Consequences of Ignoring the Curvature of the Earth in Nineteenth-Century Large Surveys: A Case Study of Geometrical Geodesy and the Survey of the Texas and Pacific Railway Company Eighty-Mile Reserve
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VIEW CORRECTIONPublication: Journal of Surveying Engineering
Volume 150, Issue 4
Abstract
This paper is a case study and historical account of nineteenth-century surveying of the Texas and Pacific Railway Eighty-Mile Reserve, and the consequences from ignoring curvature of the earth allowances in large surveys extending beyond the horizon. The methods used in the survey of the Eighty-Mile Reserve in Texas are compared to the way surveyors of the Public Lands of the United States carried out their work by making allowances for the curvature of the earth. When Texas became a republic in 1836, it was rich in land extending as far north as present-day Wyoming and Colorado, but financially broke. The first governmental agency in the Republic of Texas was the General Land Office and its instructions in the survey of the Texas public domain required boundary corners to be square, when practicable. The first land grants in Texas were very large, with no formal system of surveying to make allowances for the curvature of the earth. Consequently in later years, large errors were found, creating boundary misclosures, overlaps, gaps, and huge excesses in acreage over what was patented; and vacancies of unsurveyed, unsold land were not listed in the General Land Office as permanent school fund lands. When Texas was annexed by the United States in 1845, it still had enormous outstanding debts. By 1850, the State of Texas sold 67-million-acres (37,113,938 ha) of its public domain to the United States in order to clear its public debts. Ignoring curvature of the earth corrections in surveys continued until around 1930 when prominent surveyors, geodesists, and engineers convinced the Texas General Land Office to embrace a Texas coordinate system that would project a survey onto a flat map and accurately represent the surface of the earth in the least distorted way by creating the state plane coordinate system of Texas.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request including data performed in Trimble Business Center software under file name “Texas-NewMexico Boundary Line.vce.”
Acknowledgments
The author wishes to thank Carr B. (Ben) Thomson, R.P.L.S., L.S.L.S., P.E., M. ASCE for his review of the draft manuscript and his comments and suggestions. Ben is my friend and mentor, and undoubtedly the most knowledgeable and respected land surveyor in Texas.
References
Alder, K. 2002. The measure of all things: The seven-year odyssey and hidden error that transformed the world. New York: Free Press.
Bessel, F. W. 1825. The calculation of longitude and latitude from geodesic measurements. Kaliningrad, Russia: Konigsberg Observatory.
BLM (United States Department of the Interior Bureau of Land Management). 1947. Manual of instructions for the survey of the public lands of the United States 1947. Washington, DC: Government Printing Office.
BLM (United States Department of the Interior Bureau of Land Management). 1956. Standard field tables and trigonometric formulas. Washington, DC: Government Printing Office.
Bowden, J. J. 1962. “The Texas and Pacific Railway Company reservation land grant.” In Report of the Eleventh Annual Texas Surveyor’s Association Short Course. October 8, 9, 10, 1962. Texas General Land Office Document No. 62213. https://historictexasmaps.com/collection/search-results/search/identifier:62213.
Bowditch, N. 1802. American practical navigator—An epitome of navigation and nautical astronomy. Springfield, VA: National Geospatial Intelligence Agency.
Bowie, W., and O. S. Adams. 1919. Grid system for progressive maps in the United States special publication no. 59. Revised ed. Washington, DC: Dept. of Commerce, US Coast and Geodetic Survey.
Burkholder, E. F. 2001. “Geometrical geodesy.” Chap. 13–5 in The surveying handbook, 2nd ed., edited by R. C. Brinker and R. Minnick. Boston: Klewer Academic.
CG & S (Department of Commerce and Labor, Coast and Geodetic Survey). 1911. Formulæ and tables for the computation of geodetic positions. Special Publication No. 8. 5th ed. Washington, DC: Government Printing Office.
Cowan, T. 2015. “History of the Texas public domain.” In Texas society of professional surveyors annual convention & technology exposition. Austin, TX: Texas Society of Professional Surveyors.
Davis, R. E., F. S. Foote, and J. W. Kelly. 1966. Surveying: Theory and practice. 5th ed. New York: McGraw-Hill.
Deakin, R. E. 2009a. “The curve of alignment on an ellipsoid.” In Lecture notes, school of mathematical & geospatial science. Melbourne, VIC, Australia: RMIT Univ.
Deakin, R. E. 2009b. “The normal section curve on an ellipsoid.” In Lecture notes, school of mathematical & geospatial science. Melbourne, VIC, Australia: RMIT Univ.
Deakin, R. E., and M. N. Hunter. 2009. “Geodesics on an ellipsoid–Bessel’s method.” In School of mathematical & geospatial science. 1st ed., 1–66. Melbourne, VIC, Australia: RMIT Univ.
Featherstone, W. E. 1999. “The use and abuse of vertical deflections.” In Sixth Southeast Asian surveyor’s congress. Freemantle, Australia.
Halsted, G. B. 1913. “French geodesy.” A translation of an essay by Henri Poincare (1854–1912). In The popular science monthly, February 1, 1913.
Hirt, C., and B. Bürki. 2006. “Status of geodetic astronomy at the beginning of the 21st century.” In Univ.-Prof. Dr.-Ing. Prof. H.C. Günter Seeber on the occasion of his 65th birthday and the farewell to retirement. Scientific work in the Department Geodesy and Geoinformatics at the University of Hanover, 81–99. Bentley, WA, Australia: Curtin Univ.
Kuechler, J. 1879. “Jacob Kuechler’s field notes (field book), Texas & Pacific Ry. Co. 80 Mile Reserve, 1879.” Texas General Land Office Map Collection Document No. 3050. Accessed February 2, 2023. https://historictexasmaps.com/collection/search-results/3050-jacob-kuechlers-field-notes-field-book-texas-pacific-ry-co-Eighty-Mile-reserve-general-map-collection.
Lee, T. J. 1873. A collection of tables and formulae useful in surveying, geodesy, and practical astronomy, including elements for the projection of maps, and instructions for field magnetic observations. 3rd ed. Washington, DC: Government Printing Office.
McCombs, P. 1883. “Paul McCombs field book on 80 mile reservation west of the Pecos.” Texas General Land Office Map Collection Document No. 2238. Accessed February 2, 2023. https://historictexasmaps.com/collection/search-results/2238-paul-mccombs-field-book-on-Eighty-Mile-reservation-west-of-the-pecos-general-map-collection.
McCombs, P. 1905. “Report from Paul McCombs to W. H. Abrams on his retracement of Jacob Kuechler’s survey of the T.&P. Ry. Co. Eighty-Mile Reserve.” El Paso County Sketch File 19. Texas General Land Office Map Collection Document No. 22009. Accessed February 2, 2023. https://historictexasmaps.com/collection/search-results/22009-el-paso-county-sketch-file-19-general-map-collection.
McCombs, P. 1916. “Map Blocks 81 and 82, township 1 T.&P. Ry. Co. surveys El Paso Co. Tex.” El Paso County Surveying Sketch Files. Texas General Land Office File No. 29346. Accessed February 2, 2023. https://s3.glo.texas.gov/ncu/SCANDOCS/archives_webfiles/arcmaps/webfiles/landgrants/PDFs/8/2/4/824586.pdf.
Moritz, H. 2000. “Geodetic reference system 1980” J. Geod. 74 (Mar): 128–133. https://doi.org/10.1007/s001900050278.
NBS (National Bureau of Standards). 1963. “Weights and standards of the United States—A brief history.” In US department of commerce national bureau of standards nbs special publication 447, 28. Washington, DC: US Government Printing Office.
NOAA (National Oceanic and Atmospheric Administration). 2023a. “National oceanic and atmospheric administration, national geodetic survey.” Computation of DEFLEC 18 deflection of the vertical. Accessed April 23, 2023. https://geodesy.noaa.gov/GEOID/DEFLEC18/computation.html.
NOAA (National Oceanic and Atmospheric Administration). 2023b. “National oceanic and atmospheric administration, national geodetic survey.” INVERSE/FORWARD/INVERS3D/FORWRD3D. Computation Utilities. Accessed April 23, 2023. https://geodesy.noaa.gov/TOOLS/Inv_Fwd/Inv_Fwd.html.
NOAA (National Oceanic and Atmospheric Administration). 2023c. “Survey mark datasheets.” Accessed April 23, 2023. https://www.ngs.noaa.gov/datasheets/.
Office of Chief of Engineers. 1879. Annual report of the chief of engineers to the secretary of war for the year 1879. Part III. Washington, DC: US Government Printing Office.
Piper, J. S., and J. W. Leamons. 2021. “Texas & pacific railway: Surveying the land certificates.” In Texas society of professional surveyors chapter 18–West central Texas seminar, 1–26. Austin, TX: Texas Society of Professional Surveyors.
Powell, W. J. 1931. “Report of a resurvey of texas and pacific railway lands in the Eighty-Mile reservation made in 1930–31 for Kloh, Rumsey & Abrams.” Texas General Land Office Current Document No. 2247. Accessed August 10, 2023. https://historictexasmaps.com/collection/search-results/search/identifier:2247.
Powell, W. J. 1934. “Letters to and from Maj. W. J. Powell regarding surveys of Texas and Pacific Ry. Lands west of the Pecos. Blks 53–55, Township 1 & 2 map within.” Texas General Land Office Document No. 2249. Accessed February 2, 2023. https://historictexasmaps.com/collection/search-results/search/identifier:2249.
Rapp, R. H. 1991. Geometrical geodesy part I. Columbus, OH: Ohio State Univ.
Rapp, R. H. 1993. Geometrical geodesy part II. Columbus, OH: Ohio State Univ.
Rashid, M. 1996. “The plan is the program: Thomas Jefferson’s plan for the rectilinear survey of 1784.” In Proc., Association of Collegiate Schools of Architecture 84th Annual Meeting-Regional Papers, edited by J. Kinnard and K. Schwartz, 615–619. Washington, DC: Association of Collegiate Schools of Architecture.
Rebert, P. 2001. La Gran Linea–Mapping the United States-Mexico boundary, 1847–1857. Austin, TX: University of Texas Press.
Rolbiecki, D. A., and S. D. Lyle. 2008. “Hybrid state plane coordinate system for transforming a citywide survey control network to surface values: Case study for Frisco, Texas.” J. Surv. Eng. 134 (4): 105–114. https://doi.org/10.1061/(ASCE)0733-9453(2008)134:4(105).
Schwarz, C. R. 1989. “North American Datum of 1983.” In National oceanic and atmospheric administration professional paper NOS 2, 249–250. Rockville, MD: US National Geodetic Survey.
Senate Bill 73. 1919. “Act creating qualified licensed state land surveyors to survey land in which the state or the permanent school fund has an interest or perform other original surveys for the purpose of filing field notes in the general land office.” In Proc., 36th Texas Legislature, 2nd Called Session. Houston: Texas Society of Professional Surveyors.
Shine, D. 2008. “Darrell D. Shine’s guide to [mostly] Texas surveying.” In Surveyors short course, 79–80. Houston: Texas Society of Professional Surveyors.
Sjöberg, L. E. 2012. “Solutions to the direct and inverse navigation problems on the great ellipse.” J. Geodetic Sci. 2 (3): 200–205. https://doi.org/10.2478/v10156-011-0040-9.
Smith, D. A. 2011. “True zero.” Point Beginning Mag. 37 (3): 20–25.
Soler, T., A. E. Carlson, and A. G. Evans. 1989. “Determination of vertical deflections using the global positioning system and geodetic leveling.” Geophys. Res. Lett. 16 (7): 695–698. https://doi.org/10.1029/GL016i007p00695.
Soler, T., and L. D. Hothem. 1988. “Coordinate systems used in geodesy: Basic definitions and concepts.” J. Surv. Eng. 114 (2): 84–97. https://doi.org/10.1061/(ASCE)0733-9453(1988)114:2(84).
Standefer v. Vaughan, et al. 1920. 219 S.W. 484 (Tex. Civ. App. 1920)), Decided Mar 3, 1920. Amarillo, TX: Court of Civil Appeals of Texas.
Truett, F. M. 1982. “Texas was his land—Willis day Twichell pioneer.” In Surveyor. 1st ed. Austin, TX: Eakin Press.
TSA (Texas Surveyors Association). 1950. One league to each wind—Accounts of early surveying in Texas. Austin, TX: TSA.
TXGLO (Texas General Land Office). 2023a. “Texas General Land Office Bexar scrip file number 27167, Culberson County, Texas.” Accessed September 20, 2022. https://s3.glo.texas.gov/ncu/SCANDOCS/archives_webfiles/arcmaps/webfiles/landgrants/PDFs/8/5/2/852670.pdf.
TXGLO (Texas General Land Office). 2023b. “Survey report and plat in Culberson county sketch file 35.” Accessed September 20, 2022. https://historictexasmaps.com/collection/search-results/20295-culberson-county-sketch-file-35-general-map-collection.
USGS. 1916. “Geographic tables and formulas.” In Bulletin 650. 4th ed. Washington, DC: US Government Printing Office.
Vincenty, T. 1975. “Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations.” In Survey review XXII, 176. Tolworth, Surrey: Directorate of Overseas Surveys of the Ministry of Overseas Development.
Walsh, W. C. 1884. “Letters to and from W. J. Powell (Major) Re Surveys of Texas and Pacific Ry. Lands West of the Pecos Blks 53-55 township 1 & 2 map within.” Texas General Land Office Current Miscellaneous File 11. Accessed August 10, 2023. https://historictexasmaps.com/collection/search-results/2249-letters-to-and-from-maj-w-j-powell-regarding-surveys-of-texas-and-pacific-ry-lands-west-of-the-pecos-blks-53-55-township-1-2-map-within-general-map-collection.
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Journal of Surveying Engineering
Volume 150 • Issue 4 • November 2024
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© 2024 American Society of Civil Engineers.
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Received: Oct 30, 2023
Accepted: Mar 1, 2024
Published online: Jun 21, 2024
Published in print: Nov 1, 2024
Discussion open until: Nov 21, 2024
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