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.     

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.     

LATERAL DISPLACEMENT OF SIGNALS OBSERVED

Abstract

I notice that in the last two numbers of the Empire Survey Review a lateral displacement is mentioned or implied.     

TRIALS OF A SURVEYOR-MODERN VERSION

Abstract

Reading the Empire Survey Review of 20 years ago, with the tales of raw jungle and untrodden country, as in Sir Charles Arden-Close's retrospective accounts, I am tempted to give a brief picture of surveying in the Colonies today, away from the beaten track.     

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.     

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.     

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).     

SURVEY OF PALESTINE: THE FIRST TWENTY YEARS

Abstract

I suppose most of you look at a map nearly every day and I expect you know a good deal more about them after following the blitzkriege of armies in Europe—and Africa. My advice is, go on learning, for a map has become the means of picturing allsorts of things closely connected with our lives ; modern methods of reproduction have made maps so picturesque and useful that they should be companions to all those who take the trouble to understand them.     

SOME EFFECTS OF PULLEY ECCENTRICITY IN BASE MEASURING APPARATUS

Abstract

The comprehensive paper on the suspension of tapes by M. Hotine in the January, 1939, issue of the Empire Survey Review (v, 31, 2) did not contain any reference to this question, as was pointed out by A. J. Morley in a letter published on page 261 in the same volume (v, 34, 261). A brief analysis has been made by F. Yates of the theoretical effects of pulley eccentricity and misalignment (“Gold Coast Survey Department Records” VoL III, 1931, page 43) but I have not seen any further reference to the subject and have recently experienced the effects of such a defect in our own apparatus, so the followingnotes nlay be of interest. Before proceeding to details I will describe briefly those parts of the apparatus which are considered here and give a short summary of the whole paper.     

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.     

ELIMINATION OF ERRORS OF LATITUDE AND REFRACTION IN THE PAIRING OF AZIMUTH OBSERVATIONS

Abstract

In a previous Article (Empire Survey Review, ii, II) I described a simple graphical method for the elimination of latitude error in observations for azimuth. It was pointed out that the ideal method of adjustment of azimuths would be a simultaneous elimination of both latitude and refraction errors and, with that in view, a purely theoretical method of such an adjustment was demonstrated in the last paragraph of the article. It has now occurred to me that a fairly simple mathematical solution is possible.     

COMPENSATION AS A CONSEQUENCE OF TWO KINDS OF ROCK STRUCTURE

Abstract

The following points occurred to me when reading the interesting paper on crustal equilibrium in E.S.R. No. 23. The principle of compensation or isostasy necessarily involves the idea of two different kinds of rock structure—one strong, the other weak or in extreme cases fluid; for example, there is the familiar case of the strong iceberg resisting change of shape in the liquid sea. In dealing with crustal problems of the earth then, we should make up our minds which part is to be considered as strong, e.g. the granite crust, and which part as weak or fluid, e.g. material at a depth x km. (say roo km.); by weak or fluid I mean that a possibility exists of horizontal movement.     

DIRECT USE OF AIR PHOTOS FOR CADASTRAL PURPOSES IN ZANZIBAR

Abstract

Since a number of factors have combined to separate the second part of this paper from the first appearing in the E.S.R., issue No. 63, Volume IX, pp. 1–14, and written by Sir Ernest Dawson, I feel that some emphasis, already given, may reasonably be reproduced. To quote from Sir Ernest's paragraph on the Main Problem :—“The crux of the matter which I had been invited to solve, was the definition and record in a simple, sure and economical way, of the increasing number of unstable small holdings in their tangled setting throughout the Protectorate.”     

THE EFFECT OF ALTITUDE ON TRAVERSE ERRORS

Abstract

I. These notes are the results of following up in some detail the well-known fact that the horizontal distance between two points at altitude h is greater, by an amount proportional to h, than the distance between the corresponding points at sea-level. Traverses based on rectangular coordinates are considered, with special reference to the residual errors left after adjusting the misclosures of such traverses without first eliminating errors due to altitude.     

RELATIONS OF BEACON AND DEED-PLAN IN SOUTH AFRICA

Abstract

MR. C. O. GILBERT'S article on “Beacon versus Deed-plan” (E.S.R., Jan. 1932, pp. 98–99) raises a question of very great importance in those countries which have a system of land registration. In addition to the legal and technical aspects of the question, it raises the very important question of preservation of beacons and replacement of lost beacons. As he mentions the South African practice, the experience of the Transvaal may be of interest to readers, the more so as the case, The African and Buropean Investment Co., Ltd. and Others versus John Warren and Others, which he quotes, concerned farms situated in the Transvaal. I also wish to refer specially to the Transvaal, because there the diagram or deed-plan is of great legal force when there is a conflict between the position of a beacon on the ground and the position accorded it by a confirmed diagram.     

TACHEOMETRIC SURVEYING AND THE USE OF THE DIFFERENTIAL SLIDE RULE

Abstract

In the E.S.R. No. 17 of July 1935, page 138, there appeared an article by Prof. F. A. Redmond on “The use of Even Angles in Stadia Surveying”. Since I have given this method a six-months' test in the field, using Prof. Redmond's “Tacheometric Tables” for the reduction of the measurements, the conclusions reached may be of some interest.     

AN ASPECT OF ATTRACTION

Abstract

Measured deviations of the vertical have been used in support, or in destruction, of such pleasant little diversions as the theory of isostasy. They have also been used to adjust a triang~lation for swing, by methods which may fairly be criticized; but they have not, as far as I know, been used for reducing the horizontal measures of a triangulation to the standard conventional level of the spheroid of reference. In most cases such corrections would, of course, be too small to worry about, but it by no means follows that they are always small. In the case of a continental arc of meridian traversing a very disturbed mountainous region exhibiting certain constant tendencies, it should at least be demonstrated that they are small before the question can be considered finally settled.     

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).     

CONDITION FOR THE CONSTRUCTION OF A CONFORMAL PROJECTION

Abstract

In the Empire Survey Review for October 1938 (iv, 30, 480) a simple demonstration of the condition to be satisfied for conformal representation was given. This condition may be expressed by the equation w = f(z), where w and z are complex variables representing corresponding points in the w-plane and z-plane respectively, and f(z) is an analytic function of z.