TRAVERSING IN ANTHILL COUNTRY

Abstract

It is laid down in the Survey Rules of Northern Rhodesia that all areas to be alienated under freehold title or long lease must be surveyed by triangulation and that traverse methods must not be employed without the permission of the Commissioner for Surveys. This of course is all very well under normal text-book conditions, but there comes a time when triangulation is neither safe nor economical. Such conditions prevail in the Copperbelt districts of N. Rhodesia, where the bush is thick, the terrain more or less flat and the haze usually considerable. To make things a little more difficult the countryside is littered with anthills, both small and large; some as much as 30 feet high and 100 feet in circumference at the base. Traversing under these conditions can be very interesting and at times definitely backbreaking.     

LEAST-SQUARE SOLUTIONS WITH WEIGHTS

Abstract

The modern abridged method of solution as applied to observation equations was given in an earlier number of this Review. The present article, applying the same abridged method to the solution of conditioned equations, shows how the weights of any functions of the adjusted values can be obtained as well as the corrections themselves. The case where the weights of adjusted functions are most frequently required in practice is that of a triangulation base extension figure. It is well known that the error generated in reaching the first side of the main triangulation proper from the measured base may be considerably greater than thereafter when sides are long and grazing shots rare. For this reason it is good practice to compute rigorously the probable error of the first main side from the base. It is usually found that the p.e. of the base itself is only a small fraction of the total. If the total p.e. of this first main side is too large, it may then be considered whether the extension figure should not be either completely reobserved or even redesigned to give a better result. Even if the observations themselves are all considered to be of equal weight (as is common practice nowadays with good instruments and good methods of observing), the weights of the adjusted functions will still differ from the mean, depending on the condition equations set up by the extension figure adopted.     

LOCAL ATTRACTIONS AND THEIR INFLUENCE ON THE DETERMINATION OF HEIGHTS ABOVE MEAN SEA LEVEL

Abstract

The Mythical Spheroid.—The preceding article dealt with the fact that the spheroid of reference is a myth and that, even if it were not, we could not get hold of it at any given place. In order to apply corrections to observed quantities or, more generally, to operate upon them mathematically, we must make some assumption such as that of the spheroidal level surface. Probably a lot of harm has been done by attaching the notion of too concrete a thing to the spheroid. Disputes and misconceptions have arisen. People talk of“putting the spheroid down at a point” and imagine that the obedient thing is still at their feet when they get to another point, perhaps distant, in their system of triangulation or what not. Actually the spheroid may be disobedient not only as regards the direction of the vertical but also because it is above their heads or below their feet. What happens is that at each point afresh the computer treats the observations as if they were made there on the surface of a spheroid. In the same way, but travelling still farther along the road of hypothesis, he may treat observations for astronomical positions as if the compensation for visible elevations were uniformly distributed as a deficiency of density down to a depth of 122·2 kilometres. That was the depth which happened to give the smallest sum of squares of residuals in a certain restricted area, but nobody imagines that it corresponds with a physical reality, especially the ·2! It was a convenient mathematical instrument which, once the theory was to be given a trial, had to be fashioned out of some assumption or another. All this has little to do with geodetic levelling but is meant to try to banish the spheroid out of the reader's mind or at least to the back of his mind. In what follows we shall be compelled to make a certain amount of use of the family of spheroids but always with the above strictures in view.     

TWO NOTES ON SHORT TERTIARY BASES

Abstract

During recent years a light apparatus has been made up in the Survey of India to provide a basis for minor triangulation. The idea originated with the writer when executing rough triangulation under war conditions, when the need was felt for checking work which had become liable to development of considerable error. The terrain was not such as to allow the measurement of an ordinary base of such a length as half a mile; nor were other facilities present. Accordingly a length of 200 feet was marked out, with the help of a 100-foot steel tape, on a fairly smooth site on rolling ground; and its subtended angle at a distance of about 1500 feet was measured carefully with numerous repetItIons. This 1500-foot length was in turn extended in a similar way to a 3-mile side of the triangulation. No great accuracy was looked for, but enough to rule out the possibility of gross mistake in the irregular triangulation.     

THE EAST AFRICAN ARC

Abstract

Choice of Beacon.—The general question as to whether luminous or opaque signals should be used in ruling triangulation has recently been discussed in the Empire Survey Review (No.9, pp. 151–2 and No. 12, pp. 335–6). It may here be summarized that opaque beacons of suitable design are sufficiently accurate and offer the considerable advantages of being immediately available for subsequent work, of requiring little or no attention, and of being visible from all directions without rearrangement. Moreover, if of the tripod or quadripod type, they need not be dismounted during occupation of the station for observing, so that 0bservations by more than one observer are not interrupted. The only occasion for using luminous beacons arises from bad visibility, whether through atmospheric haze or lack of a suitable background or through the economic necessity of completing observations at night. These conditions are not peculiar to ruling triangulation. An ”all-round” type of luminous beacon—a pressure oil lamp or a rotating mirror system—can be used for nightwork or against a dark background, but single-direction luminous beacons are necessary to overcome haze.     

LEAST-SQUARE ADJUSTMENTS OF TRIANGULATION DIRECTIONS VERSUS ANGLES

Abstract

IT has been assumed in the past that because angles for triangulation are usually observed by the direction method, therefore it must be more correct theoretically to perform the least-square adjustments by directions rather than by angles. It is fairly obvious that an adjustment of the same figure by directions will not give the same result as an adjustment by angles: the unknowns in each case are different and the number of directions is usually about 25 per cent. greater than the number of angles for the same figure. Strictly, the least square method is only applicable to observations from which all systematic errors have been eliminated, and in which the remaining errors are truly accidental. It is generally safe to assume that most survey errOlS consist of a random and a systematic part. Rarely, if ever, is it possible to state that all systematic error has been eliminated, strive how we may to take all precautions against it.     

SURVEYING INSTRUCTION AT THE UNIVERSITY

Abstract

Education at the university should in essence be concerned more with theory than technique, with principles rather than practice. Should a university lose sight of this aim it will of a certainty become a university only in name. The attention to be given to vocational training will necessarily vary from faculty to faculty—that some vocational training is deemed desirable is shown by the very presence of an engineering department in nearly all our universities, a department in which practical training is necessarily mingled with theory. It is possible to say with truth about a certain type of engineering student that he will make a good engineer if only he can get through his examinations; to make the comparable statement about, say, a mathematics student is clearly ridiculous. In other words, the engineering profession, and in particular the civil engineering profession, has room for a good practical man to whom theory does not come easily; and yet in many of our university engineering departments no allowance is made for a man's chosen career save that after his first year of general engineering work he may elect to be a civil mechanical, electrical or aeronautical engineer. Often he has no choice of subjects for study; sometimes he is given a choice of four out of five subjects, as with the external civil engineering degree of London University where his freedom of action resolves itself into a decision between Hydraulics and Mathematics. In this examination, and many others, all candidates are required to sit the same papers in a subject, irrespective of whether they are potential first-class honours men or may expect to obtain a pass degree.     

MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. Computation of a minor triangulation as if it were executed on a plane surface of course ignores spherical excess, an omission not strictly rigorous so far as azimuths are concerned. Further the reduction of such a triangulation to a system of plane coordinates again assumes that the earth's surface is a plane.     

THE RE-TRIANGULATION OF GREAT BRITAIN IV—BASE MEASUREMENT

Abstract

Accuracy and consistency in surveying are almost synonymous. It is true that no very great degree of precision in angular or linear measurement can be utilized in our final paper publications, even on the largest scales: all we need is an assurance that the results of further work, in the same or in adjoining areas, shall be in sympathy with antecedent measurement, so as to avoid the necessity for assigning several positions to the same point.     

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.     

UNITS OF LENGTH AND THEIR RELATION TO AREAS IN CADASTRAL SURVEYS

Abstract

Brought up as we are in the British Empire in a world of difficult weights and measures, we come to regard them as inevitably complex and laborious, and only when we come into direct contact with professional and business men of foreign nations is it brought home to us how pathetically foolishwe are in sticking to systems of mensuration that have not resulted from deliberate thought but have evolved from the vagaries of mensuration in history. At the commencement of our instruction in arithmetic we are informed (to quote Workman's text-book) that “when we put down a list of the number of inches that make a foot, the number of feet that make a yard, and the number of yards that make a mile, we get what is called a Table of Long Measure. Similar tables are needed for other measures. The following tables must be learnt thoroughly by heart. They are all the measures which are really needed, though a great many more are in use and will be mentioned later.” Here follows, without a word of apology, a page of historical antiquities in the shape of our tables, each one a self-contained entity, seemingly priding itself on having no connexion whatever with any other.     

A NEW METHOD FOR THE ADJUSTMENT OF A NETWORK OF TRIANGULATION

Abstract

A problem frequently encountered by surveyors in carrying out a system of triangulation, is the adjustment of a network of lower order triangulation to make it geometrically consistent with an existing triangulation of a higher order. For example, in Fig. 1 it will be assumed that the positions of the stations A, B, and C have already been determined and that it is now required to determine the positions of the stations a, b, c, d, e and f from the measured values of the internal angles of the network of triangulation shown. In practice, several different solutions have been suggested, ranging from rigorous least squares methods to semi-graphical solutions. The method described in this article is believed to be original and may prove of interest to surveyors.     

IMPLICIT CONDITION EQUATIONS IN THE ADJUSTMENT OF TRIANGULATION FIGURES

Abstract

In adjusting a triangulation network it may happen that certain condition equations, of the existence of which we know a priori (by formulæ or by plotting the network point by point), cannot be established by simple inspection of the figure. This usually happens when some of the observations are missing in the otherwise continuous network. Such equations, not readily identifiable from the diagram, may be called “implicit” condition equations.     

THE LAY-OUT OF THE EAST AFRICAN ARC

Abstract

The only essential difference between geodetic triangulation and any other of the fifteen “orders” of triangulation—which were once proposed, and happily rejected, at an International Conference—is that steps are taken to secure the high degree of accuracy necessary over the large areas to be covered. Some of the steps taken to secure increased accuracy may well be used to insure economy in secondary work, as for instance the use of fewer readings of a large instrument, or the use of luminous signals in conditions of poor visibility; while any surveyor may at any time have to connect his work to a geodetic triangulation, using much the same methods.     

RELAXATION AND THE CO-ORDINATE METHOD OF TRIANGULATION ADJUSTMENT

Abstract

Few, most certainly, will dispute the value of Mr Black's paper describing a method of “Systematic Relaxation”, which appeared in a previous number of this Review. At the same time, however, it seems to the writer to be only fair to readers to point out that the application of the method to triangulation adjustment is really a treatment, from a slightly different aspect, of methods that have long been established.     

LAPLACE AZIMUTHS

Abstract

The adjustment of a chain of triangulation for scale between measured bases is a comparatively simple matter. If it were possible to provide a similar method of adjustment for swing between measured azimuths and if the triangulation were based on a fixed datum, then there would be some hope of holding the chain fixed, without waiting until the completion of further chains rendered a net adjustment possible. This would be well worth doing.     

THE ORDNANCE SURVEY

Abstract

If, one and all in our several ways, we are absorbed in helping to win the war, there are moments when it is possible to turn to our earlier loves, if but to relieve the strain. Not one of our hobbies, not a single insti tu tion that holds our affections and our memories, can emerge from this struggle just as it was. New thoughts and new methods are in the air, new service will be required, and, if principles remain largely unaltered, they, and the lessons we have learned, will be in peril, for continuity and knowledge have been rudely interrupted. It may do no harm to restate, however inadequately, some of those lessons—political, administrative and technical.     

离散点集Delaunay三角网生成算法改进与软件开发

改进了三角形生长算法，在原算法的基础上，用均匀格网来划分离散点集，建立点集的栅格索引,快速生成初始三角形，再进行扩展；引进了封闭点的概念，在扩展过程中动态删除封闭点，加快了查找点的搜索过程；软件开发中采用VC的MPC类Carry和CList来管理数据，创建了CBuildtin和Craster两个类来生成三角网和栅格索引，提高了程序的可移植性。