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Plss Puzzle.

GEO*Trailblazer 1

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This is a PLSS puzzle.

Figure out the Longitude and Lattitude of a Township Corner.

I would like you to use your math skills,not the mapping programs.

But use what you like there is no penalty.


It is fairly strait forward in it's implementation.

6X6 mile squares.


I want to know the value VIZ+

X: Lattitude

Y: Longitude

Of the South East Corner of Township 22 North, Range 27 West of the 5th Principal Meridian.


PLSS help




Initial Points

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There are a large number of factors that will keep any theoretical computation from being accurate with what is marked on the ground. It may be possible to get a rough computation, but it won't be as accurate as scaling it off a topo and converting the datum as needed.


Of course, they aren't even theoretically 6 mile squares because of convergence of the meridians.


You need to know what the surveyor's instructions were with regard to allowance for convergence of the meridians on the correction line south of the township in question. Sometimes they measured out miles as accurately as possible, and sometimes they added half the convergence on the correction line so that the sections and townships were a little too large but by the time they got to the next correction line north, the townships and sections were as much too small as the southern ones were too big.


How accurate is the location of the principal meridian by the time you get 22 townships (132 miles) north?


There are lots of other factors in play as well.


And then there is the biggest one--you don't know how accurately the field crew did their measuring. I've seen maps showing a section 6 that was almost 2 miles across. That means the surveyor who did the township lines and the surveyor who subdivided it into sections disagreed by almost a mile in 6 due to rough terrain or mistakes.

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Would you like me to scale it off a map for you or go there and survey it in person?


PLSS was never Surveyed or held to Geodetic locationing. They turned angles with a transit and pulled measurements with a chain. It is feasible that I could re-accomplish the original survey with modern methodologies and find myself faced with a bit of error correcting to do.


Sorry man, this is really nothing more than a guess unless the corner happens to have an NGS monument surveyed at the location. Apples and oranges for the most part.



Edited by evenfall
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evenfall that would be great when can we do it? :D

It would only take a couple of days.


How did I know it wold go this way.


I mereley wanted a guesstimate or best answers the group would come up with..

say some thing like,

27 X 6 miles = 162 miles on the baseline west.=xxx xx.xxx from the Initial point

22 X 6 miles = 132 miles north on the north line.=xxx xx.xxx from Initial point


I know there are several things to take into consideration.

But the rules state the closings have to be within certian limits,and the lines are to be not more than 21' from Cardinal.

And by Law 6 miles square as can be.........regardless.


Just for fun use any means neccesary to determine the coords.

Like I said it is just a puzzle. :)

Edited by GEO*Trailblazer 1
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As others have said, one can do the math for exercise and then see how far off you are. The PLSS is not that orderly that you can reliably project that far from the initial point.


Since convergencey was built into the corrections at intervals with standard parallels and guide meridians that pattern or interval would affect where you can go 6 miles and where it is short.


For example, you are more likely in a theoretical sense to get to the right location by going north on the meridian (if it is even run all the way, not all are), and then east or west along the first standard parallel south of the township, Since those have full 6 mile measure, then north.


To know for sure where they are may in fact depend on either looking at a map, or knowing what the instructions were to the surveyors laying it out, as suggested by someone.


Also note that the Lat /Longs of the initial points in the Manual are rough in some cases and in NAD27, not that the diff there won't be washed out by accumulated errors in the PLSS going that far anyway.


For example, the initial point for the 5th is in AR and if you will notice most of the PLSS lines in AR up to southern MO have a fairly consistent bearing bias (often referred to as the Arkansas Windage), so right away you need to know what that is or drift off considerably to the east as you travel north.


Townships are not generally square even in the ideal, the east and west sides run north (converging meridians) through the 4 township blocks. In some areas the blocks are larger than 4 townships.


I will come back and work it through to show the basic process i would follow. standard parallels are 4 townships apart.


- jerry

Edited by jwahl
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So here goes. A more accurate current NAD83 position for the initial point of the 5th PM is:


NAD83: 34-38-44.5 / 91-03-07.3


Assume 4 township blocks and therefor step 1)


Guess the arkansas windage without a map?


Or ignore it.


1)We are going to T22N, therefor the standard parallel south of that will be the north line of T20N (5*4) we go 20 x 6 miles or 120 miles north from the IP


2)We need to go to the SE corner of R27W or 26 township west along the standard parallel, that might work out 26 x 6 miles at that latitude.


3) Now we can go north 12 miles to the SE corner of that township within that block.


Again that assumes that the blocks are in fact 4x4, which they are not many places.


Bearings would be assumed to be geodetic except we know that will be off due to the Arkansas windage, but we can see how far off it is.


I will use a geodetic traverse program of my own but you could use the interactive stuff on the NGS sight for the N-S part.


Elevation would theoretically affect the ideal computation because the lines were run and measured at ground elevation, not ellipsoid. However most of this will be in the mississippi basin and so assume the affect is negligible.


For 1 assuming no windage and average elevation of 200 feet I get


M1 36-23-10.7 / 91-03-07.3


For 2, to go west is hard to do on the NGS program because if you start out with a forward bearing of west you will head more and more southwest as you go west and not be west. To follow the standard parallel the line will actually curve to the right looking west. My program figures this out so I am cheating a bit.


Forward bearing to get there is 270d49'48.4"


W1 36-23-10.7 / 93-51-01.1


For 3, we go north again 12 miles if I had figured it right.


SE 36-33-37.2 / 93-51-01.0


Expressing way more places of accuracy than is justified.


Now we go to the maps and see what went wrong with all my assumptions.


1) are the blocks of townships 4 miles N-S?

2) what is the windage and how far does it extend north?

3) etc.


Early work like this may not have dealt with the convergency in the way that evolved slightly later.


Now I made some mistakes and just edited this. Lets look at the map and see how far off it is.


- jlw

Edited by jwahl
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After uncovering several errors including a wrong value for the IP, I now follow on the map.


M1 TopoZone


M1 by map 36-25-08 / 91-01-14


I think that is the right township corner. It is sometimes hard to tell when looking at topozone maps as the Tp and Rg numbers are usually on the map collars which we don't see.


Okay so now on west to W1


Well if you look at the maps, it is a real mess as the PLSS crosses a few rivers there are offsets of several miles. At this point the exercise becomes futile.


- jerry

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For the Initial Point which is a NGS Point.


This Is also(theory)the True Line as Observed For the making of the Topographical Maps in the 60's.

Now if you project a True Line North

(That is one to me that has the same value as the Initial point).

It is 2 miles off(approximately).



It is south of this cache.


More to come I will add the references and caches.

If you check my hidden caches it will evidence of more hints.

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Is anyone really interested?:antenna:



If not I will close the thread.


I was looking for some help in determinations and wanted to try and make it fun,but I guess this seems like too much work.


If you go by the Law and explanations it is easy as I see it.

It is when It comes to the miles off no one wants to tackle that.


We discuss these measurement's being within minute quantities,but from what?

If the Topographic maps are so precise why has this(large) error occurred.


The Initial Point is an NGS Control(benchmark).

It fares the system should at least be within a few 100 feet.

Even when you use the curvature of the Earth equation.


That curvature was not used to determine a plane coordinate system(PLSS).

Edited by GEO*Trailblazer 1
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Well if you look at the maps, it is a real mess as the PLSS crosses a few rivers there are offsets of several miles.  At this point the exercise becomes futile.


- jerry



About Jerry,


Jerry is a Career Surveyor and has worked at BLM in many Capacities all over the country. He has even authored a Paper or two on the subject of the PLSS and how it related to Geodesy.


To be honest, He is probably one of the best guys in the country who could give your idea a go and look at what he said?


I weighed in on it too, with pretty much the same answer.


Now that you know where Jerry is coming from, and that Jerry told you what he told you, What do you think? I am not going to be coming to survey that point Geo. No one is. :-)


Fun thought though, Just not a workable one.


Good Luck,



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I meant the surveying it as a joke,

It is a major undertaking to say the least.


Thank you Jerry you hit the nail on te head,a mess.

(Is that the reason for the revamping of the BLM web site as we discuss this)???


I have worked on it for wellllllllllllllll tooo long.


Maybe I should make my point clearer,If a LEGAL description is based on the Initial Point and it is miles off.

How can a surveyor today say(claim) his measurments are within 6 feet of this Original Survey 156 mi. West and 132 mi. North?


And if all legal descriptions(of the Louisiana Purchase States) are based upon it how can it be legally described (being so far off)?


I am not looking for mistakes or a reason to put anyone down.

It was a (subject) that was brought to my attention by research.


I could go back to when this first started(inquiry) in 1995 when (S>A>) was still on no web maps like today,or the Interactive TOPO!.

It took major research for me to find the (point)stone in the swamp,all grown up and let go.

Now it is a National Monument.


Again as always thank you for your continued knowlege and friendships.



I have had many people tell me I should go and get my Survey licence since I do these things all the time.

But then it would be WORK!!!!

Nor do I think I am ready to tackle some of the things you as professional surveyors have to.

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Well I did a computation assuming I knew nothing else than what was provided. I then offered a discussion of what I do know beyond that. The only thing I did not do was follow through the true location as found on maps for comparison, you can do that and judge for yourself. I saw no feedback or interaction about the issue after my posts until now.


So I guess I am not sure what the question is. If it was not as stated an abstract computation of where a township 'should be' we can go more into that.


Or is it now why is the PLSS so bad? Well it was done in the wilderness on the frontier and in a way that was reasonable for the time in line with a number of acts of congress to get the public domain surveyed platted and sold both as support for the Centerl U.S. Government, and to allow for the expansion of the country providing for any citizen to buy and possess land in an agrarian age.


Topo maps didn't exist, the GLO plats were the first maps of most of the country. NGS or CGS control didn't exist either except in a few coastal areas. The PLSS is pretty good overall. It's goal was to get the land surveyed, monumented, described and sold. In 1805 an act was passed which provided that the corners and lines as actually marked on the ground represented those line. This was done to allow stability based on the work done on the ground versus a mathematical abstraction. The initial point NOW has control on it, from what date? (not 1820)


A legal description BASED on the PLSS is referenced to the initial point by way of description, but not mathematically or geographically. The land is fixed on the ground by the actual survey done for that township. The initial point is no more critical than saying what state it is in, or what county it is in as to it's position on the ground is only roughly informative.


The PLSS was based on the true meridian and is not in ANY way a plane coordinate system, or even a coordinate system at all. E-W lines are curved parallels of latitude, and N-S lines are converging meridians. As the system was developed past the first surveys in Ohio the problem with convergency was beginning to be recognized and so a system was developed to deal with it. As the townships and ranges were laid out and approved by the GLO the monuments established in them control over any idea of where they 'should have been'.


Second, the very nature of surveying with relatively crude tools, for not too much money, under adverse conditions, and in a relative hurry lead to error, and in some cases blunders. The PLSS was extended in a non uniform way from the initial points entering different areas from different directions.


Without extensive specific research on the actual order and progression of surveys in AR from the initial point it would be difficult to speculate on why the errors are where they are. Such work might require many months of work after months of collection all the records and then laying them out in chronological order and comparing each with where they are found today on the ground, followed by speculation as to why a particular error may have occurred. Often it can only be guessed.


One explanation is that the stuff on each side of the rivers were extended for many miles independently on each side. Another factor was that indian title had to be extinguished before surveys could proceed and lands offered for sale. There are a number of these old indian lines that cross Arkansas.


There are GLO maps out of old GLO reports on some of the map web sites that can provide some insight.


If anyone is interested I could hunt down some links. I would first try the Library of Congress map library, and then the David Rumsey Collection


http://www.davidrumsey.com/ search by state for Arkansas and there is a GLO map from 1866, the PLSS is already in, but the offsets are shown, so they knew they had them. The earliest atlas map there which appears to be derived from GLO work is 1840's with similar data. So that doesn't help. We may need to go back earlier which gets hard to do.


There are some maps on the library of congress site which so some of the PLSS incomplete along the rivers Burr Atlas 1839 for example.


Lots of interesting stuff though.


I thought about using the comps in Ozi explorer or in my Garmin instead, but had a program on the PC at hand.


- jerry


PS, often language on monuments or in books or on web sites make some kind of point about all the lands in such and such an area are based on this point. This slightly over emphasizes and may mislead one a little as to the importance of the initial point. The surveys progressed from them, and are numbered from them, but once the surveys were marked on the ground the initial point has no more signficance than that historical thing. If you lost the initial point monument (some have been), no ones property is affected or influenced in the slightest.

Edited by jwahl
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I am Not saying the PLSS is bad.


I read deeper and did some more study as always,found you in there on the manual.


The original transcription was made in 1985 by the BLM's Carson City Project Office, converted to HTML in 1996 by j.wahl

73 Survey Manual-1


I am just trying to understand all the concepts.

I have found a number of the Original GLO monuments and am working the details(Personal enumerated domain).

It is a massive project and want to be correct in what I find and document.


The entire collection of Joseph C. Brown and Prospect K. Robbins Surveys are on disc now at the Arkansas Archives.

The cost is $25.00.


I am thankful that you (all) take the time to explain the details,please do not get me wrong.

Most of the finer details come from the field experience's.

And answers from the online experience.


Yes M1 Warm Springs Quadrant is right for T., 22N., R.1,E-W.


I have found evidence in the correct (as near as can be)calculated area for the GLO TWP. Corner.T. 22N,R. 26W of the 5th Principal Meridian.

Some of the Original marked trees and some newer follow up marked trees.

Along with the stated evidence in the Original Field notes from this Township.


I never wanted to put all this out but I feel it is neccesary for me to say some of these things.


I will not go into detail,but the few things that I did show to ???? got removed within the last 4 years.

I was not smart enough to keep them to myself till I had more proof's.

Nor did I get good pictures of every detail,now I do and document it.


Meanwhile back at the Ranch......................

Edited by GEO*Trailblazer 1
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