Ok sports fans, here's a VERY simple question to ponder.
You have a PLSS Section (say Section 16). The Section was conveyed to the State in its entirety back in the 19th Century.
This Section has NEVER been settled, occupied, claimed, or otherwise been of interest to anybody for over one hundred years.
Fast forward to today.
The owner (State) wishes to convey one of the sixteenths (say NW¼ NW¼) by aliquot part description (NW¼ NW¼, Section 16, T.yN.,R.xE., SLB&M) ,to a third party.
You get out there and find ALL of the requisite Corners (4 ¼ Corners, and the Northwest Corner), all of which are in situ Stones as described in the Official GLO Records.
Now....here's the question;
Do you compute the C¼ “on the curve?”
See 2009 Manual 2-13, and 3-114
🙂
Loyal
Yes -and- all of the east west lines.
I will duck now.
> Yes -and- all of the east west lines.
Thinking out loud (i.e. without thinking too hard), won't calculating a straight-line intersection on a competent projection (e.g. SPC) accomplish this?
Loyal,
Good to see ya back... I normally set the monument on a parallel of latitude from the E and W 1/4 corners and on the meridional line of the N S 1/4 corners and punch mark the intersection for the button pushers and retards...always like to leave something behind to confuse the confused.. B-)
Pablo
It'll be at the intersection of two straight lines
It will not fall on a curve of latitude. The Manual is only a recommendation, not a mandate on non-Federal lands.
As "I" am now the first to survey within the section, whatever "I" decide is correct is how it is going to be and how it is going to stay.
Granted that if the party who set all of the original stones had actually set them all according to the rules in effect at the time of their work had also been charged with setting the center corner, then it is conceivable that it would have been set on a curve, but, not likely, especially in areas where the quarter oorners were intervisible. The difference being less than a link in my corner of the world.
Go ahead and blast me. Then ask the other 99.9999 percent of all surveyors who will put it at a calculated straight line intersection.
No, the SPC midpoint is what you get by sighting between quarter corners and going half the distance. SPC preserves angles perfectly at the expense of some distortion of distances.
---------------
Here's an exercise to show what happens in SPC.
Assume an arbitrary location
lat/lon E quarter corner N41 W111
Wyoming West zone by Corpscon
SPC N 511566.625 E 2371650.229
From starting point, go west about a mile (I neglected elev factor) by NGS Forward program to get a close-enough longitude, but keep the original latitude as if GLO perfectly followed the parallel of latitude.
lat/lon W quarter corner N 41 00 00.0 W 111 01 8.85692
SPC N 511622.622 E 2366370.790
Note that Northing changed a lot due to the convergence angle.
Mean of SPC coordinates "midpoint"
SPC N 511594.623 E 2369010.510
lat/lon N 41 00 00.00143 W 111 00 34.42848
The midpoint of the curved line, by holding latitude and averaging longitudes of quarter corners is
lat/lon N 41 00 00.0 W 111 00 34.42846
SPC N 511594.479 E 2369010.510
The difference, by which the SPC solution is north of the parallel of latitude,
is N 0.144 E 0.0
------------------------
The geodetic Inverse between quarter corners is
1609.2471 meters FAZ 270 00 22.5871 BAZ 89 59 37.4129
Forward half way at FAZ is
lat/lon N 41 00 0.00143 W111 00 34.42846
This is the same answer obtained by SPC midpoint.
It'll be at the intersection of two straight lines
I would follow the manual not as a requirement but as a recommendation as is stated on the pages contained therein. WHY? Because you do not want to screw the rest of the aliquot parts in the section that will be conveyed at some future date.
> No, the SPC midpoint is what you get by sighting between quarter corners and going half the distance.
I wasn't thinking midpoint, but rather intersection. The opposing 1/4 corners aren't going to be at the same latitude/longitude except in extremely unlikely circumstances due to the conditions under which they were set.
What I'm wondering about is the most practical method of calculating the "best" intersection under real-world circumstances. It won't be on a common parallel of latitude, nor on a common meridional line. That's why I thought a straight-line intersection on a rigorous projection might serve the purpose. Meaning the lats/longs would also work unless the deviation of the 1/4 corners from a common parallel/meridian is large.
What approach would you suggest?
It'll be at the intersection of two straight lines
A number of realworld issues comes into play in this discussion based on the specific area where this magical section has been found. First, I have never encountered a situation where all eight GLO corners are found to be the originals. The vast majority of ours were the stake and pits variety which were subsequently inundated by road construction starting 150 years ago. Some were stone and I have found many of them through the years. But, you will never, in this part of the world ever find all eight corners to be original corners.
Second, much of the work done here involved short cuts that did not conform to the intent of the Manual in force at the time. The original lines were not set on true latiitudes. That is painfully obvious. Most north and south quarter corners were stubbed in from the most convenient direction.
Third, the measured distances today do not compare to record, sometimes by several hundred feet in one-half mile.
OK, let's assume all eight original corners are in place and the original crew actually followed the intent of the Manual, they would have placed the center corner at the intersection of two straight lines and not on a true latitudinal curve as their east and west quarter corners were nowhere near being on a true latitudinal curve to start with. The only time they MIGHT have followed a true latitudinal curve is on township borders.
It'll be at the intersection of two straight lines
Speculating on what the GLO surveyor might have done is fine, but the question remains: how best to establish the position of the C1/4 now?
The intersection is expected to be somewhere in the general neighborhood of the midpoint, so I used the exact midpoint to get typical numbers, rather than make up some other example. For any intersection within many feet of the midpoint, the north-south difference between methods will be close to what was calculated for that latitude.
Having slightly different lengths and directions doesn't change the fundamental fact that SPC is going to preserve angles, in this case an angle of 0 between the line to the opposite quarter corner and the line to the center corner.
The easiest way to put the C 1/4 on the curve within hundredths, in a section that isn't grossly mis-shaped, is to calculate the idealized case (like I did) for the latitude of interest and apply that offset to the visual intersection or SPC intersection.
Edit: I think a way to get very close in any shape of section might be to find the geodetic inverse between E & W quarter corners, also the N & S quarter corners, and use those distance and forward azimuths, adjusted by convergence, to find an SPC intersection. Check that inverse geodetic azimuth from E 1/4 to C 1/4 matches C 1/4 to W 1/4, and ditto north-south. The only approximation should be in the SPC distortions in a mile throwing the proportion off a tiny bit.
The generalized precise mathematical solution is messy - it's the intersection of two rhumb lines. Maybe someone can offer a reference for it?
It'll be at the intersection of two straight lines
In the inter mountain west they would likely have had run the lines with solar compass or even magnetic compass when subdividing the section. Therefore the lines would've been curved other than their errors which as a practical matter would've been much larger than the curve deflection. Usually the opposing corners are not inter visible.
It'll be at the intersection of two straight lines
Where would the original GLO surveyor have put it if required to and he followed the instructions of the time?
The accuracy in the 1800's would have been typically several feet, perhaps many feet, per mile, so making a distinction between these positions would never have occurred to them. They did, however, have instructions for running parallels of latitude for base and correction lines. That shows the intent to do so where the difference was considered significant.
In many places the 1800's surveyor would have run a constant compass bearing for several segments within the mile, thus being closer to a constant-bearing (rhumb) line than a great circle line (if magnetic declination remained constant). In some areas, perhaps visibility allowed them to sight a mile, and the opposite would be true.
It'll be at the intersection of two straight lines
Wouldn't a constant magnetic compass bearing follow a curve? I mean absent other errors. I mean each new setup uses north at that location.
A solar compass would surely follow the curve.
Actually in reality the line would be series of short rumb line but each setup would correct to the current true bearing.
It'll be at the intersection of two straight lines
AMEN brotha! Nobody likes to argue over a square foot of ground except for them city boys!
It'll be at the intersection of two straight lines
It will not fall on a curve of latitude. The Manual is only a recommendation, not a mandate on non-Federal lands.
Doing it properly the corner would fall on a parallel of latitude between the two points by federal methods.
As "I" am now the first to survey within the section, whatever "I" decide is correct is how it is going to be and how it is going to stay.
I agree
Granted that if the party who set all of the original stones had actually set them all according to the rules in effect at the time of their work had also been charged with setting the center corner, then it is conceivable that it would have been set on a curve, but, not likely, especially in areas where the quarter oorners were intervisible. The difference being less than a link in my corner of the world.
The corner would have been set on a curve by the original surveyors even if intervisible.
Pablo B-)
Setting ORIGINAL C¼ - Trick Question
> Ok sports fans, here's a VERY simple question to ponder.
> [...]
> Do you compute the C¼ “on the curve?”
Obviously, this is a trick question. Anyone who has read this message board for at least a year will know that in PLSSia the center of section is typically a multiple guess scenario. So the real question is "should you also set a very old fence corner post with bits of rusty, old fence wire attached to it about ten feet in any cardinal direction from where you mark "THE" corner and then randomly drive several pipes of obvious age at locations within five feet of either the post or your brand new marker? Should you use different colors of plastic flagging?
Setting ORIGINAL C¼ - Trick Question
Actually it is not a trick question at all.
It comes down to the year the GLO surveyed the township and then a referral to the instructions in effect at the time for the subdivision of sections.
That would be the proper procedure EXCEPT that some states, although given full jurisdiction over previously patented lands by the US Supreme Court, have kicked the ball back to the BLM and it's most recent "Manual".
Pablo the proper way
To do this is the alternate method: one time on the curve, next time a straight line that way you please everybody.
The New Manual Does Not Apply
Section 3-87. Intersect 2 straight lines.
The center of section and all other aliquot parts were established at the time of the original PLSS survey. It is neccessary to now monument it where it was established.
That one can do that more precisely now than back then is nothing to be ashamed of.
Paul in PA
