MACHINE METHOD OF INTERSECTION

Abstract

The following method will be found better and quicker than the usual logarithmic process in computing the co-ordinates of intersected points in minor triangulation and traverse work. Let A and B be two stations whose co-ordinates (x ₁ y ₁), (x ₂ y ₂) are known. Let P be an intersected point whose co-ordinates (x, y) we wish to determine. Let α and β be the observed angles at A and B respectively.     

CHECKING TRAVERSE COMPUTATIONS

Abstract

Traverse Computations must be Checked.—A traverse is a chain of points connected by angular and linear measurements. The check on observations is provided by the agreement, obtained in computations, between the terminals of the traverse (terminal bearings and terminal co-ordinates) taken as fixed. This check is not sufficient, however, to serve as a check on the computations. As a matter of principle, computations should be free of errors; there are no limits of tolerance in computational work except for discrepancies arising from inaccuracy of last figures. Secondly, errors in computation may occur that are not revealed by the traverse misclosures, not to speak of compensational errors, the field for which is very favourable in traverse work.     

TWO SIMPLIFIED CHECKS

Abstract

The usual method employed is to plot or to compute the traverse from each end; the poin t having the same coordinates in each route is the station where the gross angular error occurred. There is, however, a method of finding the error by plotting the traverse one way only. Let us consider the traverse having the known terminals A B (see Fig.). Suppose that the error occurred at the point P and that the final point obtained (plotting the traverse from A) was B′ in place of the correct point B. We can easily see that the triangle PBB′is isosceles, and that therefore a straight line bisecting BB′at right angles will meet the traverse in the required point P.     

TRAVERSE REDUCTION WITH AN ELECTRONIC DIGITAL COMPUTER

Abstract

The article describes work carried out by the authors on the Manchester Universal Digital Computer at Manchester University. The general characteristics of the computer are discussed. The requirements for traverse reduction for Ordnance Survey work are summarised, with the help of a specific example. The technique required to present the details of a traverse to a computer for reduction is then described, and some details of the operation of the programme are given. The article is concluded with some details of the time taken to carry out the reduction, and remarks about special features of computer design which would have proved advantageous for this work.     

TRAVERSES—AND OTHER THINGS

Abstract

In the last numbers of the Review there have been five contributions on the subject of traverse adjustment. Since the present writer started the ball rolling it may be permissible to him to make a rejoinder.     

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.     

TRAVERSING WITH THEODOLITE AND CHAIN

Abstract

As Mr H. F. Rainsford (E.S.R., no. 37, vol. v, July 1940) says, the ordinary accurate survey traverse, through its “ordinariness,” has been neglected in the printed word. The technique—perfected by much practice—has been handed down by word of mouth only from father to son, from surveyor to pupil.     

A MODIFICATION OF BOWDITCH'S RULE,TO PRESERVE THE BEARING OF THE DATUM LINE IN A CLOSED TRAVERSE

Abstract

The article derives formulae for adjusting the lengths and bearings of a traverse so as to obtain an exact closure, whilst obeying the Least Squares condition and an added condition that the original bearing of one of the traverse lines is to remain unaltered.     

AREAS BY EQUIDISTANT OFFSETS

Abstract

In chain and traverse surveys areas are frequently required between chain lines and crooked fences. Commonly these areas are computed from offsets measured at equal intervals, which are so much the shorter according as the sinuosity is the greater. Most frequently Simson's Rules are employed for this computation; for (2m+1) offset ordinates, Simson's First Rule may be used; for (3m+1) ordinates, Simson's Second Rule. The First Rule assumes that the fence is made up of arcs of ordinary parabolae; the Second Rule, of arcs of cubic parabolae.     

A statistical filter for geodetic observations

A method for filtering of geodetic observationwhich leaves the final result normally distributed, is presented. Furthermore, it is shown that if you sacrifice100.a% of all the observations you may be (1−β).100% sure that a gross error of the size Δ is rejected. Another and, may be intuitively, more appealing method is presented; the two methods are compared and it is shown why Method 1 should be preferred to Method 2 for geodetic purposes. Finally the two methods are demonstrated in some numerical examples.     

THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

BOOK REVIEWS

Book review in this Article DIGITAL IMAGING. By R. Graham . Whittles Publishing, Caithness, 1998. ISBN 1 870325 12 5. 234 × 156 mm. 240 pages. 18 colour plates, 93 figures, 9 tables. Price £35.00 paperback. PARALLEL PROCESSING ALGORITHMS FOR GIS. Edited by R. Healey , S. Dowers , B. Gittings and M. Mineter . Taylor & Francis, London, 1998. ISBN 0 7484 0509 7. xviii + 460 pages. Price £24.95. FRAMEWORK FOR THE WORLD. Edited by D. Rhind . Geoinformation International, Cambridge, 1997. ISBN 1 8624 2021 1. 240 × 160 mm. 325 pages. Illustrated and 12 colour plates. Price £45.00 casebound. SEMANTIC MODELLING FOR THE ACQUISITION OF TOPOGRAPHIC INFORMATION FROM IMAGES AND MAPS. Edited by W. F$ourstner and L. Pl$uumer . Birkhäuser Verlag, Basel, 1997. ISBN 3 7643 5758 4. 235 × 160 mm. 227 pages. Diagrams and illustrations. Price CHF88.00. GEOGRAPHICAL INFORMATION SYSTEMS AND COMPUTER CARTOGRAPHY. By C. Jones . Addison Wesley Longman Ltd., Harlow, 1997. ISBN 0 582 04439 1. 190 × 245 mm. 319 pages. 16 colour plates, 202 black and white illustrations and 14 tables. Price £21.00 paperback. MAPPING: WAYS OF REPRESENTING THE WORLD. By D. Dorling and D. Fairbairn . (Insights into Human Geography Series.) Edited by P. Knox and S. Smith . Addison Wesley Longman Ltd., Harlow, 1997. ISBN 0 582 28972 6. 234 × 155 mm. vii + 184 pages. Price £11.99 softbound. MANUAL OF PHOTOGRAPHIC INTERPRETATION. Second edition. Editor-in-chief W. R. Philipson . American Society for Photogrammetry and Remote Sensing, Bethesda, MD, USA, 1997. ISBN 1 57083 039 8. 285 × 225 mm. xvi + 689 pages. 489 figures, including 87 in colour, and 75 tables. Price for non-members US$124.00. FLATTENING THE EARTH. TWO THOUSAND YEARS OF MAP PROJECTIONS. By J. P. Snyder . University of Chicago Press, Chicago and London, 1997. ISBN 0 226 76747 7. 235 × 165 mm. xviii + 365 pages. 173 figures and 6 tables. Price £15.95 paperback. EUROPEAN SPACE DIRECTORY 1998. Thirteenth edition. Edited by D. Shirvanian . Sevig Press, Paris, 1998. ISSN 0765–0574. 270 × 210 mm. 324 pages. 1 figure and 43 tables. Price FFr965 paperback. TERMINOLOGIE DE TÉLÉDÉTECTION ET PHOTOGRAMMÉTRIE. By S. Paul , G. Ducher , I. Jobard , C.-H. Latarche and M. Lenco . Conseil International de la Langue Française, Paris, 1997. ISBN 2 85319 270 9. 247 × 168 mm. 455 pages. Price FFr250 hardback. AUTOMATIC EXTRACTION OF MAN-MADE OBJECTS FROM AERIAL AND SPACE IMAGES (II). Edited by A. Gruen , E. P. Baltsavias and O. Henricsson . Birkhäuser Verlag, Basel, 1997. ISBN 3 7643 5788 6. 238 × 171 mm. ix + 393 pages. 241 figures and 25 tables. Price CHF128 casebound.     

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.     

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.     

BOOK REVIEWS

Book review in this Article GIS DATA CONVERSION: STRATEGIES, TECHNIQUES AND MANAGEMENT. Edited by P. Hohl . Onword Press, Santa Fe, 1998. ISBN 1 56690 175 8. 180 × 228 mm. xiii + 416 pages. Illustrated. Price £33.95 paperback. GEOGRAPHICAL INFORMATION SYSTEMS FOR ECOLOGY: AN INTRODUCTION. By R. Wadsworth and J. Treweek . Addison Wesley Longman Ltd., Harlow, 1999. ISBN 0 582 24652 0. 156 × 234 mm. xiii + 184 pages. Four colour plates, appendix, references and index. Price £14.99 paperback. GENERATION OF DIGITAL ELEVATION MODELS THROUGH SPACEBORNE SAR INTERFEROMETRY. Remote Sensing Series, Volume 30. By D. Small . Remote Sensing Laboratories, Department of Geography, University of Zurich, 1998. 147 × 207 mm. xvi + 150 pages. 84 figures, including images, and 8 tables. Price SFr 40 paperback. TRIANGULATION. By P. Whitaker . Phoenix House, London, 1999. ISBN 1 816590 80 6. 140 × 200 mm. 272 pages. Price £12.99. OEEPE SURVEY ON 3D‐CITY MODELS. By C. Fuchs , E. G$uulch and W. F$ourstner . PERFORMANCE OF TIE‐POINT EXTRACTION IN AUTOMATIC AERIAL TRIANGULATION. By C. Heipke and K. Eder . OEEPE Official Publication No. 35. Bundesamt für Kartographie und Geodäsie, Frankfurt am Main, 1998. ISBN 3 88648 075 5. 175 × 245 mm. 198 pages. 42 figures, 27 tables and 7 appendices. Price DM47, paperback, plus DM7 for postage and packing and DM20 for foreign exchange charges, if applicable. EUROPEAN SPACE DIRECTORY. Fourteenth edition. Edited by D. Shirvanian . Sevig Press, Paris, 1999. ISSN 0765 0574. 210 × 270 mm. 316 pages. 1 figure and 30 tables. Price FFr990 (£150) paperback. CAMERA AT SEA. THE HISTORY OF THE ROYAL NAVAL PHOTOGRAPHIC BRANCH, 1919–1998. By N. Mercer . Airlife Publishing Ltd., Shrewsbury, 1999. ISBN 1 85310 889 8. 218 × 306 mm. 144 pages, including a 72 page portfolio of colour plates. Price £24.95 hardback. ESSENTIAL DARKROOM TECHNIQUES. Third edition. By J. Eastland . Cassell, London, 1999. ISBN 0 304 35086 9. 190 × 247 mm. 208 pages. 144 figures and 22 tables. Price £18.99 paperback. ADVANCES IN MOBILE INFORMATION SYSTEMS. (MOBILE COMMUNICATIONS SERIES.) Edited by J. Walker . Artech House, Inc., Norwood, USA, 1999. ISBN 0 89006 951 4. 159 × 235 mm. xxi + 468 pages. 104 figures and 42 tables. Price £67 hardback.     

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).     

APPROXIMATE METHODS OF SOLVING NORMAL EQUATIONS

Abstract

My attention has recently been drawn to an article by G. H. Menzies (E.5.R., vi, 46, 474) on this subject. The present note is intended to point out improvements in the Anér method, which he favours, and to refute some of his criticisms of the Relaxation method. References are to page and table numbers in Menzies's paper.     

EXPANSION OF PAPER AS AFFECTING BEARING

Abstract

The problem of the influence of the paper itself on bearings taken off maps or plans has been recently discussed by G. T. M. in this Review (iii, 22, 479). The following alternative method of solving the problem may be of interest; the same figure and symbols are used as in the article mentioned.     

TEMPERATURE ERRORS IN PRECISE TRAVERSING

Abstract

It is assumed that a precise traverse would be used only where triangulation would be impracticable, that an absolute accuracy of I in 100,000 would be required, and that reasonable speed would be necessary.