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 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.     

THE REVIEW AND ITS FUTURE

Abstract

As a consequence of the death of the late editor, the responsibility for conducting this REVIEW now rests on other shoulders, and, in view of the high standard which Captain McCaw set at the beginning of the journal's existence and maintained, in spite of many difficulties, until the time of his death, his successor feels that a few words concerning the future of the REVIEW, and an appeal for continued co-operation on the part of readers, may not be out of place in this, the first number of a new volume.     

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.     

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 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 MILITARY SURVEY SERVICE AND THE CIVILIAN SURVEYOR

Abstract

When Colonel Lambton of Indian fame wanted funds for his Survey a leading melnber of the Finance Committee of Madras observed that “if any traveller wished to proceed to Seringapatam he need only say so to his palankeen bearer and he vouched he would find his way to that place without having recourse to Colonel Lambton's map”. Those who have had the privilege of dealing with finance branches will recognise in this quotation a powerful tradition and it is a measure both of the great march of events since Lambton's time and of the deterlnination of military surveyors not to lag behind them, in spite of finance committees, that good military maps are nowadays taken for granted and that the large survey organisations, required to produce them are accepted as a necessity. The struggle to maintain this position however goes on.     

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 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 TWO METRES: THE STORY OF AN AFRICAN FOOT

Abstract

Introductory.—From time to time the question of the relation between the metre and the foot is raised, most frequently perhaps from Africa. Had there been no more than a single metre to consider the question would no doubt arise but seldom: the most recent authoritative comparsion would be generally accepted. But actually it is the existence of two metres—the “ legal” and the “international”—which complicates the question, so much indeed that there is no metrological factor which has influenced survey, British and foreign, more than the relation between these two metres. The question was discussed in this Review (I, 6, 277, 1932), but memories grow shorter, attention is more diffused, and besides there is required a more explicit statement of the situation as it affects British surveyors, especially in Africa, whence the question has been raised anew. To illuminate it, unfortunately the need recurs to repeat some well-known facts.     

LOCAL ATTRACTIONS AND THEIR INFLUENCE ON THE DETERMINATION OF HEIGHTS ABOVE MEAN SEA LEVEL

Abstract

Preliminary Note.—The substance of this article was written in 1921 at the request of Lieut-Col. Wolff, who was then in charge of the Levelling Division of the Ordnance Survey and with whom the author collaborated in writing “The Second Geodetic Levelling of England and Wales, 1912–21” under the direction of Sir Charles Close. It was not intended for publication and was not again considered until 1928, when a discussion by correspondence was started by the Surveyor-General of Ceylon on the subject of hill circuits in levelling. In this discussion the survey authorities in Great Britain, Canada, India, and South Africa took part, but the main theme was the accumulation of error due to the large number of sightings necessary in hilly country and the question whether a common formula for such country and for flat country was justifiable. In his contribution Dr. van der Sterr made a brief allusion to the subject of the present paper and Dr. de Graaff Hunter went into details. His contribution and the following remarks therefore have some arguments in common.     

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).     

LENGTH AND AZIMUTH OF LONG LINES ON THE EARTH

Abstract

In the E.S.R., viii, 59, 191–194 (January 1946), J.H. Cole gives a very simple formula for finding the length of long lines on the spheroid (normal section arcs), given the coordinates of the end points. In the course of the computation the approximate azimuth of one end of the line is found, the error over a 500-mile line being of the order of 3″ or 4″. If the formula is amended so that the azimuth at the other end of the line is used in computing the length of the arc, the error is then less than 0″·1 over such a distance. An extra term is now given which makes this azimuth virtually correct over any distance. Numerical tests show that Cole's formula for length and the new one for azimuth are very accurate and convenient in all azimuths and latitudes.     

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.     

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.     

PERSONALIA

Abstract

The death occurred suddenly on 2nd February, 1935, of Mr. WILLIAM ERNEST BARRON,of Fort Jameson, Northern Rhodesia. Mr. Barron, who was 55 years of age, held the Certificate of Land and Mine Surveyor of the School of Mines, University of Otago, New Zealand, and the Mine Surveyor's certificate of competency, Transvaal, and in 1913 was licensed as a surveyor in Northern Nigeria. In 1921 he was licensed as a surveyor for private practice in Northern Rhodesia. He was for over four years Chief Surveyor to the Van Ryn Gold Mines Estate, Ltd., and for two years to the Bantjes Consolidated Mines, Ltd., and for some time to Modderfontein East, Ltd. He was first employed in Northern Rhodesia as Mine Captain in charge of survey work at Broken Hill Mine, and from 1923 to 1928 was engaged by the Rhodesia Broken Hill Development Co., Ltd., in the survey and setting out of all work in connexion with that Company's Hydro-Electric Power Scheme at Mulungushi. Upon the completion of this work, in which Mr. Barron showed the greatest skill and accuracy under difficult conditions, he was engaged by the North Charterland Exploration Company as surveyor, and at the time of his death he was carrying out the survey of that Company's Land Concession, an area of 10,000 square miles on the south-eastern border of Northern Rhodesia. By his death the survey profession has lost an able and keen personality, and he will be greatly missed by the many friends he made in this country. He leaves a widow and son to mourn his loss.     

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.     

THE KEEPING OF SURVEY RECORDS

Abstract

Although the title of this paper may appear to some to refer to a rather humdrum subject which hardly deserves much serious thought or consideration, it is the writer's experience that the vital necessity for keeping clear records of survey work in a permanent form in which they can easily be referred to at any future time is not always sufficiently appreciated by those whose duties do not involve constant or frequent reference to the records of old work. Accordingly, the following notes and suggestions, which are based on practical experience, may be of service in drawing attention to a matter which is really of great practical importance.