THE CONFORMAL TRANSFORMATION OF A NETWORK OF TRIANGULATION

Abstract

In a recent issue of this Review, an example is given of the conformal transformation of a network of triangulation using Newton's interpolation formula with divided differences. While the application of the method appears to be new, attention should be drawn to the fact that Kruger employed Lagrange's interpolation formula in a discussion and extension of the Schols method in a paper which was published in the Zeitschrift für Vermessungswesen in 1896. A reference to this paper was given at the end of the paper, “Adjustment of the Secondary Triangulation of South Africa”, published in a previous issue of the E.S.R. (iv, 30, 480).     

THE CALCULATION OF THE HEIGHT OF KILIMANJARO

Abstract

The observations to height Kilimanjaro were made from two ground stations, Domberg (5,081·6 ft.) and Lelatema (5,323.1 ft.) and from a point called Kibo near Kaiser Wilhelm Spitze which is regarded as the highest point on the crater rim. It was originally intended to include a third ground station, Kifaru, but it was discovered that the ice cap obstructed observations between this point and the top.     

THE TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID

Abstract

In January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method.     

THE ADJUSTMENT OF TRIGONOMETRICAL LEVELS AND THE EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

This paper is written primarily with the object of ascertaining how other Colonies and Dominions deal. with the adjustment of their trigonometricallevels; further, since the greater part of Nigeria is now covered by a framework of levels of primary accuracy it is of interest to examine the results. Moreover, the evaluation of the coefficient of refraction, and from it the temperature lapse-rate, is of some importance in view of the recent publication of the War Office Aneroid Tables. These tables are based on a standard lapse-rate of temperature.     

DEVIATION OF THE VERTICAL. DISCUSSION

Abstract

The following is a report of the discussion on the paper by Mr. A. R. Robbins on “Deviation of the Vertical” which was read at a meeting of the Land Surveying Division of the Royal Institution of Chartered Surveyors held on Tuesday, 12th December, 1950, and which was published in the January issue of this Review (xi, 79, 28–36).     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

At the suggestion of Mr. T. H. Corfield, who has himself given two solutions (E.S.R., No. 12, pp. 345–6) of Mr. A. J. Potter's problem, I venture to submit a third solution, which has at least the merit of simplicity.     

TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject.     

A METHOD FOR THE DETERMINATION OF THE DISTORTIONS OF THE IMAGE FORMED BY A MULTIPLEX PROJECTOR

Abstract

A Method is described for the determination of the resultant of the radial and tangential components of the distortion of the image produced by a Multiplex projector.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

THE ACCURACY OF TOPOGRAPHICAL MAPS

Abstract

“Accuracy” in relation to maps is a term very frequently and widely used. Nevertheless it is hard to obtain any comprehensive precise definition of the word in this connection.     

THE ORTHOMORPHIC PROJECTION OF THE SPHEROID

Abstract

Chesterton did not, of course, intend this gibe to be taken literally. But the more we consider what he would doubtless have called the “Higher Geodetics”, the more we must conclude that there is some literal justification for it. Not only are straight lines straight. A sufficiently short part of a curved line may also be considered straight, provided that it is continuous (i.e. does not contain a sudden break or sharp corner), and provided we are not concerned with a measure of its curvature. Similarly a square mile or so on the curved surface of the conventionally spheroidal earth is to all intents and purposes flat. We shall achieve a considerable simplification, without any approximation, in the treatment of the present subject by getting back to these fundamental glimpses of the obvious, whether the formalists and conformalists accept them or not.     

THE COOLING OF THE EARTH BY CONVECTION AND SOME OF ITS CONSEQUENCES

Abstract

In this Review (24, 68, 1937) attention was drawn to the need, in considering isostasy, of recognizing the existence of two separate weak layers, i.e. layers in which material can flow horizontally. One of these is a deep layer under both oceans and continents, the other being a layer of plastic basalt, immediately under the continents only, in which mountain ranges and other local surface masses are compensated. That suggestion formed part of a wider theory which has been developed in recent articles in the Pan-American Geologist. A brief review of that theory may be of interest.     

THE DERIVATION OF CERTAIN PROJECTION FORMULAE FOR THE SPHERE

Abstract

The purpose of this article is to make available to readers of the Review a simple method of derivation from first principles of the projection farmulae for same of the more impartant normal conical projections.     

THE PRIMARY TRIANGULATION OF SARAWAK

Abstract

Historical.—When my predecessor, Mr N. A. Middlemas, was seconded from the Survey Department of Malaya in 1925, the survey framework of the State was technically negligible.     

BATTLE SONG OF THE FAR-FLUNG SURVEYORS

Abstract

Air.—Any good Guest Night tune which happens to fit to a first order, and remains more or less in tune after subsequent orders. “Coming down the Mountain” and “Kabul River” would do.     

SIR DAVID GILL AND THE GEODETIC SURVEY OF SOUTH AFRICA AND THE ARC OF THE 30TH MERIDIAN

Abstract

In the memoir of the late Capt. G. T. McCaw which appeared in the January number of this Review (vii, 47,2), reference was made to the part which the late Sir David Gill played in the origin of the work on the survey of the Arc of the 30th Meridian in Africa. This year is the centenary of Gill's birth, as he was born in June 1843, and it is therefore timely to give some account of his work during his long term of office as Her Majesty's Astronomer at the Cape which resulted inthe inception and completion of the Geodetic Survey of South Africa and the survey of the Arc to the southern shores of Lake Tanganyika. He died on 24th January 1914.     

THE POST-WAR PROGRAMME OF THE ORDNANCE SURVEY OF GREAT BRITAIN

Abstract

In 1938 the committee to investigate the activities of the Ordnance Survey, presided over by Lord Davidson, issued its final report. One of the terms of reference of this committee was “to review the scales and styles of Ordnance Survey maps placed on sale to the public and to recommend whether any changes are desirable”.     

DEVIATION OF THE VERTICAL

Abstract

This paper endeavours to put forward good reasons, practical as well as academic, for needing a knowledge of the deviation of the vertical in all countries, and it then describes the instruments and methods used by the writer in his first season on the observation of a geoidal section through Great Britain. Unfortunately there has been no time as yet for the computation of the latter, so this cannot be a full report on it.     

THE ISLANDS OF THE TRISTAN D'ACUNHA GROUP

Abstract

In January, 1934, a report was received from the Royal Research Ship Discovery II that the positions of Inaccessible and Nightingale Islands in the Tristan d'Acunha group were incorrectly shown on British Admiralty chart No. 1769. The report originated from local information, and was to some extent confirmed by patent log distances run by Discovery II, and by sea sights, but no really definite evidence as to the correct position of the two islands was received. In effect, the report merely stated that both Inaccessible and Nightingale Islands were considerably nearer to Tristan Island than as charted.