GLO Surveying: Fractional Sections and the Relationship of Chains to Acres

A 171Kb PDF of this article as it appeared in the magazine—complete with the maps necessary to understand what the author is discussing—is available by clicking HERE

One of the interesting aspects of the U.S. Public Land Survey System (USPLSS) is the unique relationship between chains and acres. For those who work with the USPLSS, and the records of same, often the Township Plats contain acreage and fractional part distances that are either difficult to read, partially missing or, in some instances, incorrect.

There are three convenient rules available to apply in working with these matters when one understands the unique relationship between chains and acres. Before discussing these rules it might be helpful to review this relationship through deductive definitions, as follows: 
• 1 Chain = 66 feet, by definition 
• 1 Statute Mile = 5,280 feet, by definition 
• 1 Acre = 43,560 square feet, definition
Thus, 5,280/66 = 80, and 80 chains = 1 Statute Mile

One theoretical Section of Land is one mile on a side, or 80 chains, or 5,280 feet
5,280 X 5,280 = 27,878,400/43,560 = 640 acres
Or, 80 Chains X 80 Chains = 6,400/10 = 640 acres
Thus, Area (in acres) = Width (in chains) X Length (in chains)/ 10

For example, in a theoretical Quarter-Quarter Section, being 20 chains by 20 chains, the product is 400. Divided by 10, the result is 40 acres.

Given the above definitions and relationships, and working with lengths of sides in chains, and areas in acres, one can derive the following three rules:
• By multiplying the average width (in chains) of a fractional lot or aliquot part by the average length (in chains), and dividing by 10, one can derive the area in acres.
• The area of an aliquot part (in acres), minus an adjoining side (in chains), will equal the length of the opposite side (in chains).
• The area of a lot (in acres), added to the area (in acres) of an adjoining lot, divided by 4, will equal the distance (in chains) of the common side. This rule does not work, however, when applied to aliquot parts of differing size (e.g., a 40 ac. and an adjoining 80 ac. part), but is valid where convergence of meridians is involved in fractional lots adjoining the west boundary of a township. And, the area in acres of each lot in the west tier is found by adding the lengths in chains of its north and south boundaries, or for the north tier of lots (except Lot 4 of Section 6), by adding the lengths in chains of the west and east boundaries.

It should be noted that minor differences will sometimes occur using these rules. These differences should be averaged to resolve the discrepancies. On can also check the results from these rules by proportioning, for example, the exterior dimension shown on a tier of fractional lots across the Section’s north or west side, to the opposite exterior, using the difference divided by 4, and distributing across to derive the three interior lot dimensions of the tier of four lots. The three rules can also be applied to determine if, and to locate where, an error has occurred on the Township Plat.

Above is a diagram from the Manual of Surveying Instructions 1973, published by the U.S. Department of the Interior, Bureau of Land Management, so the reader can test the above rules. The diagram on the left shows a Section 6 breakdown into aliquot part and fractional lots along the north and west side of the township, indicating the areas in acres only. The diagram on the right shows the same Section 6 with corresponding dimensions in chains. By superimposing data from the two diagrams, one can run through the rules to see how they work.

Licensed surveyor Terry McHenry, the editor of the Nevada Traverse (the newsletter of the Nevada Association of Land Surveyors), has been writing a series in the newsletter titled "Key Practice Pointers". Our thanks to Terry for allowing us to reprint his interesting explanation.

A 171Kb PDF of this article as it appeared in the magazine—complete with the maps necessary to understand what the author is discussing—is available by clicking HERE