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.     

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 I entirely agree with him that the sole use of heliographs—heliostats to the purist—is in most parts of the world out of date. I also think, and indeed am prepared to state categorically, that the use of acetylene lamps is out of date and was out of date many years ago.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.     

THE YEAR 1935 IN CEYLON

Abstract

I Was on special short leave in England in June and personally represented Ceylon at the Empire Surveyors' Conference and the Empire Meteorologists' Conference in London, returning to. Ceylon in October. During my absence Mr. R. W. E. Ruddock, Deputy Surveyor-General, acted for me.     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

At the suggestion of Mr. T. H. Corfield, who has himself given two solutions (E.S.R., No. 12, pp. 345–6) of Mr. A. J. Potter's problem, I venture to submit a third solution, which has at least the merit of simplicity.     

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.     

THE PRIMARY TRIANGULATION OF SARAWAK

Abstract

Historical.—When my predecessor, Mr N. A. Middlemas, was seconded from the Survey Department of Malaya in 1925, the survey framework of the State was technically negligible.     

INTERPOLATING FROM TRAVERSE TABLES TO SECONDS

Abstract

In the Empire Survey Review, no. 4, 1932, Mr. Clendinning has described a method of interpolating from traverse tables to seconds. Below is another method, due to Prof. Nekrassov, for use with traverse tables published by him. The method is described in The Geodezist, Moscow, 1936, no. I, pp. 47–52.     

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”.     

THE APPLICATION OF A RED FILTER TO SURVEYING INSTRUMENTS

Abstract

I regret that my note on this subject (vol. ii, no. 7,PP· 32-3) should have apparently provoked so little comment or interest. I feel that the silence may be either that accorded to my Impetuous Inrush or that produced by alarm at the possible complications to be overcome before theory can be reconciled with practice. If the latter, then my original title is perhaps in some measure responsible. It is really very simple; let two facts suffice.     

SURVEY NEWS ITEMS FROM CEYLON

Abstract

Personnel.—Mr G. K. Thornhill, O.B.E., F.R.G.S., F.S.I., F.R.Met. S., Surveyor-General, retired from the Public Service on the 7th June, 1937.     

GEOGRAPHICAL POSITIONS IN MAURITIUS AND RODRIGUEZ

Abstract

The desirability of determining as accurately as possible the latitudes and longitudes of a number of points in Mauritius appears to have first appealed to the French astronomer M. L'Abbé de la Caille, who was sent to the island by the French East India Company in 1753. His observatory was situated 4,730 feet east and 2,610 feet north of Port Louis Time Ball, and in addition to determining the geographical position of this. 0bservatory (the house, later demolished, of a Mr Mabile, where Mr D'Après had made observations the previous year)—

Latitude 20° 09′ 42″ S.; Longitude 55° 08′ 15″ E. of Paris—,

he succeeded in effecting a triangulation of the island. Four bases were measured with wooden scales which previously had been compared with an iron toise (6.394 feet—the French fathom) approved by the Academy of Sciences, Paris; a I4-inch quadrant fitted with micrometer was used to measure the angles.     

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.     

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.     

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.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour.     

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.     

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.     

NOTES ON LEVELLING WITH THE ANEROID BAROMETER

Abstract

In chapter 5, page 12, of my “Report on a Rapid Geological Survey of the Gambia” (Gold Coast Geological Survey Bulletin, NO. 3) I have stated the opinion of Prof. Julius Hann of Vienna that the barometric curves may be analysed into two components:- <list list-type="alpha"> <list-item>

semi-diurnal, constant, depending on latitude and altitude (with a slight yearly alteration);</list-item> <list-item>

diurnal, depending chiefly on temperature (and humidity ?).</list-item> </list>