Thursday, February 23, 2012

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.
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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.



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Original composition by Steven E. Weible