TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

THE COOLING OF THE EARTH BY CONVECTION AND SOME OF ITS CONSEQUENCES

Abstract

In this Review (24, 68, 1937) attention was drawn to the need, in considering isostasy, of recognizing the existence of two separate weak layers, i.e. layers in which material can flow horizontally. One of these is a deep layer under both oceans and continents, the other being a layer of plastic basalt, immediately under the continents only, in which mountain ranges and other local surface masses are compensated. That suggestion formed part of a wider theory which has been developed in recent articles in the Pan-American Geologist. A brief review of that theory may be of interest.     

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.     

TRIGONOMETRIC HEIGHTS AND REFRACTION

Abstract

In the past there has been considerable discussion on the above subject in this Review. There is a bibliography at the end of this article in which the full titles of previous articles are given. For brevity, reference to them in the following text is made by number only. Recently, Gulatee summarized present knowledge and asked how other Survey Departments dealt with this matter. Consequently, it was considered that it would be helpful to set out in detail the procedure adopted by the Directorate of Colonial Surveys for obtaining trigonometric heights, with particular reference to primary and seoondary chains and nets.     

THE ENGINEER SURVEYOR

Abstract

Survey Training for the Civil Engineer at the University has been discussed in four articles in the Review. (R. N. Ray, M.A., xii, 89, 104–110; H. Biesheuvel, B.Sc., xii, 90, 159–165; A. Stephenson, O.B.E., M.A., F.R.I.C.S., xii, 91, 217–222; K. R. Peattie, B.Sc., Ph.D., A.R.T.C., A.M.I.C.E., xii, 94, 376–379.) Cost of equipment for a large class and limitation of time in an already heavily loaded curriculum prevent the student acquiring enough training to undertake the survey work required on alarge engineering scheme. The schemes of training described in the four articles are greatly to be admired and it is hard to see how any improvement can be made.     

THE SEVEN-LENS AIR-SURVEY CAMERA

Abstract

By kind permission of the Editor of the Royal Engineers Journal, this paper has been adapted from the article by the Author in the issue of June 1937 (Vol. li, pp. 217–223). We are also indebted to the Editor for placing generously at our disposal the blocks used to illustrate the paper.     

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).     

Terrain radiometric calibration of airborne UAVSAR for forested area

In the field of biomass estimation, terrain radiometric calibration of airborne polarimetric SAR data for forested areas is an urgent problem. Illuminated area correction of σ -naught could not completely remove terrain features. Inspired by Small and Shimada, this paper tested gamma-naught on one mountainous forested area using airborne Uninhabited Aerial Vehicle Synthetic Aperture Radar data and found it could remove most terrain features. However, a systematic increasing trend from far range to near range is found in airborne SAR cases. This paper made an attempt to use the relationship between distance to SAR sensor and γ-naught to calibrate γ -naught. Two quantitative evaluation methods are proposed. Experimental results demonstrate that variation of γ -naught can be constrained to a limited extent from near range to far range. Since this method is based on ground range images, it avoids complicated orthorectification.     

HORIZONTAL ANGLES IN TRIANGULATION: SOME PRACTICAL SUGGESTIONS REGARDING THEIR OBSERVATION AND ADJUSTMENT

Abstract

MR. RAINSFORD'S paper on Directions versus Angles in the Least Squares Adjustment of Triangulation in the October 1950 issue of the E.S.R. (x, 78, 353–366) has raised some interesting points and has prompted me to put on paper my own views and some of the results of my own experience.     

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.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION

Abstract

Mr. Rainsford's paper in E.S.R. No. 78 establishes as thoroughly as one can wish by computational example that there is little to choose in relative accuracy between direction adjustment and angle adjustment, and that the deciding factor is really ease and speed of computation.     

DISTORTING A NETWORK TO FIT CONTROL POINTS: AN ALTERNATIVE EXPRESSION FOR THE SCHOLS ADJUSTMENT

Abstract

Another form of Mr. Lauf's expression for a conformal adjustment of a system of coordinated points may be of interest. These are assumed to be already in harmony with i control points and are to be brought into agreement with j further points. (Mr. Lauf deals explicitly in his paper with the special case i = 2, j = 1, but he adumbrates a general solution.)     

DEVIATION OF THE VERTICAL. DISCUSSION

Abstract

The following is a report of the discussion on the paper by Mr. A. R. Robbins on “Deviation of the Vertical” which was read at a meeting of the Land Surveying Division of the Royal Institution of Chartered Surveyors held on Tuesday, 12th December, 1950, and which was published in the January issue of this Review (xi, 79, 28–36).     

TWO PROBLEMS OF RESECTION

Abstract

That admirable annual, The Surveyor (Ceylon), was generously forwarded to us some months ago. In this issue, vol. 2, no. 4, p. 93, there is given the solution of a question on resection in an examination paper. Since the solution appears rather laboured and the problem is interesting in itself and by no means valueless, it seems not out of place to attempt a simpler and more obvious answer.     

EXPANSION OF PAPER AS AFFECTING AREA

Abstract

For the sake of the junior reader we may repeat an old and simple investigation. Let us suppose that the paper on which a map is printed undergoes a regular expansion p in one direction, say the X direction, and another regular expansion q in the Y direction, perpendicular to the former; it is required to know the effect of these expansions on the area of any parcel on the map. Note that, so far as the mathematics are affected, X and Y are not necessarily parallel to the margins of the sheet; we shall take them here as axes of any rectangular coordinate system. The symbols p and q are regarded as ratios, so that 100p and 100p represent the percentage expansions; if the paper contracts instead of expanding, no more is necessary than to change the sign.     

The free nonlinear boundary value problem of physical geodesy

Summary Within potential theory of Poisson-Laplace equation the boundary value problem of physical geodesy is classified asfree andnonlinear. For solving this typical nonlinear boundary value problem four different types of nonlinear integral equations corresponding to singular density distributions within single and double layer are presented. The characteristic problem of free boundaries, theproblem of free surface integrals, is exactly solved bymetric continuation. Even in thelinear approximation of fundamental relations of physical geodesy the basic integral equations becomenonlinear because of the special features of free surface integrals.     

SURVEYING TECHNIQUES FOR NIGERIAN UNIVERSITY STUDENTS

Abstract

Several articles which deal with instruction in surveying at the university have appeared recently in the E.S.R., notably ones by P. N. Ray (xii, 89, 104–110), A. Stephenson (xii, 91, 217–222)and K. R. Peattie (xii, 94, 376–379). Particular attention is given in them to courses for engineering students. It may be of interest to readers of this Journal to hear of a survey course for geography students. Although the pattern varies at different universities, it is common to find instruction, for all geography students, in simple surveying, with practice in chain and compass surveys and the use of the plane table, while Honours students may select surveying at a late stage in the course as one of the branches of the subject in which they are to specialize. Below are set out details of a course given at University College, Ibadan, Nigeria.     

TRANSVERSE MERCATOR FORMULAE

Abstract

The Transverse Mercator Projection, now in use for the new O.S. triangulation and mapping of Great Britain, has been the subject of several recent articles in the “Empire Surpey Review. The formulae of the projection itself have been given by various writers, from Gauss, Schreiber and Jordan to Hristow, Tardi, Lee, Hotine and others—not, it is to be regretted, with complete agreement, in all cases. For the purpose for which these formulae have hitherto been employed, in zones of restricted width and in relatively low latitudes, the completeness with which they were given was adequate, and the omission of certain smaller terms, in the fourth and higher powers of the eccentricity, was of no practical importance. In the case of the British grid, however, we have to cover a zone which must be considered as having a total width of some ten to twelve degrees of longitude at least, and extending to latitude 61 °north. This means, firstly, that terms which have as their initial co-efficients the fourth and sixth powers of the longitude ω (or of y) will be of greater magnitude than usual, and secondly that tan² ? and tan⁴ ? are likewise greatly increased. Lastly, an inspection of the formulae (as hitherto available) shows a definite tendency for the numerical co-efficients of terms to increase as the terms themselves decrease—e.g. terms in η⁴, η⁶, etc.