A DIRECT METHOD OF TRANSFORMING RECTANGULAR COORDINATES FROM THE CASSINI PROJECTION TO THE GAUSS CONFORMAL PROJECTION

Abstract

6. Further Expansions.—Equations (4.3) and (5.5) enable a computer to transform coordinates from the Cassini projection to the Gauss projection without recourse to geographical coordinates. If applied to one or two points, no doubt these equations would be quite satisfactory; but if applied to 100,000 points their use would be laborious and it would be difficult to adapt them to machine computing.     

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.     

DISTORTING A NETWORK TO FIT CONTROL POINTS: AN ALTERNATIVE EXPRESSION FOR THE SCHOLS ADJUSTMENT

Abstract

Another form of Mr. Lauf's expression for a conformal adjustment of a system of coordinated points may be of interest. These are assumed to be already in harmony with i control points and are to be brought into agreement with j further points. (Mr. Lauf deals explicitly in his paper with the special case i = 2, j = 1, but he adumbrates a general solution.)     

ALTITUDES OF POINTS SEEN ON THE HORIZONTAL WIRE OF A THEODOLITE

Abstract

Many surveyors, even those of wide experience, would, if questioned, assert that, at any given pointing of a theodolite, all points in the field of view which lie on the horizontal wire are at equal angular altitudes above the horizon, provided that the horizontal wire is in correct adjustment to the trunnion axis.     

THE ADJUSTMENT OFA BLOCK OF AERIAL TRIANGULATION EVALUATED WITH THE WILD A5

Abstract

The procedure for aerotriangulation on the Wild A5 and similar plotting instruments is well known. The first overlap is set up in absolute orientation on well spaced plan and height control and successive overlaps are set up relatively, each to the previous overlap, by eliminating want of correspondence and preserving the height agreement of points falling in the common portion of successive overlaps. When each overlap is correctly set, the co-ordinates of selected points are measured on the instrument (machine co-ordinates). These co-ordinates differ from true ground co-ordinates only in origin, azimuth and scale, provided the settings and measurements are precisely done on error-free models, precisely connected together. However, such ideal conditions are never obtained, and the errors in azimp.th, scale and height datum increase with the number of overlaps added along a strip.     

INSTRUCTIONS FOR THE USE OF THE PRISMATIC ASTROLABE AND PROGRAMME FINDER

Abstract

The problem of finding the latitude and longitude of various points on the surface of the earth is one which has been studied for hundreds of years.     

ON THE CLASSIFICATION OF MAP PROJECTIONS

Abstract

1. Classes and Varieties. A map projection can be considered from different points of view, each such point of view representing a “class” of projections. The classes, in their turn, are subdivided into “varieties”.     

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.     

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.     

FORMULAE FOR THE ADJUSTMENT OF SURVEY ERRORS

Abstract

The formulae given in this paper can be used for a station adjustment at a trigonometric station and also for the adjustment of errors in a level survey. As applied to levelling, the problem consists in finding the most probable values of the reduced levels of a number of points where the observed level differences between the points are not consistent with each other. It can be shown that the required values of the reduced levels are those which reduce the sum of the squares of the residual errors to a minimum, where the residual error is defined as the difference between the calculated and observed levels.     

A SIMPLIFIED ANALYTICAL METHOD FOR THE ADJUSTMENT OF AERIAL TRIANGULATION

Abstract

This method, which has been used in connection with Wild A5 and A6 stereoplotting machines, was developed in an endeavour to retain as many as possible of the advantages of the analytical method without incurring the corresponding disadvantage of excessively lengthy computation. It is capable of being quickly learnt by even an inexperienced computer, and adequate checks on the accuracy of the numerical work are easily applied where not automatically provided. It has the advantage over the graphical method formerly used, that no control point is accepted as more reliable than another, equal weight being given to all, and an indication of the relative reliability of the individual control points is furnished by the table of residual errors obtained.     

NOTES ON THE BASE LINES OF THE CEYLON TRIANGULATION

Abstract

The triangulation of Ceylon depends for its scale upon two bases, each about 5½ miles long, situated at Negombo on the West Coast (latitude 7° 10′) and at Batticaloa on the East Coast (latitude 7° 40′). Both bases are in low, flat country; brick towers up to 70 feet high had to be built over the terminals to enable observations to be taken to surrounding points. These lines have recently been re-measured.     

A METHOD FOR THE DETERMINATION OF THE DISTORTIONS OF THE IMAGE FORMED BY A MULTIPLEX PROJECTOR

Abstract

A Method is described for the determination of the resultant of the radial and tangential components of the distortion of the image produced by a Multiplex projector.     

IMPROVING THE PERFORMANCE OF WILD PRECISION THEODOLITES

Abstract

IN the July issue of the Empire Survey Review, vol. ii, no. 13, pp· 424–8, there appeared a review of precise theodolite investigations carried out by the present writers; the original papers were published in the March, 1934, number of the Canadian Journal of Research of the National Research Council, Ottawa. The elaboration of some points which could not be given much space either in the original papers or in the review may be of interest.     

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 ADJUSTMENT OF TRAVERSE NETS

Abstract

The weakest point in a straight traverse between two fixed points is well known to be in the middle. The uncertainty or p.e. perpendicular to the general direction of the traverse can be shown to be a maximum at the midpoint. Yet subsidiary traverses are usually tied in at or near this point, and consequently may show closing errors which are well in excess of what may be expected. A rigorous least squares solution would overcome this difficulty but only at the cost of a very laborious computation if the network is at all extensive. A compromise between rigour and labour can be achieved, however, which retains the major advantage of a fully rigorous solution, namely that the subsidiary traverses are not tied in at the weakest points of the main traverse system.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

TRIANGULATION BEACONS AND THE WILD THEODOLITE

Abstract

Following recent discussions in the E.S.R. some experiences in Sarawak may be of interest.

The argument for opaque beacons has been strengthened by the experience here of the past season, when combined day-and-night observing was carried out on the primary series, the daylight pointings being made to black-painted opaque beacons. No difference in the accuracy obtained by the two methods was noticeable in the results. Beacons were necessary in any case for the breaking down to secondary points.     

A CHANCE CORRECTION OF A TRAVERSE

Abstract

It sometimes happens that from a point on a line of theodolite traverse two fixed points are visible. In the absence of a visit to at least one of these points, B or C, or a precise knowledge of a bearing, it is not possible to fix absolutely the station, say A, of the traverse. Nevertheless, the fact remains that if the angle subtended by the fixed points is measured and found to be α, say, the station A must lie on an arc of a circle through BC “capable of” this angle α. Is there any assumption which is justifiable under these circumstances?     

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).