Journal of Surveying Engineering

Federal land surveys were mandated by Indian treaties, executive orders, and acts of Congress to expedite the allotment of Indian reservations. Congressional funding for these surveys seldom equaled the costs of the task. Various federal agencies were responsible for establishing allotment boundaries. The three‐mile method was the technique developed to subdivide a section, with monuments established at equidistant points on a line instead of at intersections with perpendicular lines, as public‐land surveys require. This reduced survey mileage and costs. Also, Indian allotment corners were set by the federal surveyor, rather than protracting the section subdivision on the plat and leaving monumentation to private surveyors hired by the land claimant. Only on exterior section boundaries are the allotment corners in the same position as their counterpart aliquot‐part corners. Problems arise when modern resurveys ignore, or do not discover, existing three‐mile method surveys, and sections are resubdivided by aliquot‐part public land methods. The result is mislocated boundaries, which may place allotment land and resources outside the erroneous resurvey lines.

It is often desirable, especially in deformation surveys, to use a free net adjustment where minimal control is used. An alternative view of free net analysis is provided using the squared error loss criterion and compared to the conventional methodology of deleting appropriate columns of the design matrix when implementing minimal constraints. Both methods are shown to be special cases of a generalized free net adjustment.

This paper analyzes the structural features of pipeline signs through the application of graph theory. The term pipeline is being used to describe a large number of linear objects encountered in survey field‐work. The paper illustrates establishing and automatically defining a pipeline graph from its complete graph. The purpose is to demonstrate the insertion of object signs in large‐scale maps according to the principles of surveying. It deals with processing of field data collected on several linear objects during ground surveys. At the same time, the paper establishes a mathematical model for automatic configuration and a calculation program, which increases the efficiency of the coding work in the field. Thus, it improves the capability and application of computer‐assisted mapping for the ground survey method.

The current methods of estimating the excavation volume for a rectangular pit use excavation depth measurements at lattice points of a grid formed by marking off each of the x‐ and y‐axes in intervals of equal length. The excavation volume is estimated by using the trapezoidal rule or Simpson's 1/3 and 3/8 formulas along with these depth measurements to estimate the double integral of the excavation depth function. In this paper we first derive a generalized Simpson (GS) 3/8 formula to estimate the integral of a function over an interval partitioned into three possibly unequal intervals. We assume the function is approximately a cubic with known ordinates at the four points that partition the interval. We then assume that the excavation depth measurements of the rectangular pit are taken as the lattice points of a grid in which the axes are partitioned into intervals of unequal length and use the GS 3/8 formula with the known GS 1/3 formula to derive the excavation volume estimate. A numerical example is included.

The existing methods of land subdivision have been based on trialand‐error procedures and normally involve intermediate computations of geometric and trigonometric elements. This paper presents a method, which is in the form of general formulas that can be applied to any land shape, that provides the subdivision results directly. The method is based on the Cartesian coordinates of the land boundary. The subdivision satisfies a specified area and another requirement of the subdividing line. Three such requirements are considered: one boundary point of the subdividing line is fixed, its orientation is fixed, or the line must pass through an interior point. For some special cases, the method involves the rotation of the Cartesian axes before the formulas are applied. A computer program employing the presented method is included.

Modern geodetic space techniques, such as Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging, (SLR), and Global Positioning Systems (GPS), can accurately determine the seven parameters of similarity transformations between different terrestrial (i.e., earth-centered and earth-fixed) frames. For the benefit of the surveying engineers utilizing portable satellite receivers (e.g., Doppler, GPS), this article compiles (adopting conventional notations) recently estimated values of the shifts, rotations, and scale relating the most frequently used (e.g., WGS-72, WGS-84) reference frames. The sign of these parameters are consistant with the standard matrix form of the similarity transformation equation, which for completeness is also included in the appendix. This should be kept in mind when they are compared to other tabulated values recently published in the geodetic literature.

This paper presents a free tension concept for taping of horizontal or sloping distances. When free tension is used during taping, no corrections would be required to the measured or layed out distance. Free tension formulas are developed for cases in which the tape is supported at two ends only and fully supported.