Analysis of Section 6, Township 47 North, Range 29 West, 5th Principal Meridian, Missouri

Back in March 2009, it was brought to my attention that there were some problems in Section 6 of Township 47 North, Range 29 West of the Fifth Principal Meridian.  A question was posed concerning how the location of the north quarter corner (a blank corner) would be determined.  Here is my analysis.
-----------------------------------------------------------------------------------------

Section 6, T47N R29W, 5th PM
Missouri Township Plats, Volume 11, page 52
image courtesy of the Missouri Department of Natural Resources

The distance along the north side of Section 6, generally, was not measured directly in the field by the GLO deputy surveyor, nor was the north quarter section corner actually set. The distance, therefore, must be computed using the south line distance of Section 31 in Township 48 North and the distances from the closing line between Ranges 29 and 30 West in Township 47 North to the range line between Ranges 29 and 30 West in Township 48 North and from the closing line between Sections 5 and 6 to the corner between Sections 31 and 32 in Township 48 North, as follows:

distance along south side of Section 31, T48N R29W = 80.00 chains

lap distance from range line of T47N to range line of T48N = 2.47 chains

lap distance from closing line of 5 and 6 to east corner of Sec. 31 = 3.83 chains

North line distance of Section 6, T47N R29W = 80.00 - 3.83 + 2.47 = 78.64 chains

distance along north line of the NW 1/4 Sec. 6 = 78.64 chains - 40.00 chains = 38.64 chains

An examination of the GLO plat in Volume 48, page 29 (MoDNR microfiche location: 720/0647B3) and the old GLO plat in Volume 11, page 52 (MoDNR microfiche location: 720/0158A2) indicates that the clerk computed the distance of the north line of the NW 1/4 of Section 6 to be 36.17 chains.

If we take 80.00 chains minus 3.83 chains minus 40.00 chains we get a distance of 36.17 chains, which is the distance from the north blank quarter corner of Section 6 to the range line between Ranges 29 and 30 West in Township 48 North.

To properly locate the north blank quarter corner of Section 6, we would use the overall distance of 78.64 chains, as computed from the actual field measurements, to proportion the distance by single proportionate measurement:

(our measured overall distance)*(40.00 ch)/(78.64 ch) = the proportionate distance along the north line of NE1/4

or

(our measured overall distance)*(38.64 ch)/(78.64 ch) = the proportionate distance along the North line of NW1/4
　

What can we find by looking at acreages in Section 6:

Northeast quarter:

Acreage on plat for NE1/4 = 71.60 acres

71.60 acres = (1/10)*(40.00 ch)*(0.5)*(18.00 ch + x)

x = 17.80 chains = protracted distance from the center quarter corner to the north blank quarter corner

protracted distance of N-S line between east half and west half of the NE 1/4 =
(0.5)*(17.80 ch + 18.00 ch) = 17.90 chains

Acreage for E1/2 NE 1/4 = (1/10)*(20.00 ch)*(0.5)*(17.90 ch + 18.00 ch) = 35.90 acres

Acreage for W1/2 NE1/4 = (1/10)*(20.00 ch)*(0.5)*(17.80 ch + 17.90 ch) = 35.70 acres

An examination of the GLO plats mentioned above indicates that the clerk who performed the calculations got the acreages switched around.

Subdividing the NE1/4 into halves should not be a problem. The dividing line would be constructed from the midpoint of the south line to the midpoint of the north line.

Southwest quarter:

Acreage on plat for SW1/4 = 147.59 acres

(147.59 acres)/4 = 36.8975 acres = the acreages shown on the GLO plat for each quarter of the SW1/4

Thus, we can conclude that the intent was to divide the SW1/4 into aliquot parts (quarters) instead of lots. Subdividing the SW1/4 should not be a problem. The quarter-quarters of the SW1/4 would be constructed by intersecting lines connecting midpoints on the opposite sides of the SW1/4.

A notation included on the old GLO plat (Volume 11, page 52) indicates that the southwest quarter of Section 6 was subdivided on February 25, 1844 in accordance with the Act of Congress of the 5th of April 1832, so as to conform to a previous sale as reported by the Register on June 6, 1843.

Northwest quarter:

The Northwest quarter is the real problem child. Let's see what we can figure out:

Acreage for NW1/4 = 64.44 acres

64.44 acres = (1/10) * [(0.5)*(17.60 ch + 17.80 ch)] * [(0.5)*(36.17 + y)]

y = 36.644 chains = distance of E-W line between NW1/4 and SW1/4

Acreage for SW1/4 = 147.59 acres

147.59 acres = (1/10)*(40.00 ch)*(0.5)*(37.14+y)

y = 36.655 chains = distance of E-W line between NW1/4 and SW1/4

Let's use an average distance of 36.65 chains for the distance of the E-W line between the NW1/4 and the SW1/4.

Computing an acreage for E1/2 NW1/4

(1/10) * [(0.5)*(17.70 ch + 17.80 ch)] * [(0.5)*((0.5*36.17 ch) + (0.5*36.65 ch))] = 32.31 acres

(compare to 32.12 acres on GLO plat)

Computing an acreage for W1/2 NW1/4

(1/10) * [(0.5)*(17.60 ch + 17.70 ch)] * [(0.5)*((0.5*36.17 ch) + (0.5*36.65 ch))] = 32.13 acres

(compare to 32.42 acres on GLO plat)

32.31 acres + 32.13 acres = 64.44 acres as shown on the GLO plat for the NW1/4

Upon examination of the GLO plat, it would appear that the clerk who performed the calculations once again got the acreages switch around. Although these calculations do not precisely match the GLO plat acreages, they are close enough to tell us that the clerk subdivided the NW1/4 by constructing a line from the midpoint of the south line to the midpoint of the north line. Thus, we would subdivide the NW1/4 into halves by constructing a line from the midpoint of the E-W line between the NW1/4 and the SW1/4 to the midpoint between the closing range line between Ranges 29 and 30 West of Township 47 North and the north blank quarter corner of Section 6.



----------------------------------------
Original composition by Steven E. Weible

See New Plat?

This is the text of my article, "See New Plat?" from the September 2011 issue of Missouri Surveyor.  See link under Published Articles at right.
-----------------------------------------------------------------------------------------
The first thing to catch the eye are the words "SEE NEW PLAT" scrawled in pencil across the middle of the document. The thought enters the mind, "Who would do that?" The next thought that enters the mind might be, "If there is a new plat, is this old one of any value?"

The old plat referred to here is a Missouri township plat from the period of 1816 to 1824. During this period, William Rector served as Principal Deputy Surveyor of the Territory of Missouri (Act of February 28, 1806, chapter 11, U. S. Statutes at Large, Volume 2, page 352), Surveyor of the public lands for the Territories of Illinois and Missouri (Act of April 29, 1816, chapter 151, U. S. Statutes at Large, Volume 3, page 325) and Surveyor of the public lands in the States of Illinois and Missouri and the Territory of Arkansas. The contracts into which he entered with deputy surveyors for the subdivision of townships required the contractors to "make out three neat and accurate plats and descriptions" and to calculate the quantities of each fractional section, which were to be shown on the completed plats. It appears that this practice was abandoned as a quality control measure, beginning in 1825, by the succeeding Surveyor of the public lands, William McRee (American State Papers, Public Lands, Volume 6, page 402, Number 1033). The township plats were thereafter prepared by clerks within his office. The old plats prepared by the deputy surveyors remained in use until new plats were prepared in the 1840s, 1850s and 1860s prior to the closure of the office of the Surveyor of the public lands on October 31, 1867 (MoDNR microfiche location: 720/3375A04).

So now that there is a new plat, is the old one of any value? The answer is ... maybe. There are some seventeen volumes of old plats and most of these do not contain any more than what can be found on the new plat. Some, however, contain interesting information that may provide insight on how to deal with many of the "oddities" of the Public Land Survey System in Missouri.

The old plats appear to have served as a record of activity within some of the townships. Confirmed private claims were added as the surveys were completed and the northern and western tiers of sections were protracted into lots as laws changed to provide for the sale of land in smaller units. The Act of February 11, 1805, chapter 14, (U. S. Statutes at Large, Volume 2, page 313) only anticipated the sale of public lands in tracts as small as the quarter section. The Act of April 24, 1820, chapter 51, (U. S. Statutes at Large, Volume 3, page 566) provided for the sale of public lands in half quarter sections. Then the Act of April 5, 1832, chapter 65, (U. S. Statutes at Large, Volume 4, page 503) provided for the sale of public lands in quarter-quarter sections.

Township plats returned by the U. S. Deputy Surveyors prior to April 1820 would only have been subdivided into quarter sections as the smallest unit with the protraction of "80 acre" tracts being added later. Likewise, township plats returned by the U. S. Deputy Surveyors after April 1820 and prior to 1825 would only have been subdivided into "80 acre" tracts as the smallest unit with the protraction of smaller units being added later. Those plats that contain later subdivisions into lots usually contain notations indicating the date on which they were protracted and the date on which a copy was sent to the Register of the district land office and/or the Commissioner of the General Land Office.

The majority of notations of protraction begin to appear on the old plats after April 1832. The general form of the notation is as follows:

"Subdivided under the Act of Congress of the 5th of April 1832 and sent a copy

of the plat to the Register and to the Commissioner of the General Land Office."

In some instances parts of the northern and western tiers of sections, where lotting is expected, were protracted into aliquot parts, creating one of the "oddities" of the Missouri system. The following notation on the old plat gives insight into the reason why this was done:

"Subdivided under the Act of 1832 so as to conform

to previous sales as reported by the Register ..."

It appears that in these cases the district land offices were selling the tracts as aliquot parts, as authorized by the Act of April 5, 1832, before the clerk in the Surveyor's office protracted them into lots. The Register of the district land office reported the sales as made and the clerk, then, adjusted the plat accordingly and made the area computation.

How the clerk was instructed in the task of protracting the northern and western tiers of sections into lots is not known to the author, but the method seems to have differed either by time period or by the particular clerk performing the calculation. In many of the cases where protraction was performed prior to about 1843, the lot area of those lots not adjoining the township or range line was held fixed at 80 acres and the unknown lot dimensions were calculated accordingly, resulting in different distances on each side of section lines and center of section lines. In cases where protraction was performed after about 1843, the distance on each side of these lots was fixed at 20.00 chains and the lot area was simply labeled as a nominal "80 acres." These are not absolute rules, however, because in some cases the lot distance was fixed at 20.00 chains and the lot area was computed as something other than 80 acres.

An example of an old township plat on which two different methods of protraction appear side-by-side on the same plat is Township 42 North, Range 10 West (Missouri Plats Volume 9, page 13, MoDNR microfiche location: 720/0123A03). See figure 1. The northwest quarter of Section 3 was subdivided on February 18, 1839. The North half of Section 2 was subdivided on May 27, 1845. A look at the handwriting between the two sections reveals that each was subdivided by a different clerk. In Section 3 that clerk held the area of Lot 1 of the northwest quarter fixed at 80 acres and then calculated the north-south lot distance to be 18.95 chains. In Section 2 the other clerk set the north-south distance of Lots 1 in the northeast and northwest quarters at 20.00 chains and simply labeled the lots as being a nominal "80 acres."


Figure 1
Sections 2 and 3, T42N R10W, 5th PM
image courtesy of the Missouri Department of Natural Resources

See figure 2 for another example from Township 48 North, Range 3 West (Missouri Plats Volume 12, page 27, MoDNR microfiche location: 720/0168B03). The northwest quarter of Section 4 was subdivided on April 17, 1839. The northeast quarter of Section 4 was subdivided on October 6, 1840 to conform to a previous sale as reported by the Register. The north half of Section 5 was subdivided on September 27, 1841.


Figure 2
Sections 4 and 5, T48N R3W, 5th PM
image courtesy of the Missouri Department of Natural Resources

See figure 3 for an example from Township 39 North, Range 6 East (Missouri Plats Volume 3, page 44, MoDNR microfiche location: 720/0043A01). The north half of Section 3 was subdivided on July 13, 1839.

Figure 3
Section 3, T39N R6E, 5th PM
image courtesy of the Missouri Department of Natural Resources

Was it simply up to the clerk to decide or were there explicit instructions on how to proceed? It's hard to know. That's why it is important to examine all of the available information ... including the old township plats. Most of the notes and calculations that appear on the old plats were not transferred to the new plats, so this information would be missed if only a new plat was used.

As Missouri Surveyors we have all been taught protraction procedures that are consistent with the Bureau of Land Management's Manual of Surveying Instructions. The fact is, however, that the clerk in the office of the Surveyor of the public lands may not have actually done it that way. So, if there is an old plat, it's worth a look. You may find the answer to your "oddity." Another point to remember is that the plat in effect at the time that the patent was issued is the one that will control. In many cases that's the old plat!

----------------------------------------

Original composition by Steven E. Weible

Analysis of an EDM Baseline Comparison

This is the text from my article, "Analysis of an EDM Baseline Comparison," from the March 2011 issue of Missouri Surveyor.  See link under Published Articles at right.
--------------------------------------------------------------------------------------------
For those who have ever wondered how to interpret the "Calibration Report" of an EDM baseline comparison that was produced by a Missouri Department of Natural Resources (MoDNR) application, perhaps the following discussion will help.

Referring to NOAA Technical Memorandum NOS NGS-10, "Use of Calibration Base Lines" (click here to see the publication), the following discussion is found under the heading of "Analysis of Calibration Base-Line Observations" (page 9 of that publication):

"Most EDMI manufacturers routinely attribute certain accuracies to their instruments.  Although these accuracies should reflect the instrument's ability to measure a "true value," they may, in fact, indicate only the repeatability (precision) of the instrument or test results performed under laboratory conditions.  Theoretically, if the accuracy statistic is given in terms of a standard error (sigma), 68.3% of the differences between a "true value" and an observed value should fall within the stated specification.  Therefore, this value could be used for decision purposes, i.e., as a test statistic.  However, the above is true only for large samples and for known standard errors.  Both of these requirements are rarely satisfied.  In addition, by using this test statistic for rejection purposes, another type of error may be committed, i.e., the rejection of valid observations.  To reduce the possibility of rejecting a valid observation, a limit of 3sigma (three times the standard error value) is usually chosen for deciding if an observation is acceptable or not acceptable.  Theoretically, 99.7% of the differences should fall within the 3sigma range...

If 99.7% of the observations fall within three times the manufacturer's stated accuracy and 68.3% fall within the manufacturer's stated accuracy, the instrument can be accepted as working accurately and reliably."

One method of analysis of EDM baseline observations, then, is to examine how the observations compare to a standard specification.  Since the distance observations from a baseline comparison are not different measurements of the same segment, some means must be used to ensure an "apples to apples" comparison.  This is accomplished by computing the difference between the known distance and the observed distance of each segment measured. On the MoDNR report these differences are shown at the lower portion of the page.

A typical comparison on a Missouri EDM baseline will result in twelve (12) distance observations.

68.3% of 12 observations = (0.683)*12 = 8 observations

99.7% of 12 observations = (0.997)*12 = 12 observations

The standard specification for comparison is the manufacturer's stated precision of the instrument being tested, so, if 8 of the differences are equal to or smaller than the manufacturer's stated precision and all 12 of the differences are equal to or smaller than 3 times the manufacturer's stated precision, then "the instrument can be accepted as working accurately and reliably."

For an instrument with a manufacturer's stated precision of +/-(0.002 m + 2 ppm*Distance) and a known distance of 1234.5678 meters,

sigma = 0.002 m + (2 ppm) * (1234.5678 m)
sigma = 0.002 m + (2 / 1,000,000) * (1234.5678 m)
sigma = 0.004 m

and

3sigma = 3 * [ 0.002 m + (2 ppm) * (1234.5678 m) ]
3sigma = 3 * [ 0.002 m + (2 / 1,000,000) * (1234.5678 m) ]
3sigma = 0.013 m

See example data below:

Manufacturer's stated precision: constant = 2 mm
                                 scale factor = 2 ppm

Known        Observed                  One Sigma    3 Sigma
Distance     Distance      Delta       Value        Rejection Limit
(meters)     (meters)     (meters)     (meters)     (meters)
--------     --------     --------     --------     --------
149.9649     149.9633     0.0016       0.002        0.007
399.9523     399.9523     0.0000       0.003        0.008
1374.9235    1374.9207    0.0028       0.005        0.014
149.9649     149.9644     0.0005       0.002        0.007
249.9874     249.9899    -0.0025       0.0025       0.0075
1224.9584    1224.9572    0.0012       0.004        0.013
399.9523     399.9520     0.0003       0.003        0.008
249.9874     249.9897    -0.0023       0.0025       0.0075
974.9712     974.9683     0.0029       0.004        0.012
1374.9235    1374.9171    0.0064       0.005        0.014
1224.9584    1224.9540    0.0044       0.004        0.013
974.9712     974.9664     0.0048       0.004        0.012

For this set of data, nine observations are equal to or smaller than the manufacturer's stated precision and all twelve observations are smaller than the rejection limit of three times the manufacturer's stated precision.  Therefore, according to this evaluation criteria, the instrument that was tested "can be accepted as working accurately and reliably."

Referring again to NOAA Technical Memorandum NOS NGS-10, the discussion there continues:

"If the differences do not agree within above specifications, then a different method must be used to determine an instrument's acceptability...  One such approach is to examine the differences between observed values and published values and determine if the difference is a constant or is proportional to the distance being measured (scale error)...  The preferred approach is a least-squares solution that simultaneously determines a scale and a constant correction.  This solution is based on the supposition that the differences can be attributed either to a scale correction or to a constant correction, or both."

The MoDNR processing application performs a least-squares computation, using the formulas presented in NOAA Technical Memorandum NOS NGS-10 and the results can be found on the report near the center of the page. If the instrument is performing acceptably, the computed system constant and scale factor should be comparable to the manufacturer's stated precision.

For the example data shown above, the computed system constant is -1.4 millimeters and the computed scale factor is 4.2 parts per million.

A primary assumption of this discussion and an important fact that should be recognized by the user is that an EDM baseline comparison is meaningful only if the known distances of the baseline have been determined to a higher degree of precision than that of the equipment being tested, as described in NOAA Technical Memorandum NOS NGS 8, "Establishment of Calibration Base Lines" (click here to see the publication).


----------------------------------------
Original composition by Steven E. Weible

MoDNR's EDM Baseline Comparison Rejection Limit

If you are familiar with the Electronic Distance Measurement Baseline Calibration Report produced by the Missouri Department of Natural Resources (see application at MoDNR EDM Calibration) and you read my article in the March 2011 issue of Missouri Surveyor, entitled "Analysis of an EDM Baseline Comparison," you may be wondering about the "Rejection Limit" shown on the MoDNR report.  It doesn't correspond with the discussion that I presented in the article, so how does MoDNR derive their rejection limit?

On March 12, 1984, former Missouri State Land Surveyor, Robert E. Myers, issued a memorandum, addressed to "Users of the EDM Baselines," providing an "Explanation of the Calibration Report," in which he states,

"The rejection limit is based on three times the standard deviation determined by this calibration procedure. Some values will be outside the rejection limit."

Since the rejection limit values are being "determined by this calibration procedure," a look at the "calibration procedure" may provide an answer. The original DOS version of the processing application used by the MoDNR was written by John Paulsmeyer, using the Q-BASIC programming language. This program was the analysis tool used prior to the implementation of the online application (see link above). Examining the source code of this DOS version reveals the following in regard to the rejection limit:

     DRL = 3# * 0.000005 * DH(X) + 3# * 0.005

where     DRL = rejection limit and

     DH(X) = the measured horizontal distance in meters for the segment. 

Rearranging this equation produces the following result:

     rejection limit = 3 * (0.005 m + (measured distance) * 0.000005), or

     rejection limit = 3 * (5 mm + (measured distance) * 5 ppm)

With the equation in this form, it is apparent that the rejection limit in the processing program is based on a fixed system constant of 5 millimeters and a fixed system scale factor of 5 ppm. Referring again to Mr. Myers’ memo, the following statements are found:

"The system constant is composed of two components, the prism constant and the error of the phase difference determination. In the ideal situation, the prism constant will be known, so the error in phase determination will be the only unknown. For most EDM equipment the phase difference determination error will be plus or minus five millimeters."

and

"... all the error which would be shown by the system scale factor would be a result of the error in the modulation frequency. The standard error in frequency would be approximately 10 megaherts or approximately an error of 5 parts per million."

So, the rejection limit shown on the MoDNR report is based on EDM equipment having a manufacturer’s stated precision of ±(0.005 m + 5 ppm*D), which represents the equipment being used by land surveyors at the time that Mr. Myers composed his memo in 1984. 

***************************
Note:  In August 2013 the Missouri State Land Survey was transferred from the Missouri Department of Natural Resources to the Missouri Department of Agriculture.



----------------------------------------
Original composition by Steven E. Weible

Response to Stan Emerick's article, "Quixotial Quest Part II"

In the September 2010 issue of Missouri Surveyor, Professional Land Surveyor Stan Emerick composed an article entitled, "Quixotial Quest Part II," in which he discussed proposed changes to Missouri Minimum Standards for Property Boundary Surveys (see page 28, Missouri Surveyor, Septemer 2010).  Following is the response that I submitted to Stan on October 4, 2010:

Having read your article in The Missouri Surveyor, entitled "The Quixotial Quest Part II," I have no argument with your analysis of traverse measurements or your suggested modifications to field procedures, but I must disagree with your analysis of satellite-based measurements and your suggested modifications to the current standards.

In your article you stated:

"For analysis, we looked at three basic approaches to utilizing GPS technology: Static Surveys (including OPUS solutions), Real Time Kinematic Surveys (RTK, utilizing base stations and rovers) and Virtual Reference Systems (VRS, a network of continually operating reference stations). Each employee a slightly different method of determining positions, but all work on the same general framework, the computation of positional values by resection."

and

"In the other system, positional values are determined by resection from satellites, whose primary component measurement is distance. With the exception of some real-time kinematic surveys, the value of any given point in a survey is nearly independent of any other given point. The only connection they share is the condition of the satellites at the time of the survey and any atmospheric influences that the signals might have endured."

The concept of satellite-based observations being based on resection does not fit with my understanding of satellite-based technology. To refresh my memory on the precise meaning of resection, I consulted a few surveying texts. One reference defined resection as a means of determining the position of an unknown point by occupying the point and measuring the horizontal angles between at least three, and preferably more, control points. The other references that I consulted indicated similar definitions with all emphasizing the determination of position by either horizontal angles or directions, from which the horizontal angles could be computed. From these definitions we see that resection is based on the measurement of horizontal angles, not distances, as you have stated. So, resection is definitely the wrong word to use.

I agree that satellite-based measurements are more analogous to distance measurements, as in trilateration, although I wouldn’t use that word to describe it either. I cannot agree, though, with your statement that "positional values are determined by resection from satellites." Aside from resection being the improper word to use, your statement implies that the direct result of satellite-based observations is a positional value. This is true if point positioning is being used. Point positioning with a single receiver to a degree of precision acceptable for surveying applications, however, simply is not available to the ordinary civilian user.

The high precision measurements obtained for survey applications are achieved by relative positioning, which requires two receivers collecting data from the same satellites at the same time. At each epoch interval, measurements are recorded to each of the satellites from which the receivers can detect a signal. For as long as the receivers continue to collect data, measurements continue to be recorded at each epoch interval, so that a significant number of measurements are available. These measurements are the raw data just as traverse observations are raw data. For this raw data to be meaningful it must be processed just as traverse observations must be reduced to be meaningful. Provided that enough measurements have been obtained to produce a solution, processing techniques are employed to make computations using all of the available data, resulting in a vector solution that defines the orientation of one receiver relative to the other receiver. This vector is the basic piece of usable information obtained from the observation process, having both magnitude and direction, just as a traverse observation from one control point to the next has magnitude and direction, each with a corresponding uncertainty based on the quality of the measurements obtained. It is then from this vector solution that the positional values can be computed.

The process just described is applicable for all satellite-based observations used in surveying applications, whether static or real time kinematic (single base or network). The main difference in the techniques is the time at which the processing takes place. In static applications the processing takes place at a later time, whereas in real time kinematic applications the processing takes place in real time. The computers do all the work, so it’s easy to misunderstand what is actually taking place.

So, your statement that "the value of any given point in a [satellite-based] survey is nearly independent of any other given point" is totally false for relative positioning. The value of any given point is dependent upon at least one other point. If two points can be traced back to a common point, then a positional relationship between the two points is determinable.

You also state that "GPS or sky-based surveys ... normally are not viewed as tools for measuring direction." With satellite-based measurements, even without a fixed position, it is possible to determine a usable direction, so I would have to disagree with this statement. Azimuth determinations are made by satellite-based observations all the time, replacing the less convenient methods of solar and polaris observations.

Your article seems to emphasize the differences between ground-based traverse measurements and satellite-based measurements, based upon the concept of traverse closure and a manual analysis of component distance and direction errors. If, however, we recognize the limited application of traverse closure and turn to an analysis of positional accuracy/uncertainty and/or relative positional accuracy/uncertainty, then I think the similarities become more apparent and the results more comparable. If we consider that there are really only two classes of methods in collecting survey information, the real differences in analysis are revealed.

The first class of methods consists of those methods which employ redundant observations, providing a mathematical check and a measure of quality. Methods in this class would include: ground-based closed traverses; networked ground-based traverse observations; ground-based surveys in which sideshots are observed from more than one instrument setup; static or rapid static satellite-based surveys in which vectors form a closed figure or connect points whose positions have been precisely determined; real time kinematic satellite-based surveys in which each point is observed from more than one base setup; and satellite-based observations submitted for OPUS processing.

The second class of methods consists of those methods which do not employ redundant observations, thereby providing no mathematical check and no verification of quality. Methods in this class would include: ground-based open traverses; ground-based single setup radial observations; static or rapid static satellite-based surveys in which vectors do not form a closed figure and do not connect points whose positions have been precisely determined; and satellite-based real time kinematic surveys in which only one base setup is used or in which points are occupied only once.

With the first class of methods, the redundancy makes it possible for a least squares analysis or other statistical analysis to be performed to evaluate the quality of the measurements actually obtained. This analysis includes information about the quality of individual measurements (whether ground-based observations or satellite-based vectors), the relative positional accuracy/uncertainty between points and the positional accuracy/uncertainty of points relative to the overall survey. These results, then, provide information as to whether the accuracy requirements have been satisfied or not.

With the second class of methods, any evaluation of the quality of the measurements must be based on the accuracies that one might expect to obtain using those procedures, because no checks are available on the actual measurements. These expected accuracies may be based on prior field testing or established specifications that can be relied upon to provide a certain level of quality of results.

You may have noticed that I did not include real time kinematic networks in either of the two classes delineated above. Into which class of methods real time kinematic networks would be placed depends upon how the resulting position is determined. If the position is determined as the result of multiple vectors, then the network method would fit in the first class of methods which employ redundant observations. If, however, the position is determined by a single vector from a single network station, then the network method would fit in the second class of methods, which have no mathematical check or verification of quality. The information that I have read would seem to indicate that real time kinematic networks have a network determined correction, but a position that is ultimately based on a single vector from a network station, which would place it in the second class of methods.

It should be noted that your "suggested modifications to field procedures," if implemented, would produce surveys that fit into the first class of methods described above.

Having said all of this, I believe that you see why I must disagree with your suggested modifications to the current minimum standards that refer to resected survey measurement or resected survey method, since they are based on a misunderstanding of satellite-based observations.

As for your other suggested modifications to the current minimum standards, the only ones that I like are the changes to "the required relative position tolerance and traverse closure," stating the accuracy standards as a constant and a scale factor and eliminating the Suburban Property Standard.

An additional note of one thing that I think really needs to be corrected in the current minimum standards for property boundary surveys is the terrible misuse of the word "tolerance." It should be noted that a tolerance is a "not-to-exceed" value. In other words, it is the standard to be met. The current minimum standards use the word interchangeably as the standard to be met and the accuracy achieved in the performance of the survey. There is a distinction and it needs to be clarified.


----------------------------------------
Original composition by Steven E. Weible

Interesting comments by J. W. Nations, former Sainte Genevieve County Surveyor

While researching information in preparation for boundary surveys, I often come across interesting comments that surveyors have included in their field notes.  Following are a few comments left by J. W. Nations, former County Surveyor for Sainte Genevieve County, Missouri.

The first comment is found in the old Sainte Genevieve County Survey Record Book at page 48 (MoDNR microfiche location: 186/0038A03) and is dated June 12, 1885:

"It often happens that we cannot subdivide a section strictly as it should be for the reason that parties cannot, or will not, afford to pay the necessary expenses of such subdivision;  We therefore must be content to measure some of the boundaries and make our subdivisions approximately correct."

The next comment is found in the old Sainte Genevieve County Survey Record Book at page 116 (MoDNR microfiche location: 186/0131A02) and is dated April 22, 1892:

"Unfortunately the notes taken at the time have been misplaced, but I have a very good recollection of about all important facts except distances."

The last comment is found in the old Sainte Genevieve County Survey Record Book at page 124 (MoDNR microfiche location: 186/0132B01) and appears to be Mr. Nations' farewell and closing comments at the end of his term in 1892:

"Several other comparatively unimportant surveys were made which are not herein recorded.

It often happens that parties have surveying done, not to establish lines definitely, but rather to know approximately where lines and corners are, as in many cases the lands being surveyed are not valuable and parties think it will cost too much to make careful and reliable surveys, and the surveyor must do the best he can under the circumstances.  But it would be next to useless to record such work, work that the surveyor himself knows to be anything but perfection.  I have done considerable of this kind of work.  Some I have recorded and some I have not.

Another thing:  The office while I have been the incumbent, has not been furnished with the necessary, and almost indespensable, plats and field notes, and as I could find time to copy hurriedly, and then when it comes to recording I have often been at a loss for the lack of information that a glance at the official plat would make clear.

In conclusion I would say, I have tried to do my duty as an officer.  I have doubtless made mistakes, as others do; I have made many acquaintances and I trust many friends; I have been treated courteously by all and now as my term of office expires I take my leave and bid all a hearty farewell."

Thanks, J. W., for leaving some interesting comments, allowing us some insight into how things were done, so that we may make informed judgments in the work that we do today.  Perhaps you (the reader) would consider leaving some comments in your field notes that could provide a smile, a chuckle or particular insight for those that follow in your footsteps.

Resolutions for 2012

I've never been one for new year resolutions, but there are a few bible verses that are particularly meaningful to me that I'd like to offer as resolutions for 2012.

The first is found in Micah 6:6-8 (NIV):

With what shall I come before the LORD

 and bow down before the exalted God?

Shall I come before him with burnt offerings,

with calves a year old?

Will the LORD be pleased with thousands of rams,

with ten thousand rivers of oil?

Shall I offer my firstborn for my transgression,

the fruit of my body for the sin of my soul?

He has showed you, O man, what is good.

And what does the LORD require of you?

To act justly and to love mercy

and to walk humbly with your God.

For 2012, I resolve to acty justly, to love mercy and to walk humbly with my God.

The next passage is found in 1 John 2:15-17 (NIV):

Do not love the world or anything in the world.  If anyone loves the world, the love of the Father is not in him.  For everything in the world -- the cravings of sinful man, the lust of his eyes and the boasting of what he has and does -- comes not from the Father but from the world.  The world and its desires pass away, but the man who does the will of God lives forever.

For 2012, I resolve to not love the things of the world, to not boast about what I have and what I've done and I resolve to do the will of God.

The next passage is found in Proverbs 3:5-6 (NIV):

Trust in the LORD with all your heart

and lean not on your own understanding;

in all your ways acknowledge him,

and he will direct your paths.

For 2012, I resolve to not lean on my own understanding, but to trust in the LORD with all my heart and to acknowledge him in all that I do.

The last passage is found in 1 Chronicles 28:9 (NIV):

... acknowledge the God of your father, and serve him with wholehearted devotion and with a willing mind, for the LORD searches every heart and understands every motive behind the thoughts.  If you seek him, he will be found by you; but if you forsake him, he will reject you forever.

For 2012, I resolve to serve God with wholehearted devotion and a willing mind.

These are my resolutions for 2012 and I hope that you will consider adopting these as well.