own it, but what is it and what are its boundaries?  If they want to convert the land to portable wealth, they must sell it.  To sell it, they must establish ownership and a legal description of what it is that passes muster in the courts to be able to convert it to money. 

Owning and trading land is still a viable road to family wealth but one would be well advised to engage a Licensed Professional Surveyor (they carry Errors and Omissions insurance) to completely establish what ‘it’ is that you are buying or selling as well as where it is.  Professional Surveyors solve many of the sphere-to-plane problems by using local government surveys that map parts of each township on a plane to reduce the errors covered by the map.  It is a legally accepted technique in common use.  Haven’t you always wonder why Greenland, an island, appears to be larger than Australia, a continent, on a Mercator map?  It is the problem in converting a spherical surface to a plane surface.

As I told my students at the beginning of their basic Surveying class – “Everything you do is wrong.  You are plotting a map of the surface of an irregular, oblate spheroid on a plane piece of paper.  What you will learn in this class is to make it less wrong, more accurate, and acceptable for use in the task at hand. It will always be wrong, in the strictest sense, but you can make it ‘good enough’.

Before you write the check or cash the check for land, engage a Licensed Professional Surveyor.



Part 3 of a 3 Part Article by Gilbert C. F. Brunnhoeffer, III  PhD, P.E., Ret.

Roger Williams University, Bristol, Rhode Island


Many thanks to our friend and guest blogger for this scholarly work.




Morgan Diebold