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.     

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.     

A NOVEL METHOD OF MEASURING THE COEFFICIENT OF THERMAL EXPANSION OF INVAR

Abstract

In a letter published in a recent issue of Nature, Prof. L. F. Bates and Mr J. C. Wilson, of University College, Nottingham, have described a new and novel method of determining the coefficient of thermal expansion of invar. Although this method is hardly likely to be applied to the measurement of the coefficient of expansion of long invar tapes, such as are used by surveyors, yet it is so novel and ingenious in itself that a short reference to it may not be out of place in this Review. One extremely interesting thing about it is that no measurements of a length, or of changes of length, are involved.     

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.     

THE APPLICATION OF THE GAUSS METHOD OF COLLIMATION TO THE ADJUSTMENT OF SURVEY INSTRUMENTS

Abstract

Gauss's method of collimation is usually given scant attention in survey text-books. The following notes are based on experiments carried out at Accra in making a collimation base, the collimator being a Watts 2I-inch self-adjusting level fitted with a parallelplate micrometer.     

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 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.     

A NEW METHOD FOR THE ADJUSTMENT OF A NETWORK OF TRIANGULATION

Abstract

A problem frequently encountered by surveyors in carrying out a system of triangulation, is the adjustment of a network of lower order triangulation to make it geometrically consistent with an existing triangulation of a higher order. For example, in Fig. 1 it will be assumed that the positions of the stations A, B, and C have already been determined and that it is now required to determine the positions of the stations a, b, c, d, e and f from the measured values of the internal angles of the network of triangulation shown. In practice, several different solutions have been suggested, ranging from rigorous least squares methods to semi-graphical solutions. The method described in this article is believed to be original and may prove of interest to surveyors.     

THE DERIVATION OF CERTAIN PROJECTION FORMULAE FOR THE SPHERE

Abstract

The purpose of this article is to make available to readers of the Review a simple method of derivation from first principles of the projection farmulae for same of the more impartant normal conical projections.     

REPRODUCTION OF THE 1/1,250 AND 1/2,500 SCALE NATIONAL PLANS,OF GREAT BRITAIN

Abstract

Field work for the 1/1,250 scale re-survey of Great Britain was fully described in an article by Brigadier R. P.Wheeler in the April, 1948, issue of this Review (ix, 68, 234–247). The object of this article is to outline the method’ of reproduction of these plans and of the resultant 1/2,500 scale plans of urban areas. The 1/2,500 series covering rural areas is a separate problem, one of revision rather than re-survey. Experiments are in hand now to find out the best ways to provide field material and produce the final plans on National Grid sheet lines. The 1/1,250 scale series will contain about forty thousand plans and the 1/2,500 series of the same areas about nine thousand. It is therefore important that production methods should be straightforward and maintain an economical balance between the use of men and machines.     

THE CHOICE OF MAP PROJECTIONS

Abstract

Most books on the technique of map compilation omit a detailed consideration of projections on the grounds that this subject is adequately treated at length elsewhere. Texts on map projections, however, are largely theoretical and rarely consider the practical problem of the proper choice and use of the graticules which are otherwise so ably described. An investigation of this little explored field has produced the following picture which it is thought may be of wider interest. A study of the fundamental properties which influence the choice of map projections is followed by a survey of projections in use, considered in relation to the fundamental properties.     

NOTE ON THE REDUCTION OF CIRCUMMERIDIAN ALTITUDES TO THE MERIDIAN

Abstract

The method of reducing circummeridian altitudes or zenith distances to the meridian, using the factors m and n as tabulated by Chauvenet, is well known. The following method, which does not use these factars, has been faund both more convenient and more accurate in practice. The formula can be easily obtained by expanding m and n in powers of t, but far the sake af campleteness the derivatian is here given from the beginning.     

ADJUSTMENT OF THE SECONDARY TRIANGULATION OF SOUTH AFRICA

Abstract

The Secondary Triangulation of South Africa consists of a uniform network of triangles of from 5- to 10-mile sides, enmeshed in the Geodetic and Primary Triangulations. As a rule the Primary Triangulation is rigorously adjusted by least squares, and the Secondary made to conform to it by an approximately rigorous method which was introduced into the Trigonometrical Survey in 1920 by the late Dr van der Sterr.     

RELAXATION AND THE CO-ORDINATE METHOD OF TRIANGULATION ADJUSTMENT

Abstract

Few, most certainly, will dispute the value of Mr Black's paper describing a method of “Systematic Relaxation”, which appeared in a previous number of this Review. At the same time, however, it seems to the writer to be only fair to readers to point out that the application of the method to triangulation adjustment is really a treatment, from a slightly different aspect, of methods that have long been established.     

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.     

NOTES ON THE OBSERVATION OF ALTITUDE FOR TIME

Abstract

Observations of the altitude of stars is a common method for the determination of local time. When the time is required with no great accuracy and when, therefore, simple instruments are employed, the method is particularly suitable. In the conduct of the observation with a theodolite there arise certain questions to which some reference may be made here with a view to lending some assistance to the student.     

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.     

THE PROJECTIVE TRANSFORMATION IN AERIAL SURVEYING

Abstract

The paper describes an algebraic method of forming linear equations, giving the coordinates of points in space in terms of the coordinates of their images on the photographic plates. The coefficients which enter into these linear equations form a matrix of the third order. When stereoscopic or similar methods are used for plotting detail, the elements of this matrix give in a convenient form and with the utmost obtainable accuracy the quantities required for setting the photographs in their correct relation to the map and to one another.

An easy and rapid graphical method of obtaining good approximations to all the solutions of the problem of resection in space is described. A method of refining the solutions is given. When the coordinates of the air station are known with fair accuracy an alternative procedure is described. In the absence of ground control suitable for finding the air station by resection a method of eliminating most of the uncertain quantities is obtained. The indeterminate quantities relate to strip photographs as a whole and not to individual photographs. A method of dealing with the coefficients for the complete strip is described.

In finding air stations by resection, point-coordinates in the photographs must be converted into directional coordinates. In other calculations this transformation is unnecessary.     

A NOTE ON THE CALCULATION OF POSITION LINES

Abstract

Since the computation of a set of star observations generally takes far longer than the actual observing, the method used in computing the results should be carefully chosen in those cases where a choice exists. The calculation of Position Lines is such a case.