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.     

THE COLOURS QUESTION

Abstract

The foundation of my former paper was nothing more substantial than a recollection of reading or hearing long ago that the property of the four colours existed in practice but had never yielded to strict theoretical analysis. I am therefore most grateful to Col. G. S. C. Cooke and Mr. G. W. Ross Jackson for their letters to the Editor (vol. iii, no. 15, pp. 52–5) citing the relative authorities, as they enable me to locate and acknowledge my debt to Mr. W. W. Rouse Ball, whose book was certainly in my hands in the Oxford Union Library some forty years ago. I wish I could remember his demonstration of the problem, but my subconscious faculties seem, from what Col. Cooke says, to have evolved a tolerable imitation of it, and until I have an opportunity of seeing the book again or of consulting any of the other authorities, I shall rest content in the assurance that, wherever my arguments may differ in substance from those of Mr. Rouse Ball, my errors will be so flagrant as to deceive none but myself, though my serenity in this connexion is somewhat shaken by the fate that seems to have attended the first welcome efforts to unmask a few of them.     

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.     

THE LATE CAPTAIN McCAW'S CONTRIBUTIONS TO THE E.S.R.

Abstract

The volume of this Review which has just been completed commenced with a memoir of the first Editor, the late Captain G. T. McCaw, C.M.G., O.B.E., M.A., who died in October 1942, and, in view of his great services to the Review and to the survey world in general, it is thought to be not in-appropriate that this, the first number of a new volume, should contain a list of his contributions to the Review. The power and versatility that they display are remarkable.     

THE ENGINEER SURVEYOR

Abstract

Survey Training for the Civil Engineer at the University has been discussed in four articles in the Review. (R. N. Ray, M.A., xii, 89, 104–110; H. Biesheuvel, B.Sc., xii, 90, 159–165; A. Stephenson, O.B.E., M.A., F.R.I.C.S., xii, 91, 217–222; K. R. Peattie, B.Sc., Ph.D., A.R.T.C., A.M.I.C.E., xii, 94, 376–379.) Cost of equipment for a large class and limitation of time in an already heavily loaded curriculum prevent the student acquiring enough training to undertake the survey work required on alarge engineering scheme. The schemes of training described in the four articles are greatly to be admired and it is hard to see how any improvement can be made.     

Remapping Fictional Worlds: A Comparative Reconstruction of Fictional Maps

ABSTRACT

This article presents a quantitative analysis of fictional maps and their relation to historic maps from different periods. Fictional maps are maps of imaginary territories. This type of map is now common in fiction, but they arose relatively late, in the second half of the nineteenth century, and are considered an independent branch of cartography today. They stand out through the way they are published because they are component parts of books and not independent cartographic works, and therefore their creators are not cartographers but rather the authors of these books. Fictional maps are mostly subordinate to the story, but they serve to give a sense of historical authenticity and draw the reader into the story. Without networks of coordinates and with labels such as ‘the end of the world’, they are spatially indeterminate, but they establish a connection between the fictional landscape and its identity. This study deals with 89 fictional maps from recent children’s and young adult literature. First we present a historical overview of these works and fictional maps, and then a cartographic analysis of fictional maps. We examined seventy-seven books with fictional maps and evaluated the maps according to five groups of standard cartographic elements: natural elements, built elements, toponyms, mathematical elements, and explanatory elements. We discuss the differences between cartographic representation of fictional maps and historic maps, and build a cartographic model based on the frequency of cartographic elements to put fictional maps into historic and geographical contexts.     

The Military Map of the United Kingdom and its Impact on Mapping in the Twentieth Century

Abstract

Considerable attention has been paid in the literature to the changing style of Ordnance Survey mapping in the twentieth century. However, little has been written about the origins of the characteristic appearance of the first multi-colour editions, other that the Ordnance Survey used a military edition that was already in production. The distinctive style grew out of the work of a committee established in 1892 by the War Office to consider future army requirements for a map of the UK. This paper explores the work of the committee and its long-term implications for the look of mapping in the twentieth century.     

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 AFRICAN ARC OF THE 30th MERIDIAN

Abstract

This project, which is now well known to surveyors not only in Africa but all over the world, was first visualised by Sir David Gill, who for many years was H.M. Astronomer at the Cape Observatory. It is fitting to commence by giving in his own words his conception of the work, the part of which from South Africa to the Equator has now been completed. The following extracts are taken from the paper “On the Origin and Progress of Geodetic Survey in South Africa, and of the African Arc of Meridian”, by Sir David Gill,K.C.B., F.R.S.     

Observations Italian Composite Atlases and a Belgian Undescribed Copy

Abstract

Although Italian composite atlases of the 16th century are seldom mentioned in the literature on historical cartography, these collections are very important for preserving a large number of maps that might otherwise be lost forever. With this paper we want to realize a few things: bringing those atlases back into the spotlight, focusing attention on the need for more research and collaboration on this subject, and last but not least we will reveal the story and the content of a composite atlas not known yet to most authors who are trusted with the subject.     

EXPANSION OF PAPER AS AFFECTING AREA

Abstract

For the sake of the junior reader we may repeat an old and simple investigation. Let us suppose that the paper on which a map is printed undergoes a regular expansion p in one direction, say the X direction, and another regular expansion q in the Y direction, perpendicular to the former; it is required to know the effect of these expansions on the area of any parcel on the map. Note that, so far as the mathematics are affected, X and Y are not necessarily parallel to the margins of the sheet; we shall take them here as axes of any rectangular coordinate system. The symbols p and q are regarded as ratios, so that 100p and 100p represent the percentage expansions; if the paper contracts instead of expanding, no more is necessary than to change the sign.     

STANDARDIZING EQUIPMENT OF THE GOLD COAST SURVEY DEPARTMENT

Abstract

The following account of the standardizing equipment of the Gold Coast Survey Department has been written, at the request of the Editor of the Review, because this equipment includes a completely enclosed standard of length 300 feet long which is believed to be one of the very few enclosed standards of this length in any of the Crown Colonies.     

CORRECTION OF PLANE-TABLE HEIGHTS FOR CURVATURE OF THE EARTH AND ATMOSPHERIC REFRACTION

Abstract

Most text-books on surveying limit their discussion of the correction of vertical angles for curvature of the earth and atmospheric refraction to the correction of angles taken with a theodolite during triangulation and omit any reference to those taken with a clinometer. This is rather illogical, as in well-observed triangulation, with all vertical angles measured in both directions, no correction for these effects is necessary, whilst in plane-tabling on small scales where sketching at considerable distances is frequently employed the application of corrections for these effects is essential.     

GEOGRAPHICAL NAMES IN UNINHABITED REGIONS AND THE CONTROVERSY OVER THE MOUNT EVEREST MAP

Abstract

(I) The deserts of India and Baluchistan.—In the eastern half of the Great Indian Desert there are rock-outcrops projecting above the sand at in tervals averaging twenty miles; these have been landmarks for travellers for centuries, and consequently they all have native names. In the western desert there are no outcrops and no objects to name; but the desert nomads and the camel-breeders do have names for vague undefined areas, which seem to move as the sandhills move. The rock-outcrops in Baluchistan are larger and more numerous, and many are consequently without Baluchi names. Nothing would have been gained from inventing names; names are for use, not for show, and the desert people know their own requirements. It is better on a map to limit the nomenclature to the names that have been born of the people and that have stood the test of time than to supplement them with fictitious names. Survey stations on unnamed hills are therefore generally designated by symbols such as B45.     

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.     

John Stanley Keates: Curriculum Vitae and List of Publications

Abstract

The first BCS President of the twenty-first century reflects on the cartography of the twentieth century and identifies those 'maps' that he believes have had significant influence on the development of the discipline during that century.     

THE NEV GEODETIC TAVISTOCK THEODOLITE

Abstract

The first instrument of the new design of the Geodetic Tavistock theodolite was received by the Geodetic Service of Canada early in 1939. It has now been well tried out both in field and laboratory, and a few minor changes have been accepted by the manufacturer. The reactions of field men and the results of laboratory tests may be of interest.     

THE STEREOSCOPIC DIAGRAM

Abstract

Wheatstone in 1838 published for the first time his remarkable discovery of Stereoscopy. To himself he had put the question, “What would be the visual effect of simultaneously presenting to each eye instead of the object itself its projection on a plane surface as it appears to that eye?” A preliminary experiment in which four objects were combined to form two resultant images at once sufficed to confirm his expectation and to demonstrate the phenomenon of synthetic solidity, to which he gave the name Stereoscopy He then proceeded to explain his discovery by means of a diagram based upon a more elementary experiment involving the formation of a single resultant image. Hitherto this experiment has been universally accepted, not only on account of the plausibility of its application, but because the movements described by Wheatstone can generally be readily seen when the experiment is repeated. These movements were regarded by Wheatstone as being of a stereoscopic character. It is the purpose of this discussion to show that the second experiment in no way represents the phenomenon of Stereoscopy, and that any diagram based upon this second experiment cannot afford a correct explanation of the stereoscopic principle.