Parenthetical Distances

Parenthetical distances on the plat are implied measurements and are considered to indicate points on a surveyed line which are not monumented. Since they are on the plat and indicate a portion of a surveyed line or of a protracted line from which area can be returned, they are considered as part of the record and must be used to protect the bona fide rights of the patentees.

Where parenthetical distances are used for the calculation of areas, they are also used to protect such area by means of proportionate measurements to the indicated (calculated or implied) points which were not previously monumented.

The parenthetical distances, which are not actually shown on the plat but can be computed from the areas, are equally as important as those which are shown on the plat. The distances were originally calculated and used to compute the areas; therefore, when the areas are given, the implied parenthetical distances based on those areas can be recalculated.

Example: When it is necessary to subdivide section 7 and monument the center-west one sixteenth section corner, the implied parenthetical distance between lots 2 and 3 can be recomputed based on the areas. The distance can be used with the method of proportionate measurement along the E-W centerline to protect individual rights represented by the area on the original plat.

The implied parenthetical distance upon which the areas in lots 2 and 3 were based is 21.30 chains.

If the west one-half mile of the E-W centerline in a subdivision of section survey is found to be 41.70 chains, the proportioned distances based upon the implied parenthetical distance to the center-west onesixteenth
section comer would be:

• 21.506 chains from the 1/4 section corner of sections 7 and 12.
• 20.194 chains from the center 1/4 section corner.
• Total 41.70 chains

Where the entire north boundary of a section abutting the north boundary of the township is shown as parenthetical distances on the plat, it implies that no 1/4 section corner for the section represented was set on that line.

It was the practice on older surveys not to set the quarter-section corners between closing section corners along the north boundary of the township. In such cases the one-sixteenth and the quarter section corners will be established by the method of proportionate measurement based upon the parenthetical distances; PROVIDED, that the areas of the lots confirm the parenthetical distances.

When the parenthetical distances on the original plat are confirmed by the area, the resurvey indicates the distances which would be the result of a retracement of 81.40 chains for the north boundary of section six. The retracement distance is proportioned based on the parenthetical distances.

Example: The ties, which are confirmed by the field notes from the closing section corners to the standard corners indicate an arithmetic error in the length of the north boundary of section 6 as shown on the plat. The parenthetical distances shown are based on the error.

A retracement between the closing section corners on the north boundary of section 6 returns a distance of 69.80 chains.

Problem: What distances should the resurvey return for the north boundary of lots 1 through 4 in section 6?

Solution: In order to “protect the plat”, distances westward along the north boundary are computed from the areas of the lots as (20) (20) (20) (17.00), and are used to proportion the retracement length which yields the distances shown on the resurvey.

Occasionally the true line distance on the plat is in error. It may reflect the random distance rather than the reduction of the random and failing distances to the actual true line distance. In such cases, the parenthetical distances, and therefore the areas, are erroneously based upon the random distance instead of the actual true line distance.

Example: Field notes 
Run west on a random line between sections 7 and 18.
40.00 set temp 1/4 cor.
81.00 intersect twp.
line 3.50 chains south of section corner common to sections 7. 12. 13. and 18.
Thence S. 87° 32′ E on the true line between sections 7 and 18.
41.00 set 1/4 corner.
8 1.00 sec. cor. 7, 8, 17 and 18.
The true line distance obtained from the random distance and falling should be 81.08 chains. The true line distance in the notes and on the plat are in error. The parenthetical distances and the areas are in
error also.
In order to “protect the plat”, the distances (20) (20) (20) (21.00) which were used to compute the areas are used to restore (proportion) the intermediate sixteenth and quarter section corners.

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