(this information taken from:) Manual of Instructions for the Survey of the Public Lands of the United States; 1973 Prepared by the Bureau of Land Management, Technical Bulletin 6;  pub. U.S. Dept of Interior

pp. 59 - 60 CHAPTER III The System of Rectangular Surveys 3-1.The extension of the rectangular system of public land surveys over the public domain in the United States has been in progress since 1785. Although few of~ the original surveys now being made cover extensive areas, all facets of the rectangular system occasionally come into use. For this reason, and to make clear the procedures which have been followed in surveying public lands, a complete discussion of the system is included in this manual. It will be seen that the underlying principle is to provide a simple and certain form of land identification and legal description of the public lands.  GENERAL SCHEME 3-2. The law provides that (1) the public lands of the United States shall be divided by lines intersecting true north and south lines at right angles so as to form townships six miles square; (2) the townships shall be marked with progressive numbers from the beginning; (3) the townships shall be subdivided into 36 sections, each one mile square and containing 640 acres as nearly as may be; and (4) the sections shall be numbered, respectively, beginning with the number 1 in the northeast section, and proceeding west and east alternately through the township with progressive numbers to and including 36 (R.S. 2395; 43 U.S.C. 751). 3-3. In accordance with the foregoing legal requirements, the public lands are surveyed under the method called the system of rectangular surveys, which embraces the following procedure: (1) The establishment of independent initial points, each to serve as an origin for surveys to be extended in separated localities. (2) The survey of principal meridians and base lines, originating at the initial points. (3) The establishment of guide meridians initiated at base lines, and of standard parallels initiated at principal meridians, at intervals short enough to maintain a workable adherence to the legal definition of the primary unit, the township six miles square. (4) The survey of township exteriors within the framework so established. Townships are numbered to the north or south commencing with number 1 at the base line, and with range numbers to the east or west beginning with number 1 at the principal meridian. (5) The subdivision of the townships into 36 sections by running parallel lines through the township from south to north and from east to west at distances of one mile. The sections are numbered commencing with number 1 in the northeast section of the township, proceeding thence west to section 6, thence south to section 7, thence east to section 12, and so on, alternately, to number 36 in the southeast section. 3-4. By law, (1) the corners marked in public land surveys shall be established as the proper corners of sections, or of the subdivisions of the sections, which they were intended to designate, and (2) the boundary lines actually run and marked shall be and remain the proper boundary lines of the sections or subdivisions for which they were intended, and the lengths of these lines as returned shall be held as the true length thereof (R.S. 2396; 43 U.S.C. 752). The original corners must stand as the true corners they were intended to represent, even though not exactly where professional care might have placed them in the first instance. Missing corners must be reestablished in the identical positions they originally occupied. When the positions cannot be determined by existing monuments or other verifying evidence, resort must be had to the field notes of the original survey. The law provides that the lengths of the lines, as returned in the field notes, shall be held as the true lengths, and the distances between identified corner positions given in the field notes constitute proper data from which to determine the position of a lost corner; hence the rule that lost corners are restored at distances proportionate to the original measurements between identified positions. (chapter V, Restoration of Lost Corners.) 3-5. In the sections that follow, the first explanations are with respect to ideal procedure in the rectangular plan. The plan must be modified in various ways in order to begin new work where the initial and closing lines already established by prior survey do not qualify under the current specifications for rectangularity and closure but cannot now be changed because of the passing of titles based on them. The purpose is to avoid the incorporation of the discrepancies of the older lines in the running of new original surveys.

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