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.     

FIGURES AND FANCIES

Abstract

I may say at once that this article has nothing to do with either the Gaiety chorus or the “Old Firm”: it is merely a statement of what seem to me the fancies in Dr. de Graaff Hunter's paper “Figures of Reference for the Earth”, E.S.R., No. 8,pp. 73–8. Many readers of the Review will share my gratitude to Dr. Hunter for his lucid presentation of the theory underlying the usual geodetic processes. I disagree with only one of his points, and its implications, but unfortunately that point is fundamental.     

FIGURES OF REFERENCE FOR THE EARTH

Abstract

1. The object of this note is to clear up what I believe to be some misconceptions regarding the use of a reference system by a surveyor of the earth's surface. In his article “An Aspect of Attraction”, E.S.R., No. 7, pp. 24–8, Major M. Hotine expressed doubts as to the validity of the process usually followed. I may say at once that I consider these doubts are unfounded.     

Jacques Bertin,from classical training to systematic thinking of graphic signs

ABSTRACT

Nearly 50 years after the publication of the first French edition of Sémiologie Graphique, Jacques Bertin’s thought is more than ever alive, in cartography as well as in various other disciplines, such as graphic design or visual data analysis. This article recalls the main elements of Bertin’s career and puts forward the salient points of his reflection on graphics. Beyond many conceptual or technical innovations, Bertin’s essential originality appears to be his attempt to propose a general framework for graphical representations.     

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.     

NOMENCLATURE OF MAP PROJECTIONS

Abstract

I Have read with interest Mr. L. P. Lee's remarkably well-informed article in the January number (vii, 51, 190) on “The Nomenclature and Classification of Map Projections”. I agree with much of what Mr. Lee says, but I cannot think that he has always been happy in his choice of names.     

ROAD LOCATION IN FOREST COUNTRY

Abstract

THE very interesting article on “Road-surveying in the East” by J. N. List appearing in NO. 6 of the Review suggests that the following notes on the methods of road location used in the Gold Coast may be of interest. These methods enter into considerably more detail than those described by Mr. List and are of proved economic value.     

STONEHENGE AND WOODHENGE

Abstract

Owing to the kindness of the editor, I have recently been able to see the article on Stonehenge and Woodhenge by Captain Learmont, together with the editor's notes in the Empire Survey Review for April 1936. I hope the editor will also allow me space to make a few comments.     

A TEST FOR THE RELIABILITY OF TRIGONOMETRICAL OBSERVATIONS

Abstract

I should like to reply to the Editor's comments on the above article, published in the E.S.R., v, 34, 226 (October 1939).     

A FIFTY-YEARS RETROSPECT

Abstract

The International Population Union.—In 1927, as President of the Geographical Association, it was my duty to deliver an address to the Association. I chose as my subject “Population and Migration” with special reference to the English-speaking peoples. One result of the publication of this in Geography, the journal of the Association, was that I was invited to attend the World Population Conference, which was held at Geneva in August-September 1927. The Conference was a very interesting affair. It was organized, and largely paid for, by Mrs. Margaret Sanger. About twenty-four countries were represented. The late Sir Bernard Mallet presided, and in one of his speeches, winding up the Conference, he truly said that we might “congratulate ourselves on having shown the world that population questions, which bristle with controversy, political, moral, and religious, can be discussed by sensible people without animosity or unseemly wrangling”.     

APPROXIMATE METHODS OF SOLVING NORMAL EQUATIONS

Abstract

My attention has recently been drawn to an article by G. H. Menzies (E.5.R., vi, 46, 474) on this subject. The present note is intended to point out improvements in the Anér method, which he favours, and to refute some of his criticisms of the Relaxation method. References are to page and table numbers in Menzies's paper.     

GEODETIC BEACONS

Abstract

Mr. Clendinning's article on “Signal Lamps” (E.S.R., vol. ii, pp. 15–18) raises a point of major importance in geodetic triangulation. I entirely agree with him that the sole use of heliographs—heliostats to the purist—is in most parts of the world out of date. I also think, and indeed am prepared to state categorically, that the use of acetylene lamps is out of date and was out of date many years ago. The Americans, who are always worth listening to on the economics of surveys, would not otherwise have replaced all their acetylene gear by electric beacons. The answer, in my experience, and for reasons which I shall endeavour to make clear, is generally, but not necessarily always, to provide both helio and electric lighting; but first I should like to summarize the conditions in which luminous signals should be used at all.     

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.     

Maps > Representation

Abstract

Colour is considered a key means of expression for use in cartographic works. This is because colours and the relations among them influence not only the aesthetic impression a map creates but also its overall utility. In addition to Newton’s spectral colour theory, today theories with origins in artistic technique are gaining ground in cartography. This article introduces J. Itten’s colour theory (first published in 1961 in The Art of Colour [Kunst der Farbe]) with special attention given to his concept of seven colour contrasts. The article also discusses the suitability and unsuitability of their application in practical cartography, and it contributes original examples employing thematic maps, a discipline with broad possibilities for the application of these inventive methods by today’s mapmakers.     

THE MODIFIED MERIDIAN DISTANCE IN THE CONICAL ORTHOMORPHIC PROJECTION

Abstract

Recently the writer of this article became interested in the conical orthomorphic projection and wanted to see a simple proof of the formula for the modified meridian distance for the projection on the sphere. Owing to the exigencies of the war, however, he has been separated from the bulk of his books, and, consequently, has had to evolve a proof for himself. Later, this proof was shown to a friend who told him that he had some memory of a mistake in the sign of the spheroidal term in m⁴given in “Survey Computations”, perhaps the first edition. Curiosity therefore suggested an attempt to verify this sign, which meant extending his work to the spheroid. This has now been done, with the result that the formula given in “Survey Computations”, up to the terms of the fourth order at any rate, is found correct after all.     

DIRECTIONS AND ANGLES IN A SIMPLE CHAIN

Abstract

Mr. Rainsford's article on “Least Square Adjustments of Triangulation: Directions versus Angles” in the Empire Survey Review No. 78, Vol. x, October 1950, leads to many speculations and interesting results. I try to show here, how, by assuming artifices to simplify the results, weights may be assigned to angles derived from directions so that the results of adjustment by angles, with these weights, will be the same as the adjustment by directions, all of equal weight.     

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.”     

JOTTINGS: CAIRNS ON THE N.W. FRONTIER

Abstract

An officer ordered his native headman to go with his party to a distant mountain, arranged a rendezvous there with him on a certain date, and concluded his instructions by saying, ‘I shall expect to find a good-sized cairn on the top when I get there.’ Subsequently the encounter on the mountain-top took place. No cairn was visible, but the headman produced in its place a seedy-looking pi-dog with the remark, His mother was a cairn, but his father was too quick.     

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.