SOUTHERN RHODESIAN MILITARY SURVEYORS IN THE WORLD WAR, 1939–1945

Abstract

For some two months prior to the formation of the two companies, an intensive course of survey training and “refreshing” had been undergone by all ranks in the field sections, culminating in a combined Royal Artillery/Royal Engineer survey exercise from 1st to 10th October, carried out under operational conditions in all respects (even down to a 30-hour non-stop period of “photo-topo” compilation for the map on which the “final shoot” took place).     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

In the course of his stimulating and suggestive paper in your recent issue, No. ro, pp. 226–38, Mr. A. J. Potter writes on p. 233 “but there is no simple construction by which X can then be found”, and again on p. 237 “a direct construction, if there be such”. This cheerful challenge invites the construction of a circle centred on a given line, passing through a given point thereon, and touching a given circle, and I have found the lure of Mr. Potter's gauntlet as irresistible as its recovery has proved delicate. In order to shoulder responsibility and by no means to claim highly improbable originality, let me confess that the problem is new to me and the two constructions I offer are my own; I venture to hope that Mr. Potter may consider one or other of them not unworthy of his epithet “simple”, though I freely admit the aptitude of his empiric procedure to its purpose. The proofs are not long, but for fear of overshooting my welcome I offer them to anyone for the asking; and for the same reason my diagrams are small and therefore mere.     

THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

THE ERRORS IN A RADIAL LINE PLOT OF AIR PHOTOGRAPHS

Abstract

Lieut.-Col. Browne's interesting method of combii1ing radial line plots (“The Application of Transformation Factors to the Adjustment of Air Photographs”, E.S.R., x, 73, 119-130) depends for its success on the basic accuracy of the radial line plots of the individual air photo strips. It therefore poses the very interesting question: What accuracy can we expect in a graphical radial line plot?     

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”.     

THE STRAIGHT POSITION LINE

Abstract

The article “Notes on the Position Line” by B. Chiat (E.S.R., xiii, 97, 137) is very informative in the conclusions reached regarding the validity of drawing the position line straight, but it seems, to me at least, that the discussion involving the effects of the earth's non-sphericity is an academic labouring of a difficulty which, in fact, is non-existent.     

THE EARLY HYDROGRAPHIC SURVEYS OF THE BRITISH ISLES

Abstract

The 200th anniversary of the publication by Murdoch Mackenzie (Senior) in May 1750 of his “Orcades, or a Geographic and Hydrographic Survey of the Orkney and Lewis Islands, in 8 maps”, is an opportune moment for a brief résumé of the contribution made by Mackenzie and his successors in the field of nautical surveying. The appearance of this work ushered in a new era in marine survey, for it was the first charting carried out in this country based on a rigid triangulation framework. The importance of this fact can further be appreciated when it is remembered that a contemporary topographic map like General Roys' famous “Map of the Highlands” begun in 1747 was little more than an elaborate compass sketch; thus under Mackenzie's influence, marine surveying at this period was ahead of its topographic counterpart.     

A NOTE ON AZIMUTH DETERMINATION

Abstract

The purpose of this note is twofold; first, to criticize the “azimuth” section of the paper “Some Notes on Astronomy as Applied to Surveying”, by R. W. Pring (E.S.R., July 1952, xi, 85, 309–318),and secondly, out of these criticisms to develop an alternative method of making observations for azimuth. It will be apparent that this method owes much to the ideas put forward by Mr. Pring.     

TWO PROBLEMS OF RESECTION: FURTHER NOTE

Abstract

An additional note on these problems, which were considered in No. 23, pp. 49-53, appears desirable. The “alternative form” on p. 51 was presented in a manner calculated to demand an explanation; since none has been forthcoming no apology is necessary for a further reference.     

THE SIERRA LEONE TOPOGRAPHICAL SURVEY

Abstract

The survey of Sierra Leone was fortunate enough to be completed just in time before the economic blizzard (if I may be permitted a well-worn journalistic cliché) descended on West Africa in common with the rest of the world and largely curtailed such activities. I do not propose to deal here with its technical side to any great extent. An excellent account of bush surveying is to be found in the “Handbook of the Southern Nigerian Survey”, which account always filled me with the greatest awe and respect for the men working there, their output being vastly greater than anything we were able to achieve in Sierra Leone. Truly “there were giants … in those days”.     

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.     

TACHEOMETRIC SURVEYING AND THE USE OF THE DIFFERENTIAL SLIDE RULE

Abstract

In the E.S.R. No. 17 of July 1935, page 138, there appeared an article by Prof. F. A. Redmond on “The use of Even Angles in Stadia Surveying”. Since I have given this method a six-months' test in the field, using Prof. Redmond's “Tacheometric Tables” for the reduction of the measurements, the conclusions reached may be of some interest.     

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.     

Toute la Geodesie sans ellipsoide Les reperes laplaciens Application plus particuliere aux travaux a latitude elevee

Resume Après de nombreuses années d’hésitation, on a finalement reconnu, au Congrès de Florence, en 1955, que dans le repérage des altitudes, seule la notion depotentiel était claire et sans ambigu?té, l’altitude au sens courant du terme étant conventionnelle. De la même fa?on, pour le repérage géométrique des points à la surface de la Terre, les coordonnées (X Y Z) des points, dans letrièdre cartésien terrestre général, sont les inconnues fondamentales; les coordonnées géodésiques couramment utilisées (longitude, latitude altitude H au-dessus de l’ellipso?de) sont conventionnelles. Mais pratiquement, afin d’écrire commodément les relations d’observation, il para?t intéressant de passer par l’intermédiaire detrièdres locaux (trièdres laplaciens), liés de fa?on invariable au système cartésien général, et de repérer toutes les grandeurs dans ces trièdres locaux. Toutes les observations utilisées en Géodésie s’expriment de fa?on simple et sans singularités dans ces trièdres locaux. La jonction des triangulations classiques, l’Astrogéodésie, la synthèse des Géodésies classique et spatiale sont facilitées. En astronomie de position, les grandeurs longitude, latitude, azimut, sont avantageusement remplacées par: déviation Est-Ouest, déviation Nord-Sud, azimut de Laplace. Les relations d’observation s’écrivent sans difficulté, même dans les régions polaires. L’application pratique des nouvelles formules obtenues a été réalisée avec succès par L.F. Gregerson (Service Géodésique du Canada).

---

Summary At Florence, in 1955, it was accepted that, in the problems of levelling, the notion ofpotential was scientifically clear, and that the altitude could derive from it only through a conventional process. In the same manner, when we want to have a geometric reference of the points at the earth surface, we use the coordinates (X Y Z) in thegeneral cartesian trihedron as fundamental unknowns, the geodetic coordinates (λϕH) deriving from (X Y Z) through a conventional process. Practically, in order to set up the observation equations, it is necessary to define local trihedrons (laplacian trihedrons), deriving from the cartesian general system through a fixed transformation, and to refer all the unknowns in these local trihedrons. All the observations used in Geodesy can be expressed simply and without any singularity in these local trihedrons. The links between classical geodetic nets, the astrogeodesy, the combination between classical and spatial geodesy, become easier. In astronomical controls, “longitude, latitude, azimut” must be replaced by: W-E deflection, N-S deflection and Laplace azimuth. Thus all the observation equations can be set, even in polar regions. A practical application of the new formulae was done successfully by L.F. Gregerson (Geodetic Survey of Canada).

     

THE CLARKE FORMULÆ FOR LATITUDE,LONGITUDE AND REVERSE AZIMUTH,WITH CORRECTIVE TERMS FOR USE ON VERY LONG LINES

Abstract

This extremely simple and elegant method of computing geographical co-ordinates, given the initial azimuth and length of line from the standpoint, was published by Col. A. R. Clarke in 1880. There is no other known method giving the same degree of accuracy with the use of only three tabulated spheroidal factors. Clarke himself regarded this as an approximate formula (vide his remark in section 5, p. 109, “Geodesy”); but as this article demonstrates, it is capable of a high degree of precision in all occupied lati tudes when certain corrections are applied to the various terms. These corrections are comparatively easy to compute, require no further spheroidal factors, and some of them may be tabulated directly once and for all.     

FURTHER NOTES ON FIGURES OF REFERENCE

Abstract

Major Hotine (E.S.R., No. II, pp. 264–8) still finds the location of a reference spheroid to offer insuperable difficulties. I confess that my difficulty is to see his! In my previous article (E.S.R., No. 8) at the foot of page 76, I used the word “coincidence” in error for “parallelism”. This harmonizes the article and I am glad that Major Hotine has directed attention to the error.     

COMPENSATION OF TRAVERSES WHEN LENGTHS ONLY ARE CORRECTED

Abstract

If it be assumed that the linear measurements of traversing are alone afflicted with error, the method of distribution of error demands consideration. In the present paper the notation of Wright and Hayford will be followed (“Adjustment of Observations”, 1906 edn., p. 156).     

THE NOMENCLATURE OF MAP PROJECTIONS

Abstract

Map Projections.—A matter that should have been mentioned in the original article under this title (E.S.R., vii, 51, 190) is the definition of a map projection. In the list of carefully worded “Definitions of Terms used in Surveying and Mapping” prepared by the American Society of Photogrammetry (Photogrammetrie Engineering, vol. 8,1942, pp. 247–283), a map projection is defined as “a systematic drawing of lines on a plane surface to represent the parallels of latitude and the meridians of longitude of the earth or a section of the earth”, and most other published works in which a definition appears employ a somewhat similar wording. This, however, is an unnecessary limitation of the term. Many projections are (and all projections can be) plotted from rectangular grid co-ordinates, and meridians and parallels need not be drawn at all; but a map is still on a projection even when a graticule is not shown. Objection could be raised also to the limitation to “plane surface”, since we may speak of the projection of the spheroid upon a sphere, or of the sphere upon a hemisphere. Hence, it is suggested that “any systematic method of representing the whole or a part of the curved surface of the Earth upon another (usually plane) surface” is an adequate definition of a map projection.