THE ORTHOMORPHIC PROJECTION OF THE SPHEROID—V

Abstract

To complete the picture, the reader is invited to plough through the derivation of point-to-point working formulae for the remaining projections in common use. The entire field of modern geodetic practice in this subject will then have been covered, and at least as simply, without the usual recourse to the square root of negative numbers or other complex notions.     

THE ORTHOMORPHIC PROJECTION OF THE SPHEROID—IV

Abstract

We now turn to a question which has received much attention of recent years; the possibility of transforming angular and linear field measures to an orthomorphic projection so that the results of a survey may be computed directly in plane Co-ordinates without having to go through the spheroid at all. Initially, orthomorphic projections were introduced into surveying practice for this very object. Over short lines they import so little distortion of angles that minor surveys, whose error of angular measurement is comparable with such distortion, may be reduced in the rectangular co-ordinate system of an orthomorphic projection just as if the earth were flat. But the present application goes far beyond that. We no longer ignore distortions of angles and lengths, but systematically introduce them into the field measures so that work of higher precision and of considerable extent may also be computed and adjusted in plane co-ordinates.     

THE ORTHOMORPHIC PROJECTION OF THE SPHEROID–III

Abstract

In the last instalment we were able to obtain most of the surveyor's projections in common use by applying simple scale conditions to the meridians and parallels. This method of approach naturally suggests that results of some value might be obtained by applying similar conditions to the plane co-ordinate lines. If we do so, we are immediately led to consider curves on the surface known as geodesics, which are the nearest approach to straight lines it is possible to draw on a curved surface. Accordingly, we give some account of these curves for the benefit of surveyors who have not hitherto made their acquaintance.     

A TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID ALTERNATIVE TO THE GAUSS-KRÜGER FORM

Abstract

The excuse for yet another paper on the Transverse Mercator projection, which has already received what should be more than its fair share of space in this Review, can only be that there is a fresh viewpoint to offer. It is the purpose of this paper to show that there are, in fact, two “Transverse Mercator” projections of the spheroid, of which one has hitherto almost escaped notice.     

MATHEMATICAL THEORY OF THE TRANSIT THEODOLITE—II

Abstract

In this paper we shall consider the errors in the measurement of horizontal angles arising from periodic errors of graduation of the horizontal circle, and the effect on such errors of repeating observations of the same angle on different “zeroes”. The question is not only one of interest from the point of view of mathematical and instrumental theory, but it also has practical applications.     

THE (t – T) CORRECTION FOR THE LAMBERT No. 2 (CONICAL ORTHOMORPHIC) PROJECTION

Abstract

I. The present writer has been trying for the past two years to get reasonably easy expressions for the (t – t) correction and the scale factor in the Lambert NO.2 Projection. He succeeded in obtaining a formula for (t – t) in terms of eastings and northings, but, like the author of the articles on “Grid Bearings and Distances on the Conical Orthomorphic Projection” which were published recently in this Review, he came to the conclusion that any such formula is too unwieldy for ordinary use. He then tried to get an expression for (t – t) in terms of latitude and longitude, and has now obtained one by purely empirical methods which seems to work in practice. No proof of this formula is offered, or is available at present, as this is a matter which the writer is content to leave to others with greater mathematical interests and attainments than he possesses.     

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.     

THE RE-TRIANGULATION OF GREAT BRITAIN—III

Abstract

Beacon Lamps.—The design of electric directional projector used has been altered slightly as the triangulation has progressed, but for the sake of simplicity it is proposed to describe in detail only the final form, which is now a standard article manufactured by Messrs Cooke, Troughton, & Simms.     

MATHEMATICAL THEORY OF THE TRANSIT THEODOLITE—I

Abstract

The following discussion of the mathematical theory of the transit theodolite adds, perhaps, nothing new to instrumental theory. It does, however, collect together matter which is scattered about in different text-books or, indeed, perhaps, in the same book, and may thus be of service to those interested. It was not prepared in the first place for publication in this Review, but the editor, having seen it, thinks that it may be of use to some readers and has thus asked for my permission to publish it.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION—II

Abstract

There are numerous possibilities in a Six-point Countersection. The example exhibited in Fig. 5 shows no more than one such concatenation. Here two stations, A and B, are the, only known positions in the neighbourhood; but they are over 29 miles apart and are not mutually visible.     

THE TECHNIQUE OF QUASI-LOSSLESS COMPRESSION OF THE REMOTE SENSING IMAGE

1　ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆａｅｒｉａｌａｎｄｓｐａｃｅｒｅｍｏｔｅｓｅｎｓｉｎｇｔｅｃｈｎｉｑｕｅ,ｔｈｅｄｉｇｉｔａｌｃａｍｅｒａｈａｓｂｅｅｎｅｘｐｌｏｒｅｄ ,ａｎｄｍａｐｐｉｎｇｅｘｐｅｒｉｍｅｎｔｓｗｉｔｈｔｈｉｓｋｉｎｄｏｆｄｉｇｉｔａｌｉｍａｇｅｓａｒｅｂｅｉｎｇｐｒｏｃｅｓｓｅｄａｓｔｈｅｒｅｇｕｌａｒｍｏｄｅｏｆａｒｅｏｐｈｏｔｏｇｒａｍｍｅｔｒｙ .Ｏｎｔｈｅｏｔｈｅｒｈａｎｄ ,ｔｈｅｔｅｃｈｎｉｑｕｅｏｆｉｎｔｅｇｒａｔｉｏｎｏ…     

THE RE-TRIANGULATION OF GREAT BRITAIN IV—BASE MEASUREMENT

Abstract

Accuracy and consistency in surveying are almost synonymous. It is true that no very great degree of precision in angular or linear measurement can be utilized in our final paper publications, even on the largest scales: all we need is an assurance that the results of further work, in the same or in adjoining areas, shall be in sympathy with antecedent measurement, so as to avoid the necessity for assigning several positions to the same point.     

ON THE EVALUATION OF DEFLECTIONS OF THE VERTICAL USING FFT TECHNIQUE

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｓｔＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍ (ＦＦＴ)ｔｅｃｈｎｉｑｕｅｉｓａｖｅｒｙｐｏｗｅｒｆｕｌｔｏｏｌｆｏｒｔｈｅｅｆｆｉｃｉｅｎｔｅｖａｌｕａｔｉｏｎｏｆｇｒａｖｉｔｙｆｉｅｌｄｃｏｎｖｏｌｕｔｉｏｎｉｎｔｅｇｒａｌｓ.Ｔｈａｎｋｓｔｏｔｈｅｇｏｏｄｃｏｍｐｕｔａｔｉｏｎｅｆｆｉｃｉｅｎｃｙ ,ｔｈｅＦＦＴｔｅｃｈｎｉｑｕｅ ,ｉｎｔｈｅｍｉｄ＿1 980ｓ ,ｂｅｇａｎｔｏｆｉｎｄｗｉｄｅｓｐｒｅａｄｕｓｅｉｎｇｅｏｉｄｄｅｔｅｒｍｉｎａｔｉｏｎ ,ｗｈｅｎｃｏｍｐａｒ…     

THE SEVENTIETH ANNIVERSARY OF SOVIET CARTOGRAPHY—SOME ACHIEVEMENTS AND TASKS OF RESTRUCTURING

This article, based on a presentation to the All-Union Conference on Cartography in the Era of the Scientific and Technological Revolution in November 1987, contains an eminent Soviet cartographer's evaluation of the state and development of Soviet cartography and his impressions concerning the tasks which lie ahead over the era of economic restructuring and social change. Translated from: Izvestiya Akademli Nauk SSSR, seriya geograficheskaya, 1988, No. 3, pp. 17-21 by Jay K. Mitchell, PlanEcon, Inc., Washington, DC 20005.     

KING GEORGE ISLAND GIS (KGIS) PROJECT OF WGGGI——A STATE OF THE ART

1　ＩｎｔｒｏｄｕｃｔｉｏｎＡｇｅｏｇｒａｐｈｉｃｉｎｆｏｒｍａｔｉｏｎｓｙｓｔｅｍ (ＧＩＳ)ｉｓｕｓｅｄｔｏｃｏｌｌｅｃｔ,ｄｉｓｐｌａｙ ,ａｎａｌｙｓｅａｎｄｍａｎａｇｅｇｅｏｇｒａｐｈｉｃａｌｌｙｒｅｌａｔｅｄｉｎｆｏｒｍａｔｉｏｎ .Ｉｔｉｓａｎｉｍｐｏｒｔａｎｔｔｏｏｌｔｏｉｎｔｅ ｇｒａｔｅｓｐａｔｉａｌｄａｔａａｃｑｕｉｒｅｄａｔｄｉｆｆｅｒｅｎｔｓｃａｌｅｓ,ｔｉｍｅｓａｎｄｆｏｒｍａｔｓ.ＧＩＳｉｓａｍｅａｎｓｏｆ1 )ｅｘｃｈａｎｇｉｎｇｉｎｆｏｒｍａｔｉｏｎｂｅｔｗｅｅｎｃｏｕｎｔｒ…     

THE ATTRACTION OF THE “COMPENSATION” ON THE PRATT HYPOTHESIS

Abstract

In the last issue there was given an outline of modern theories on crustal equilibrium. The assumption as to uniform attenuation of matter beneath an elevated station suggests that an explanation of a means for calculating this “compensation” would be desirable; the complete technical procedure used by those actually engaged on work of this nature could be described by themselves alone.