THE FIXATION OF MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

The fixation of Minor Triangulation in a Primary system does not, in general, warrant rigorous adjustments of figures; less laborious methods are desirable. For Secondary work a least square adjustment to approximate coordinates is quite sufficient, while, for Tertiary, graphical solutions are amply accurate. Apart from that, cases may arise to which a figure adjustment is not applicable, as in the small net shown in Fig. 2, p. 464. The line BC cannot be equated to the line AB in the ordinary way since it is not the side of a triangle. In this case an adjustment to approxima te coordina tes will overcome the difficulty.     

CHECKING REDUCTION OF NORMAL EQUATIONS

Abstract

The method of checking reduction of normal equations which will be described below was first devised by the present writer when he had to adjust in one set the whole of the Southern Block of the Major Triangulation of Palestine, involving 114 equations of condition. This method. proved to be so useful and. efficient that, when subsequently adjusting the Northern Block of the same network (117 condition equations in simultaneous adjustment), the advisability of its application was obvious. Finally, in war time, the adjustment in one set of 65 condition equations of the Northern part of the Transjordan Primary Triangulation observed by the Army, equally underwent self-checking by the same method and proved a complete Success.     

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 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).     

DEVELOPMENTS OF SURVEY IN JAMAICA

Abstract

The Primary Triangulation did not cover completely the eastern end of the Island and it was required to carry the net out to the coastline in this region. Two additional primary stations have now been selected to admit of this extension. The lines straddle the John Crow mountains, which were one of the great obstacles at this end, and one point is actually on the lighthouse t at the eastern extremity of Jamaica. Since observations are needed from one side only of the lighthouse, we have put a special bracket on the balustrade of the lantern gallery to support the theodolite; the beacon is plumbed upside down below this. I enclose three photographs to illustrate it.     

GEODETIC SIGNALS IN SOUTHERN RHODESIA

Abstract

So much has been written in the Empire Survey Review and other publications on the somewhat controversial subject of “Luminous or Opaque Signals in Geodetic and Primary Triangulation” that it may be of interest to give an outline of the types of signals used on such work in Southern Rhodesia, with particular reference to the completion of the Eastern Geodetic Circuit in 1935 and the type of signal that it has been decided to adopt for future work.     

THE CONVERSION OF CO-ORDINATES FROM THE CASSINI TO THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. The Secondary and Tertiary Triangulations of the six counties of Northern Ireland which were observed about 1900 were computed county by county each on its own meridian on a Cassini projection using Airy's figure of the earth. Although a number of points common to two or more counties were fixed no attempt was made to bring the separate counties into sympathy either with each other or even with the old Primary triangulation as adjusted by Clarke in 1856.     

AZIMUTH COMPUTATION IN THE OLD PRINCIPAL TRIANGULATION OF THE BRITISH ISLES

Abstract

The old Principal Triangulation of Great Britain and Ireland is a classic, both in execution and publication. The names of many of those who planned it, made it possible, carried it out or computed it have become legendary in the Ordnance Survey. Such are Roy, Dalby, Ramsden, Mudge, Colby, Drummond, Steele, O'Farrell and, greatest of them all, Clarke.     

GEOGRAPHICAL POSITIONS IN MALAYA AND SIAM

Abstract

Malaya.—The geographical positions of points in the “Primary Triangulation of Malaya”, published in 1917, depend upon latitude and azimuth determinations at Bukit Asa and on the longitude of Fort Cornwallis Flagstaff, Penang, the latter being supposed to be 100° 20′ 44″.4 E. This value was obtained by Commander (later Admiral) Mostyn Field in H.M.S. Egeria 1893, by the exchange of telegraphic signals with Mr Angus Sutherland at Singapore, Old Transit Circle. The longitude, 103° 51′ 15″.75 E., accepted for Singa- pore in order to arrive at this determination of Fort Cornwallis Flagstaff, was based upon that of an Observation Spot, 103° 51′ 15″.00 E., fixed in 1881 by Lieutenant Commander Green, United States Navy, by meridian distance from the transit circle ofMadras Observatory, the corresponding longitude of the latter being taken as 80° 14′ 51″.51 E.     

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.     

HORIZONTAL ANGLES IN TRIANGULATION: SOME PRACTICAL SUGGESTIONS REGARDING THEIR OBSERVATION AND ADJUSTMENT

Abstract

MR. RAINSFORD'S paper on Directions versus Angles in the Least Squares Adjustment of Triangulation in the October 1950 issue of the E.S.R. (x, 78, 353–366) has raised some interesting points and has prompted me to put on paper my own views and some of the results of my own experience.     

MINOR TRIANGULATION

Abstract

When Clarke had written finis to his account of the Principal Triangulation he and O'Farrell (his famous chief computer) framed those simple methods of computation which were to be characteristic of the work of the “tertiary computers”. The tertiary triangulation, resting upon an adjusted primary and a rather poor-class secondary, covered the country at distances of a little over a mile between points. Points were chosen not so much for visibility as for convenience of chaining.     

THE TRANSVERSE MERCATOR PROJECTION AND ITS APPLICATION TO TANGANYIKA TERRITORY

Abstract

The Transverse Mercator Projection is also called the Conformal of Gauss since it was devised by him in the early part of the nineteenth century in connexion with the Triangulation of Hanover. It belongs to the class of cylindrical orthomorphic projections. That is to say, the Earth's surface, or part thereof, is developed on the surface of a cylinder, and there is practically no angular distortion, an angle on the surface of the Earth being represented on the map by almost precisely the same angle. The representation of meridians and parallels, for instance, shows them intersecting at right angles as they actually do on the Earth's surface; but this orthotomic condition, though essential, is not in itself sufficient for orthomorphism.     

THE UGANDA MAlLO SYSTEM

Abstract

So much for the system. Now to describe the method of survey. Between 1902 and 1906 a chain of triangulation, extending from Zanzibar by way of the southern border of what is now Kenya Colony, and the northern and western shores of Lake Victoria to the Belgian Congo, had been surveyed by Anglo-German Boundary Commissions under G. E. Smith and Delmé Radcliffe as leaders. In 1902 a base line was measured near the middle of the Buganda Province by officers of the Uganda Survey Department. This was connected by triangulation to the Anglo-German chain, and several new chains were run across Buganda of an order of accuracy generally classified as that of tertiary triangulation. These chains are now known as the Uganda Main Triangulation, and form the backbone of the Buganda Cadastral Survey, popularly known as the “mailo” survey.     

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.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION

Abstract

Mr. Rainsford's paper in E.S.R. No. 78 establishes as thoroughly as one can wish by computational example that there is little to choose in relative accuracy between direction adjustment and angle adjustment, and that the deciding factor is really ease and speed of computation.     

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.     

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).     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

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.