Brain child of Professional Land Surveyor, Gary Breisch of Oklahoma.

### Land Surveyors Coop of the World

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#### Thoughts

• WOW!... the info u get when you re read something a few times... after you asked that about the units, i was thinking... hey i am assuming those are Chains and Links...

so i re read the article to be sure....

"THE PLSS DATUM
The 'PLSS Datum' is the reference system by which the majority of the PLSS surveys are theoretically reported. The data being reported on a BLM or GLO Cadastral Survey plat are, of course, bearings and distances. But bearings and distances with reference to what? The current BLM Manual of Surveying Instructions, 1973 states:

"2-1. The law prescribes the chain as the unit of linear measure for the survey of the public lands. All returns of measurements in the rectangular system are made in the true horizontal distance in miles, chains and links...."

"2-17. The direction of each line of the public land surveys is determined with reference to the true meridian as defined by the axis of the earth's rotation. Bearings are stated in terms of angular measure referred to the true north or south."

"2-74. .... By basic law and the Manual requirements, the directions of all lines are stated in terms of angular measure referred to the true north (or south) at the point of record."

"Distances. These and other references in the BLM and GLO Manuals make it clear that the frame of reference for distances is defined as horizontal measure in chains based on the U.S. Survey Foot at actual ground elevation. This is of importance when performing computations in projections or at sea-level when the actual lines are at a significant elevation. If you are computing proportions in a projection, the variation of elevation over a project can have a small effect, the elevation difference in essence weights the record ground measurements. This usually is a small effect unless the lines differ in elevation by a 1000 ft. or so.
Bearings: The above Manual sections and others identify the frame of reference for direction as something called 'Mean True Bearings' referenced to the true astronomic meridian '..at the point of record.' For those of you familiar with basic geodesy you will recognize that this is a basis of bearing that changes as you go east and west since the reference meridians are not parallel but converge towards the pole."

"Because this is a changing reference, the direction of a straight line on the ground can be described with a forward bearing based on the meridian at the beginning end, or with a differing back bearing based on the meridian at the end point. The difference between them is the angle of convergency of the two meridians. If we want to accurately describe how far north or west the line goes in a geodetic sense, we need to use the average or 'mean' of these two values. This 'mean bearing' is essentially identical to the bearing of the traverse line with reference to it's midpoint. Thus the 'point of record' for determining the bearing of a straight traverse line can be said to be the meridian at the midpoint of the line.

Straight Lines: Therefore, one unusual byproduct of the PLSS datum is that:

Straight lines on the ground are lines of constantly changing bearing.

A straight line is basically what you would lay out by double centering or projecting a direct line of sight. The only straight line that does have a constant bearing is the meridian or north and south line. An example of a boundary that might be a straight line is one that is described as a straight line running from one physical monument to another. Such a line, if reported in the PLSS Datum would have different forward and back bearings, and different bearings at each point along it.

Rhumb Lines: It is also apparent from the various GLO and BLM Survey Manuals and the actual methods that were used to lay out the public land surveys that most boundary lines in the PLSS are intended not to be straight lines but lines of constant bearing or Rhumb Lines. Such lines cross every meridian at the same angle and are thus curved as viewed on the ground.

Therefore, another unusual byproduct of the 'PLSS datum' is that:

Lines of constant bearing are curved lines on the ground.
For example, the solar compass and transit were instruments that determined bearing at each setup, and when matched with traditional chaining, measured or laid out lines of constant bearing.

something else that I re-learned while re reading the article... Mercy it is kind of complex, but im enjoying this.

The 'Manual' discussion of latitudinal arcs illustrate one example of a rhumb line. A parallel of latitude is a line that is due East and West in the PLSS Datum. Since it crosses each meridian at a 90 degree angle, it has a mean bearing of East or West. Lines of constant bearing in the PLSS datum will appear curved on the ground. It also turns out that the mean bearing of any chord or sub-chord connecting any two points along such a line is the same as the bearing of the rhumb line itself. Thus it is possible to lay out points on a rhumb line by correcting traverse lines to their mean bearing in computations."

I actually forgot about the CURVED East West Lines.. this was a major discussion that was discussed on another message board, come to find out the error produced by using Horizontal lines VS CURVED lines was about the size of a finger nail. kind of made it a mute discussion in my opinion, but good to know for testing purposes.

Again Gary thanks for bringingthis to LSU! Ive learned alot also! .
• That is one of my biggest concerns when someone writes a nice article and does not show the units. It is obvious to most that the distances he used were more than just feet, LOL. Yes, after reading the whole article I can see that Cardinal was true north that lines up with meridians and the original surveyors used the solar and other astro proceedures to head off in that direction or angle off or that north. It can be complex like the guy said but well worth the study of how they did it and the pit falls of special situations like he sited. Just think of how it would go if your were near the north pole or south pole, LOL ...guess they considered that because few would ever really build there.
• Cardinal is related to "True" North, which this term alone has been really blown out of context, don't ever say "true" north at a convention... lol... geodetic or astronomical

the original Surveyors used True Bearings by sun shot or Polaris if i remember right

what he means by cardinal here is basically using your "Otho" or F8 in auto cad or go due north/south or due east/west from the. i think he explains it in the beginning of the paper, in the link below in my first post

The Distance units are in Chains and Links take his units and times it by 66' to convert to feet, all the glo plats and notes in Oklahoma are annotated in Chains

the single and double proportion gets a little tricky when prorating is involved, when there is different platted or original distances in each section you are using the monuments to proportion from

80 chains equal 5280'

Hope this helps .
• "That is why I am still heavy on once the corner is set and of record with the current system, it should never be moved and is where it is no matter if it was set by one method or other other than by court judgement with ample records to show both positions and plenty of references. That is why I have always been for a Coop to share State Plane Coordinates of corners found for record and use by future generations. ."

I totally agree, when i used to post on RPLS.com alot, i advocated alot for just such a thing, sadly alot of folks were against it, they seen it as giving away information....common! we are all working for the same thing :)

on the distorted or skewed section lines, i have measured acrossthe township before just to see what or how it happened, the few times, i have done it, i have found someone started off of the right of way and thought it was a sectiion corner, and then it was compounded from there. In one instance i was able to prove the original Surveyor dropped a chain, i found both original monuments in there noted position undisturbed.... but what can you do? the monument is the monument in mnost cases, but i did show both lines on my plat. just reported the facts.

One thing i have done before, when working in grid AZ/BRRG in Auticad you can change your snap angle to match the inverse of the THETA or Mapping Angle to make computations easier such as he shows on the first diagram

I think the command is "snapang" then input the d.mm.ss of the crosshairs you desire, this is handy in many calculations
Small World Labs
• I read the whole article and now I have a better handle on what the hell he is writing about. Wow, he did make what appeared to be simple into a complex process. I have have only run across one area near where a buddy lives in Mannford, OK anywhere as strange. It is a sliver of land that no one has been able to explain. I wrote several people about it who I thought would help but no one could explain it. You dug up some good stuff that illustrates how things can be very complex when you consider all the rules and details that the rules may not cover cause disagreements. That is why I am still heavy on once the corner is set and of record with the current system, it should never be moved and is where it is no matter if it was set by one method or other other than by court judgement with ample records to show both positions and plenty of references. That is why I have always been for a Coop to share State Plane Coordinates of corners found for record and use by future generations.
• Now I feel really ignorant and lost. I am missing something and need to look up the meaning for Cardinal and understand the drawings better and what units are on the distances shown.

• Here is a good article by Jerry Wahl, he frequents www.rpls.com and i have had several conversations with him.

pay close attention to figure 2 and "cardinal equivelants"

Cardinal offsets

The Manual of Surveying Instructions, 1973 Section 5-26 describes a process for performing a double proportion. The Manual section states:

"5-26. In order to restore a lost corner of four townships, a retracement will first be made between the nearest known corners on the meridional line, north and south of the missing corner, and upon that line a temporary stake will be placed at the proper proportionate distance; this will determine the latitude of the lost corner.

"Next, the nearest corners on the latitudinal line will be connected, and a second point will be marked for the proportionate measurement east and west; this point will determine the position of the lost corner in departure (or longitude).

"Then, through the first temporary stake run a line east or west, and through the second temporary stake a line north or south, as relative situations may determine; the intersection of these two lines will fix the position for the restored corner."

hope this helps... this also answers my question about the distorted Section lines i was talking about!.... glad i let my mouse to do the walking :)

Ty
Small World Labs
• I have read the information again both in the article I attached previously and an old text book I used back at OSU called Surveying (fifth edition second printing, September, 1965) by Russell C. Brinker, consulting editor, that is very detailed and good but the wording could be modernized somewhat. The simple answer to my question below would be perpendicular from each proportional point from each line to intersect for the double proportional monument to re-set. Like you say, we need to draw it and show it for a better way to see it.
• HI Gary,

If i understand your question you are trying to double porportion a section corner in between calculated or existing monuments, in basically all four directions

i will try to answer this here, without a diagram, although a diagram is much better. in the past i have made a nice one highly exagerated in autocad, i may make another one, plot to pdf and post here.

when reading the blm, it just did not make sense to me, until i went to a few seminars by some very good instructors

ok, you have drawn a line from monument to monument running northerly and southerly and another line from monument to monument easterly to westerly, they intersect. a common but WRONG practice is to place the monument where they intersect, i have actually been instructed to do this b4 i was Lic.

The proper way in a perfect world, pretending GLO had measured 5280' north and south and east and west and you went out there and you measure 10560' both ways so there is no prorating involved. Find the mid point of both lines and place a mark to identify it. You then draw a line Cardinal (not perpendicular or parralel) directions east or west from the north south line (depending on where the mid point of the east/west line is.) Then draw a line from the mid point of the East/West line Due North or South to make an intersection. it is usually 1' to 5', possibly more as the crow flies from the intersection of your 2 original lines.

Where these 2 lines intersect is your double porportionate calc point.

alot of people still use total station and assumed bearings, and it is difficult to find cardinal directions, i have tried it both ways with gps and total station, drawing with ortho on in cad, and it doesnt really make that much difference. I dont want to sound sloppy, but if you were using total staion and wanted to use true cardinal directions for your double porp. point, you could traverse from 2 known monuments with a published Geodetic, or Grid AZ between them, or take a sun shot or observe polaris.

i really dont think and havent seen this yet, much error or differerence by using ortho in cad with or without gps.

I have seen some sections that had internal angles at the section corners of 88 or 87 degrees, i could see this being a problem, and would take alot more care in trying to establish a true Azimuth/Bearing, before double porportioning.

in this case, i have put a lot of thought into this, because the blm notes say these lines are very close to cardinal directions in this case, but the usgs 7.5 min topo's and measurements clearly show the skewed angles (dont get me wrong i dont rely on the usgs maps alone to determine this, but i do know they have been measureing these lines over and over for many years). In restoring corners, it almost seems to me going perpendicular would put the corner closer to its true location than going cardinal directions (otherwise it would put a major P.I. in the line, which is common but not that much of a P.I.). I havent found any info in my studies or research that show a good scenerio of this. However what i have explained above is how the BLM instructs us to do it

thankfully, i have always been able to replace a section corner monument with confidence by research, witness corners and interior corners etc, in this particular case.

hats off to you for your efforts to bring these subjects alive! I think you will do great on the exam, and I am still learning everyday, although i always strive for perfection, im only human and am capable of making mistakes or thinking i understand something when i may not.

I welcome any comments, corrections and or constructive criticism

Ty
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