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.     

REFORM OF THE CALENDAR

Abstract

The majority of readers are doubtless aware of the masterly summary of the “History of the Calendar,” written for the Nautical Almanac for 193I (pp. 734–747) by Dr. J. K. Fotheringham. Most are probably also aware that the question of Calendar Reform has been considered by the League of Nations. At the Conference on Communications and Transit of 1931, October 19, the League adopted a resolution recommending a fixed Easter, but declared that “the present time is not favourable … for considering … a reform of the Gregorian calendar.” For information on the various measures of reform proposed at Geneva the works noted below may be consulted. In the meantime, pending the coming of reform—for come it will—readers may desire to.have a summary history of the question, with a statement of a solution which is of somewhat the same nature as others which have been proposed.     

THE TRANSVAAL-SOUTHERN RHODESIA GEODETIC CONNEXION

Abstract

In the original geodetic series in Southern Rhodesia—completed by Mr Alexander Simms in 1901—the geographical coordinates of all stations were referred to the point SALISBURYas origin. The coordinates of SALISBURY were fixed by interchange of telegraphic signals with the Royal Observatory at the Cape for longitude, combined with astronomical determinations of time, latitude, and azimuth (see Vol. III, “Geodetic Survey of South Africa”).     

SURVEY IN THE GREAT WAR

Abstract

Artillery Survey.—Included in the term “Artillery Survey are two distinct problems, the first that of determining the “line” and “range” at which fire should be opened, and the second that of laying the gun in the required line. To appreciate these problems it. is necessary to know a little about the technique of gunnery, and for the benefit of those who have no acquaintance with the subject the following brief résumé may be given.     

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.     

THE STATE OF THE SURVEYS OF BRITISH AFRICA IN 1905-06

Abstract

Whilst turning over some old papers the other day I came across a copy of the first Annual Report of the Colonial Survey Committee, and the recent, much regretted death of Sir Herbert Read reminded me of his services in the development of the surveys and explorations of British possessions in Africa, especially his suggestion, which was approved by the Secretary of State for the Colonies, of the formation of the Colonial Survey Committee, an Advisory Committee which was set up in August, 1905. This Committee advised the Secretary of State “in matters affecting the survey and exploration of British Colonies and Protectorates, more especially those in Tropical Africa”.     

THE TOWN PLANS

Abstract

The town plans in question are those ranging from the “five-foot” (1/1056) to the modified “ten-foot” (1/500) scales, made by the Ordnance Survey between 1841 and 1894, and then, in principle at any rate, abandoned. This is, I fear, wholly a British matter and profuse apologies are offered to oversea readers. Yet history, repeating itself as usual, may presently add the wider interest to the tale.     

AN OLD FILE AND A NEW ARC

Abstract

In his article “Standards of Length in Question” published in the last number of this Review (Vol. i, pp. 277–-84) Captain G. T. McCawgave us most interesting and valuable history concerning the questionable past of the international metre. He has, it may be assumed, exhausted published evidence; but he states that he can find no reference to invitations from this country to France and Holland to send their fundamental standards for comparison with others at the Ordnance Survey in the eighteen sixties.     

THE EAST AFRICAN ARC

Abstract

It was suggested some time ago in the Review (E.S.R., vol. ii, no. 9, p. 182) that observing procedure in a ruling triangulation should be made the subject of a discussion at the forthcoming Empire Survey Conference. I hope it will be. We shall perhaps learn why India finds thirty measures necessary, as no doubt they are necessary in India, whereas South Africa and Southern Rhodesia are able to secure much the same degree of accuracy from the same instrument with only eight; why Canada, again with the same instrument, prefers the golden mean of sixteen; why some of us still prefer the measurement of angles to directions vvhile others would insist entirely on the measurement of directions from a “close” R.O. It is only by pooling the experiences gained in diverse circumstances that we can avoid being overborne by our own successes or failures, encountered possibly in very exceptional circumstances which may not recur.     

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.     

ON THE ORTHOMORPHIC PROPERTY OF SCHOLS ADJUSTMENT

Abstract

In vol. iv, nos. 29 and 30, of the E.S.R., there appeared an article by Mr. D. R. Hendrikz on the “Adjustment of the Secondary Triangulation of South Africa”. He shows that, in applying the Schols method of orthomorphic transmission to the adjustment of a secondary net to a primary triangle, the secondary sides suffer small displacements.     

SURVEY IN THE GREAT WAR

Abstract

Hostile Battery Location.—Among the tactical ideas current in 1914 before the outbreak of war was the conception of an artillery duel as the opening phase of a great battle. This was pictured as a “hammer and tongs” sort of business in which the opposing artilleries were drawn up in full view of one another, and the winning assets were speed in coming into action, quicker rate of fire, and superior endurance. Good drill, in short, was thought to be worth much more than preliminary calculation. Actually, in the event, it was soon discovered that no battery could come into action in the open without being immediately destroyed. Far from there being any artillery duel, the opposing artilleries soon found themselves unable to attack one another at all. For a time, in the stress of greater happenings, this unforeseen development passed unnoticed, the reason being that the British artillery, having no shells to speak of, were compelled to keep the few they possessed for helping to repel the German infantry, while the German gunners, though they had plenty of ammunition, saw no reason to expend any of it in subduing an artillery which fired so seldom. Throughout 1915, until the shell shortage had been overcome, the recognized procedure for putting a stop to hostile shelling was to retaliate by a few rounds on some reputedly sensitive spot in the infantry trenches. History does not record the precise nature of the reactions in the hostile organism set up by this procedure nor whether it was invariably effective for the purpose in view. In any case no other procedure was possible because no one knew exactly where the hostile batteries were.     

LONG LINES ON THE EARTH: THE DIRECT PROBLEM

Abstract

19. Formulae.—In Nos. 6, vol. i, and 9, vol. ii, pp. 259 and 156, there has been described a new method for dealing with long geodesics on the earth's surface. There the so-called “inverse” problem has claimed first attention: given the latitudes and longitudes of the extremities of a geodesic, to find its length and terminal azimuths. It remains to discuss the “direct” problem : a geodesic of given length starts on a given azimuth from a station of known latitude and longitude; to find the latitude and longitude of its extremity and the azimuth thereat. The solution of this direct problem demands a certain recasting of the formulae previously given. In order of working the several expressions now assume the forms below.     

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 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.     

A FIFTY-YEARS RETROSPECT

Abstract

The International Map of the World.—Officially known as the Carte du Monde au Millionième, this undertaking has the following history. At the International Geographical Congress which was held at Bern in 1891, Professor Dr. Albrecht Penck proposed the construction, by all the nations of the world, of an International Map on the scale of 1 to 1 million. This idea was unanimously approved, and a very sketchy outline was roughed out for its prosecution. Of this outline the chief item that has survived is the size of the sheets, which were to be six degrees in longitude by four in latitude. Well, time passed and nothing much happened. Year after year there were a few murmurs at congresses about the map, and a few, a very few, sheets were printed, some by Section “F” of the British War Office. There was no general organization to look after the prosecution of the map, and there were no adequate regulations for its construction. Generally speaking, the official map-making institutions were out of touch with the scheme, and geographical societies and congresses had no money and no power to carry it out.     

THE NEW GEODETIC TAVISTOCK THEODOLITE

Abstract

Work on the original Geodetic Tavistock Theodolite was commenced in the autumn of 1931, and after suitable tests this instrument was sent out to East Africa and used on the East African Arc. Bt Major M. Hotine, R.E., writing in the E.S.R. of April 1935 (no. 16, vol. iii), stated: “The Tavistock instrument, although a first model, gave uniformly satisfactory service throughout and was used for over half the main angular observations.”     

THE CONVERGENCE OF MERIDIANS

Abstract

Some publications that have dealt with the question of convergence of meridians seem, to the present writer, to be clouded with misconception, and these notes are intended to clarify some points of apparent obscurity. For instance, A. E. Young, in “Some Investigations in the Theory of Map Projections”, I920, devoted a short chapter to the subject, and appeared surprised to find that the convergence on the Transverse Mercator projection differs from the spheroidal convergence; the explanation which he advanced can be shown to be faulty. Captain G. T. McCaw, in E.S.R., v, 35, 285, derived an expression for the Transverse Mercator convergence which is equal to the spheroidal convergence, and described this as “a result which might be expected in an orthomorphic system”. Perhaps McCaw did not intend his remark to be so interpreted, but it seems to imply that the convergence on any orthomorphic projection should be equal to the spheroidal convergence, and it is easily demonstrated that this is not so. Also, in the second edition of “Survey Computations” there is given a formula for the convergence on the Cassini projection which is identical, as far as it goes, with that given for the Transverse Mercator, while the Cassini convergence as given by Young is actually the spheroidal convergence. Obviously, there is some confusion somewhere, and it is small wonder that Young prefaced his remarks with the admission that the subject had always presented some difficulty to him.     

THE MERCATOR PROJECTION AND THE RHUMB LINE

Abstract

Introductory Remarks.—A line of constant bearing was known as a Rhumb line. Later Snel invented the name Loxodrome for the same line. The drawing of this line on a curvilinear graticule was naturally difficult and attempts at graphical working in the chart-house were not very successfuL Consequently, according to Germain, in 1318 Petrus Vesconte de Janua devised the Plate Carree projection (“Plane” Chart). This had a rectilinear graticule and parallel meridians, and distances on the meridians were made true. The projection gave a rectilinear rhumb line; but the bearing of this rhumb line was in general far from true and the representation of the earth's surface was greatly distorted in high latitudes. For the former reason it offered no real solution of the problem of the navigator, who required a chart on which any straight line would be a line not alone of constant bearing but also of true bearing; the first condition necessarily postulated a chart with rectilinear meridians, since a meridian is itself a rhumb line, and for the same reason it postulated rectilinear parallels. It follows, therefore, that the meridians also must be parallel inter se, like the parallels of latitude. The remaining desideratum—that for a true bearing—was attained in I569 by Gerhard Kramer, usually known by his Latin name of Mercator, in early life a pupil of Gemma Frisius of Louvain, who was the first to teach triangulation as a means for surveying a country. Let us consider, then, that a chart is required to show a straight line as a rhumb line of true bearing and let us consider the Mercator projection from this point of view.