THE EFFECT OF ALTITUDE ON TRAVERSE ERRORS

Abstract

I. These notes are the results of following up in some detail the well-known fact that the horizontal distance between two points at altitude h is greater, by an amount proportional to h, than the distance between the corresponding points at sea-level. Traverses based on rectangular coordinates are considered, with special reference to the residual errors left after adjusting the misclosures of such traverses without first eliminating errors due to altitude.     

COMPUTATION OF DISTANCES OF LONG ARCS FOR RADIO PURPOSES

Abstract

In the E.S.R., No. 59, Vol. VIII, of January, 1946, I gave a formula which I had worked out to give a rapid and easy means of computing the lengths of long arcs, up to 1000 kilometres, between two points whose latitude and longitudes are known on a definite figure of the earth.     

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.     

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.     

A MACHINE METHOD OF RESECTION

Abstract

With the modern calculating machine in easy reach of every computer, the problem of determining the position of an occupied point from which direction observations have been made to three or more known points has become quite simple. The method outlined below is quite elegant in form and exceedingly simple on the machine. Let A, B, C be the three points whose co-ordinates (X₁Y₁), (X₂Y₂), (X₃Y₃) are known, and let (XY) be the co-ordinates of the point P which we wish to fix.     

ON THE CLASSIFICATION OF MAP PROJECTIONS

Abstract

1. Classes and Varieties. A map projection can be considered from different points of view, each such point of view representing a “class” of projections. The classes, in their turn, are subdivided into “varieties”.     

ALTITUDES OF POINTS SEEN ON THE HORIZONTAL WIRE OF A THEODOLITE

Abstract

Many surveyors, even those of wide experience, would, if questioned, assert that, at any given pointing of a theodolite, all points in the field of view which lie on the horizontal wire are at equal angular altitudes above the horizon, provided that the horizontal wire is in correct adjustment to the trunnion axis.     

INSTRUCTIONS FOR THE USE OF THE PRISMATIC ASTROLABE AND PROGRAMME FINDER

Abstract

The problem of finding the latitude and longitude of various points on the surface of the earth is one which has been studied for hundreds of years.     

CONDITION FOR THE CONSTRUCTION OF A CONFORMAL PROJECTION

Abstract

In the Empire Survey Review for October 1938 (iv, 30, 480) a simple demonstration of the condition to be satisfied for conformal representation was given. This condition may be expressed by the equation w = f(z), where w and z are complex variables representing corresponding points in the w-plane and z-plane respectively, and f(z) is an analytic function of z.     

EVALUATING THE DISTORTION INVOLVED IN THE READJUSTMENT OF A NETWORK: THE SCHOLS ADJUSTMENT AS A POSSIBLE CRITERION

Abstract

The object of the present paper is to provide a criterion for assessing the value of a network of surveyed points in the light of a subsequent accurate coordination of control points in the area.     

A CHANCE CORRECTION OF A TRAVERSE

Abstract

It sometimes happens that from a point on a line of theodolite traverse two fixed points are visible. In the absence of a visit to at least one of these points, B or C, or a precise knowledge of a bearing, it is not possible to fix absolutely the station, say A, of the traverse. Nevertheless, the fact remains that if the angle subtended by the fixed points is measured and found to be α, say, the station A must lie on an arc of a circle through BC “capable of” this angle α. Is there any assumption which is justifiable under these circumstances?     

A DIRECT METHOD OF TRANSFORMING RECTANGULAR COORDINATES FROM THE CASSINI PROJECTION TO THE GAUSS CONFORMAL PROJECTION

Abstract

6. Further Expansions.—Equations (4.3) and (5.5) enable a computer to transform coordinates from the Cassini projection to the Gauss projection without recourse to geographical coordinates. If applied to one or two points, no doubt these equations would be quite satisfactory; but if applied to 100,000 points their use would be laborious and it would be difficult to adapt them to machine computing.     

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.     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”.     

IMPROVING THE PERFORMANCE OF WILD PRECISION THEODOLITES

Abstract

IN the July issue of the Empire Survey Review, vol. ii, no. 13, pp· 424–8, there appeared a review of precise theodolite investigations carried out by the present writers; the original papers were published in the March, 1934, number of the Canadian Journal of Research of the National Research Council, Ottawa. The elaboration of some points which could not be given much space either in the original papers or in the review may be of interest.     

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 SURVEY FRAMEWORK OF NIGERIA

Abstract

Angular and Linear Errors.—In the results which follow, the number of stations quoted on the chains is exclusive of all the stations on the base-extension nets at Minna, Rijau, Chafe, and Naraguta. The total number of stations can therefore be obtained by adding the numbers on all the chains and the base-extension nets and deducting the number of points common to other chains. The quoted fractional misclosures in length are the actual misclosures obtained and the theoretical fractional misclosures which might be expected to be developed through the chains from the probable errors of the adjusted angles.     

CONNECTION OF INDIA,SIAM AND MALAYA TRIANGULATIONS

Abstract

In an article in the Review of October 1938, iv, 30,450-457, under the heading “Geographical Positions in Malaya and Siam”, Mr. A. G. Bazley gives a comparison of the Indian and Siamese, and Siamese and Malaya, triangulations at common points and discusses the possibility of an error in the longitude of the datum of the Malayan system. In the Review of April, 1939, v, 32, 112-113, he has elaborated certain points, and remarks in connection with the doubt in the longitude of the Malayan datum that connection of the F.M.S. network with that of Siam and India, and some more latitude and longitude observations by the F.M.S. Survey, are essential to a satisfactory solution of this rather involved problem. Since the above article was written, a lot more infornlation has become available about the Indo-Siamese triangulation connections and a firm connection between the triangulations of Sianl and Malaya has been established in 1946. It is hoped that a review of the present position would be of interest, especially as the various links effected open up a definite possibility of a continuous chain of triangulation from India to Australia.     

NOTES ON THE BASE LINES OF THE CEYLON TRIANGULATION

Abstract

The triangulation of Ceylon depends for its scale upon two bases, each about 5½ miles long, situated at Negombo on the West Coast (latitude 7° 10′) and at Batticaloa on the East Coast (latitude 7° 40′). Both bases are in low, flat country; brick towers up to 70 feet high had to be built over the terminals to enable observations to be taken to surrounding points. These lines have recently been re-measured.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION

Abstract

Mr. Rainsford's paper in E.S.R. No. 78 establishes as thoroughly as one can wish by computational example that there is little to choose in relative accuracy between direction adjustment and angle adjustment, and that the deciding factor is really ease and speed of computation.