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.     

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.     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”.     

MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. Computation of a minor triangulation as if it were executed on a plane surface of course ignores spherical excess, an omission not strictly rigorous so far as azimuths are concerned. Further the reduction of such a triangulation to a system of plane coordinates again assumes that the earth's surface is a plane.     

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.     

THREE YEARS AND MORE OF THE RISING SUN or A COLONIAL SURVEY DEPARTMENT UNDER A NEW MASTER

Abstract

The late war has been responsible for many unusual situations—not the least of which was that of certain British Colonial Surv1ey Offices passing under the control of an Asiatic Invader, and it is thought that the story of one of them—the Survey Department of Malaya—will not be without interest to readers of this Review.     

ANGLO-ETHIOPIAN (SOMALILAND) BOUNDARY COMMISSION, 1932-5

Abstract

Azimuth.—The method was that of star altitudes in the prime vertical, except at X. 34 where hour angles on the P.V. were observed. At B.P. 79 and 99, NE. Terminal, and X. 12 and 34, the measures were made by Major Godfrey-Faussett or Capt. Taylor with the 8-inch C.T. & S. micrometer theodolite; and at all other stations by Capt. Taylor with the Tavistock theodolite Y. 2304.     

ADJUSTMENT OF SIMPLE FIGURES: III

Abstract

5. Practical Example.—From Fig. 4 it is evident that the net of this example is made up of three polygons A, Band C, with no isolated triangles.     

SOUTH AND EAST AFRICA AND THE INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS

Abstract

THE resolutions and pious hopes (væux) passed by the International Union of Geodesy and Geophysics at Edinburgh in September 1936 have just been circulated in a formidable document of 8 pages and XXIX commandments. Of these, two affect the Cape-to-Cairo line particularly and they seem to deserve special study. The first of these, Number III—on systems of Projections—applies the meridional strips of the Transverse Mercator Projection apparently to all maps, topographical as well as cadastral.     

CRUSTAL EQUILIBRIUM

Abstract

1. Some Preliminary Considerations.—Let it be supposed that an iceberg is captured by an ice-field. It will be assumed that the field can be packed, either by opposing currents or by pressure against a land mass on one side. Compared with the vertical dimension of the berg the thickness of the field will be comparatively small.     

ADJUSTMENT OF SIMPLE FIGURES—II

Abstract

3. Adjustment of a Polygon.—The adjustment of a polygon by the method of the preceding paragraph leads to results similar to that for a quadrilateral, although not quite so simple, since there are two correlatives, k₁ k₂ , for deducing the corrections.     

SARAWAK LANDS AND SURVEY DEPARTMENT

Abstract

Financial.—The revenue collection for the year was 479,591.75, consisting of Lands and Survey Revenue 356,087.52 and Mining Revenue 123,504.23.     

SARAWAK LANDS AND SURVEY DEPARTMENT: ANNUAL REPORT FOR 1937

Abstract

General.—The excess of Revenue over Expenditure reached the unprecedented figure of 252,867; a net increase on 1936 of 23,018 in spite of a fall of 20,131 in Mining Revenue.     

GRID BEARINGS AND DISTANCES ON THE CONICAL ORTHOMORPHIC PROJECTION

Abstract

Scale Correction Factor at a Point in Terms of X and Y.—Let dσ be a small line element of the curve ACB on the plane and ds the corresponding line element on the spheroid.     

THE PROJECTIVE TRANSFORMATION IN AERIAL SURVEYING

Abstract

4.3. Having found s we may proceed to obtain the coordinates of the air station. This is the vertex of a pyramid, the base edges being of lengths a, b, c and the opposite edges measuring u, v, w respectively. Let h be the distance of the vertex from the plane of the base, and suppose d, e₁ e₂, e₃ are respectively twice the areas of the base and of the oblique faces in order.     

SARAWAK LANDS AND SURVEYS DEPARTMENT: ANNUAL REPORT FOR 1935

Abstract

General.—During the year the Committee of Administration reviewed the policy and administration of the Department and recommended no change.     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

THE PRIMARY TRIANGULATION OF SARAWAK

Abstract

Historical.—When my predecessor, Mr N. A. Middlemas, was seconded from the Survey Department of Malaya in 1925, the survey framework of the State was technically negligible.     

SARAWAK LANDS AND SURVEY DEPARTMENT ANNUAL REPORT FOR 1936

Abstract

General.—The Surplus of Revenue over Expenditure was again a record, as the following figures show: 1933, 4,538;1934, 185,387; 1935, 196,669; 1936, 225,148.     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.