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.

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. [ABSTRACT FROM AUTHOR]