ROUTINE CADASTRAL TRAVERSING

Abstract

In the table appended there are given statistics of some recent ordinary traverses in the Gold Coast Colony. These have been executed by European (E) or African (A) surveyors, departmental (D) or licensed (L). They apply to Acquisitional, Concessionary, and Proprietary Surveys of various classes of property. The traverses consist either of self-closing circuits (C), or of circuits closing on lines of fixed length and bearing (F). The equipment comprises a theodolite, steel band, and temporary wooden pegs carrying vertical, partially driven nails as centring marks. The table is self-explanatory with the exception of the final column, where the significance of “K” will perhaps be explained by some member of the Department.     

TRAVERSE ADJUSTMENT: WHY NOT LEAST SQUARES?

Abstract

In the above article by Mr H. L. P. Jolly published in a previous issue (E.S.R., vol. iv, no. 28) the author, after referring to the precision of the Nigerian traverses, makes the statement that measurements of the highest accuracy are worthy of the best possible methods of adjustment. But this argument cuts both ways. For in general the greater the accuracy of measurement the smaller will be the ultimate misclosure to be eliminated; so that different methods of adjustment will produce smaller and smaller variations in the corrections, until in the limit when there is no error we should obtain the same result however much latitude we permitted in the adjustment.     

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.     

SOME NOTES ON THE ADJUSTMENT OF TRAVERSES

Abstract

It has now become a truism that angles in traverses are observed with a far greater accuracy than the sides, and this applies to all categories of traverse work: precise, transit-and-tape, tacheometric traverses, etc. The result of this is that the effect of angular errors on misclosures in co-ordinates is sometimes so small when compared with that of linear errors that it may be considered as negligible.     

Maps > Representation

Abstract

Colour is considered a key means of expression for use in cartographic works. This is because colours and the relations among them influence not only the aesthetic impression a map creates but also its overall utility. In addition to Newton’s spectral colour theory, today theories with origins in artistic technique are gaining ground in cartography. This article introduces J. Itten’s colour theory (first published in 1961 in The Art of Colour [Kunst der Farbe]) with special attention given to his concept of seven colour contrasts. The article also discusses the suitability and unsuitability of their application in practical cartography, and it contributes original examples employing thematic maps, a discipline with broad possibilities for the application of these inventive methods by today’s mapmakers.     

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.     

FIRST-ORDER TRAVERSES IN CEYLON

Abstract

In the last three years about 250 miles of “precise” traverse have been surveyed in this country to provide control for detail surveys. A brief account of the results may be of general interest. The traverses are situated where trig. points are far apart, and the cost of subsidiary triangulation would have been excessive on account of the flat nature of the country.     

GRID BEARINGS AND DISTANCES ON THE CONICAL ORTHOMORPHIC PROJECTION

Abstract

When computing and adjusting traverses or secondary and tertiary triangulation in countries to which the Transverse Mercator projection has been applied, it is often more convenient to work directly in terms of rectangular co-ordinates on the projection system than it is to work in terms of geographical coordinates and then convert these later on into rectangulars. The Transverse Mercator projection is designed in the first place to cover a country whose principal extent is in latitude and hence work on it is generally confined to a belt, or helts, in which the extent of longitude on either side of the central meridian is so limited as seldom to exceed a width of much more than about 200 miles.     

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.     

LONG LINES ON THE EARTH: VARIOUS FORMULAE

Abstract

Extensions were given for all these formulae, so that precise results may now be obtained even for lines of 500 miles in latitudes above 45°. The present instalment gives the extension of the Clarke approximate (sic) formulae to lines of 500miles, with a practical example and general conclusions: the great advantage of the method is that 8-figuretables sufficeto give rigorous results.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION

Abstract

Cadastral Traversing.—For cadastral purposes traverses are now being executed with an accuracy wholly unnecessary for even large topographical scales. But since “accuracy” varies from a mile to a micron, according to the viewpoint of the observer, it is advisable to exhibit a cadastral traverse, care being taken that it is not an example of that not very uncommon occurrence in which fortuity apes precIsIon. If the accuracy of the example is somewhat unusual, it can be said with assurance that it is not very unusual.     

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 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.     

EARLY MEASUREMENTS OF ARC IN ‘IRAQ

Abstract

In a tale, delightfully told in vol. ii, no. 8, pp. 121–2 of this Review, Mr. Kitching revealed how he was called upon to assist in determining the length of an Arab mile. In the notes following the story a reference was made to measurements of arc carried out in the ninth century A.D. The following notes add some more details to those already given. The full table of the Arab units of length is given below; in the reference above, one step was left out.     

SURVEY IN THE GREAT WAR

Abstract

Artillery Survey.—Included in the term “Artillery Survey are two distinct problems, the first that of determining the “line” and “range” at which fire should be opened, and the second that of laying the gun in the required line. To appreciate these problems it. is necessary to know a little about the technique of gunnery, and for the benefit of those who have no acquaintance with the subject the following brief résumé may be given.     

TIDAL OBSERVATIONS IN CEYLON

Abstract

I. IN a Report which appeared in the Empire Survey Review, vol. i, no. 5, a short account was given on pp. 227-8 of the tidal observations which had been taken in Ceylon up to that time, with special reference to the selection of a datum for the geodetic levelling of the Island. The automatic tide-gauges at Colombo and Trincomalee were maintained in action till January 1934, giving five years of simultaneous continuous records of sea-level. The resul ts of an analysis of these observations may be of interest to readers. Where necessary, statements and figures appearing in the Report mentioned above will be repeated here, to make this account complete in itself and to avoid troublesome cross- reference.     

LONG LINES ON THE EARTH: THE DIRECT PROBLEM

Abstract

19. Formulae.—In Nos. 6, vol. i, and 9, vol. ii, pp. 259 and 156, there has been described a new method for dealing with long geodesics on the earth's surface. There the so-called “inverse” problem has claimed first attention: given the latitudes and longitudes of the extremities of a geodesic, to find its length and terminal azimuths. It remains to discuss the “direct” problem : a geodesic of given length starts on a given azimuth from a station of known latitude and longitude; to find the latitude and longitude of its extremity and the azimuth thereat. The solution of this direct problem demands a certain recasting of the formulae previously given. In order of working the several expressions now assume the forms below.     

A TRIGONOMETRICAL UPSET

Abstract

If the geographical co-ordinates, Φ₀, L 0, and the azimuth A ₀ at a station O of a triangulation undergo corrections, ?Φ₀, ?L ₀ and ?A ₀, the geographical co-ordinates, Φ, L, and the azimuth A have to be re-computed for all the vertices throughout the whole triangulation. This is a tedious operation. It may be vastly simplified, however, by the employment of differential formulae. The derivation of these formulae would consume considerable space, so that the results alone are given here.