THE ADJUSTMENT OF TRAVERSE NETS

Abstract

The weakest point in a straight traverse between two fixed points is well known to be in the middle. The uncertainty or p.e. perpendicular to the general direction of the traverse can be shown to be a maximum at the midpoint. Yet subsidiary traverses are usually tied in at or near this point, and consequently may show closing errors which are well in excess of what may be expected. A rigorous least squares solution would overcome this difficulty but only at the cost of a very laborious computation if the network is at all extensive. A compromise between rigour and labour can be achieved, however, which retains the major advantage of a fully rigorous solution, namely that the subsidiary traverses are not tied in at the weakest points of the main traverse system.     

CHECKING TRAVERSE COMPUTATIONS

Abstract

Traverse Computations must be Checked.—A traverse is a chain of points connected by angular and linear measurements. The check on observations is provided by the agreement, obtained in computations, between the terminals of the traverse (terminal bearings and terminal co-ordinates) taken as fixed. This check is not sufficient, however, to serve as a check on the computations. As a matter of principle, computations should be free of errors; there are no limits of tolerance in computational work except for discrepancies arising from inaccuracy of last figures. Secondly, errors in computation may occur that are not revealed by the traverse misclosures, not to speak of compensational errors, the field for which is very favourable in traverse work.     

TWO SIMPLIFIED CHECKS

Abstract

The usual method employed is to plot or to compute the traverse from each end; the poin t having the same coordinates in each route is the station where the gross angular error occurred. There is, however, a method of finding the error by plotting the traverse one way only. Let us consider the traverse having the known terminals A B (see Fig.). Suppose that the error occurred at the point P and that the final point obtained (plotting the traverse from A) was B′ in place of the correct point B. We can easily see that the triangle PBB′is isosceles, and that therefore a straight line bisecting BB′at right angles will meet the traverse in the required point P.     

中山站至A冰穹考察及沿线GPS复测结果分析

南极中山站至A冰穹（Dome-A)考察沿线布设有GPS等精度定位点，通过用高精GPS静态定位处理软件GAMIT／GLOBK对三期观测数据的处理可知，考察沿线的GPS点以8－25m/a的速度向西北方向（冰盖边缘方向）流动，越接近冰盖边缘，运动速度赵快，最快达到100m/a；而且冰川整体上以1－5m/^2的加速度流动。同时，由冰盖的流动，引起了垂直方向0－2－1m/a的沉降速度。     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

A MODIFICATION OF BOWDITCH'S RULE,TO PRESERVE THE BEARING OF THE DATUM LINE IN A CLOSED TRAVERSE

Abstract

The article derives formulae for adjusting the lengths and bearings of a traverse so as to obtain an exact closure, whilst obeying the Least Squares condition and an added condition that the original bearing of one of the traverse lines is to remain unaltered.     

TRAVERSE ADJUSTMENT: WHY NOT “LEAST SQUARES”?

Abstract

I. Introduction.—The literature of least squares is extensive and much of it is theoretical and prosy. I propose, therefore, in the present paper to scrape the jam off the bread, so to speak, and present the pabulum to the reader first; in other words, to give first the solution in as simple and neat a form as possible, then the proof, and finally an example and some notes. The problem is that of adjusting in plane coordinates a traverse beginning at a known point and closing on a known point, having also in the general case an angular closure. If, as I believe, the proof does not appear anywhere else in its present form and nowhere in the English language, I am at a loss to know why. It is not enough to say that the traverse is not a precise enough form of survey to warrant a practical application of the method of least squares. Nor does the admitted difficulty of assigning relative probable errors to linear and angular measurements, coupled with a tendency for the linear errors to be systematic, quite account for it. One has only to read what little there is on the subject of simple traverse adjustment in the English language to detect diversity, vagueness, and sometimes even uneasiness in the statements on it.     

ON THE ELIMINATION OF THE ERRORS OF PAIRING AZIMUTH OBSERVATIONS

Abstract

The perfect pairing of east and west observations for azimuth, put briefly, should consist of combinations of simultaneous observations of stars of the same altitude and of the same declination. Needless to say, this is a counsel of perfection, and in practice the surveyor has usually to rely on some sort of an approximation to this ideal. It is only on very rare occasions that the necessary time is available and the atmospheric conditions favourable enough to obtain this perfect harmony of observations. Assuming that the latitude of the azimuth station and the atmospheric refraction are accurately known, the necessity of pairing would not arise, and the grouping of the observations into two sets of east and west stars with a varying discrepancy between the members of the individual pairs would be quite unnecessary. In general one might say, when an azimuth observation is taken, neither the latitude nor the atmospheric refraction is known accurately, and the question arises as to whether there is any simple method of eliminating or reducing these two causes of error.     

FIRST-ORDER TRAVERSES IN CEYLON

Abstract

In the last three years about 250 miles of “precise” traverse have been surveyed in this country to provide control for detail surveys. A brief account of the results may be of general interest. The traverses are situated where trig. points are far apart, and the cost of subsidiary triangulation would have been excessive on account of the flat nature of the country.     

COMPENSATION AS A CONSEQUENCE OF TWO KINDS OF ROCK STRUCTURE

Abstract

The following points occurred to me when reading the interesting paper on crustal equilibrium in E.S.R. No. 23. The principle of compensation or isostasy necessarily involves the idea of two different kinds of rock structure—one strong, the other weak or in extreme cases fluid; for example, there is the familiar case of the strong iceberg resisting change of shape in the liquid sea. In dealing with crustal problems of the earth then, we should make up our minds which part is to be considered as strong, e.g. the granite crust, and which part as weak or fluid, e.g. material at a depth x km. (say roo km.); by weak or fluid I mean that a possibility exists of horizontal movement.     

THE TRANSVERSE MERCATOR PROJECTION AND ITS APPLICATION TO TANGANYIKA TERRITORY

Abstract

The Transverse Mercator Projection is also called the Conformal of Gauss since it was devised by him in the early part of the nineteenth century in connexion with the Triangulation of Hanover. It belongs to the class of cylindrical orthomorphic projections. That is to say, the Earth's surface, or part thereof, is developed on the surface of a cylinder, and there is practically no angular distortion, an angle on the surface of the Earth being represented on the map by almost precisely the same angle. The representation of meridians and parallels, for instance, shows them intersecting at right angles as they actually do on the Earth's surface; but this orthotomic condition, though essential, is not in itself sufficient for orthomorphism.     

ERRORS IN RESECTION

Abstract

I. Although surveying is generally conducted on the principle that there should be more observations than are mathematically necessary for the calculation of the required results, the determination of the position of a point by resection from three fixed points is an exception to the principle. In observing a round of angles at a point, one of them can be inferred, but it is always observed in order to obtain a check by closing the round; a point fixed by intersections is generally observed from four or five surrounding points, although only two shots are strictly necessary. But the problem of resection from three points is a “minimum-of-data” problem, that is, the observations are only just sufficient to fix the point, and there is nothing extra to give a check on the result.     

THE PROJECTIVE TRANSFORMATION IN AERIAL SURVEYING

Abstract

The paper describes an algebraic method of forming linear equations, giving the coordinates of points in space in terms of the coordinates of their images on the photographic plates. The coefficients which enter into these linear equations form a matrix of the third order. When stereoscopic or similar methods are used for plotting detail, the elements of this matrix give in a convenient form and with the utmost obtainable accuracy the quantities required for setting the photographs in their correct relation to the map and to one another.

An easy and rapid graphical method of obtaining good approximations to all the solutions of the problem of resection in space is described. A method of refining the solutions is given. When the coordinates of the air station are known with fair accuracy an alternative procedure is described. In the absence of ground control suitable for finding the air station by resection a method of eliminating most of the uncertain quantities is obtained. The indeterminate quantities relate to strip photographs as a whole and not to individual photographs. A method of dealing with the coefficients for the complete strip is described.

In finding air stations by resection, point-coordinates in the photographs must be converted into directional coordinates. In other calculations this transformation is unnecessary.     

SOME SURVEY ODDITIES FROM BRITISH NORTH BORNEO

Abstract

A Survey gang recently built a hardwood beacon on Bukit Toodan, 1,600 feet, overlooking the sleepy hollow of Kota Belud, and an observer on returning to the station a week later found that one of the four legs of the beacon had been torn to shreds by lightning and hurled many feet away, while the concrete slab marking the exact point was discovered to have been shattered to fragments. A week or two later an observer reported the Pulau Gaya hardwood trig. beacon to be lying at an angle from the perpendicular, and on observation with a powerful telescope it was disclosed that the whole beacon was covered with flying foxes roosting upside down, whose talons had in the course of time severed one of the beacon legs–rather a shock to any ordinary observer. But that is the kind of thing that surveyors in the East have to contend with quite frequently.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION

Abstract

Cadastral Traversing.—For cadastral purposes traverses are now being executed with an accuracy wholly unnecessary for even large topographical scales. But since “accuracy” varies from a mile to a micron, according to the viewpoint of the observer, it is advisable to exhibit a cadastral traverse, care being taken that it is not an example of that not very uncommon occurrence in which fortuity apes precIsIon. If the accuracy of the example is somewhat unusual, it can be said with assurance that it is not very unusual.     

FORMULAE FOR THE ADJUSTMENT OF SURVEY ERRORS

Abstract

The formulae given in this paper can be used for a station adjustment at a trigonometric station and also for the adjustment of errors in a level survey. As applied to levelling, the problem consists in finding the most probable values of the reduced levels of a number of points where the observed level differences between the points are not consistent with each other. It can be shown that the required values of the reduced levels are those which reduce the sum of the squares of the residual errors to a minimum, where the residual error is defined as the difference between the calculated and observed levels.     

FIGURES AND FANCIES

Abstract

I may say at once that this article has nothing to do with either the Gaiety chorus or the “Old Firm”: it is merely a statement of what seem to me the fancies in Dr. de Graaff Hunter's paper “Figures of Reference for the Earth”, E.S.R., No. 8,pp. 73–8. Many readers of the Review will share my gratitude to Dr. Hunter for his lucid presentation of the theory underlying the usual geodetic processes. I disagree with only one of his points, and its implications, but unfortunately that point is fundamental.     

A comprehensive framework for exploratory spatial data analysis: Moran location and variance scatterplots

Abstract

A significant Geographic Information Science (GIS) issue is closely related to spatial autocorrelation, a burning question in the phase of information extraction from the statistical analysis of georeferenced data. At present, spatial autocorrelation presents two types of measures: continuous and discrete. Is it possible to use Moran's I and the Moran scatterplot with continuous data? Is it possible to use the same methodology with discrete data? A particular and cumbersome problem is the choice of the spatial-neighborhood matrix (W) for points data. This paper addresses these issues by introducing the concept of covariogram contiguity, where each weight is based on the variogram model for that particular dataset: (1) the variogram, whose range equals the distance with the highest Moran I value, defines the weights for points separated by less than the estimated range and (2) weights equal zero for points widely separated from the variogram range considered. After the W matrix is computed, the Moran location scatterplot is created in an iterative process. In accordance with various lag distances, Moran's I is presented as a good search factor for the optimal neighborhood area. Uncertainty/transition regions are also emphasized. At the same time, a new Exploratory Spatial Data Analysis (ESDA) tool is developed, the Moran variance scatterplot, since the conventional Moran scatterplot is not sensitive to neighbor variance. This computer-mapping framework allows the study of spatial patterns, outliers, changeover areas, and trends in an ESDA process. All these tools were implemented in a free web e-Learning program for quantitative geographers called SAKWeb© (or, in the near future, myGeooffice.org).     

MACHINE METHOD OF INTERSECTION

Abstract

The following method will be found better and quicker than the usual logarithmic process in computing the co-ordinates of intersected points in minor triangulation and traverse work. Let A and B be two stations whose co-ordinates (x ₁ y ₁), (x ₂ y ₂) are known. Let P be an intersected point whose co-ordinates (x, y) we wish to determine. Let α and β be the observed angles at A and B respectively.