LEAST-SQUARE ADJUSTMENTS OF TRIANGULATION DIRECTIONS VERSUS ANGLES

Abstract

IT has been assumed in the past that because angles for triangulation are usually observed by the direction method, therefore it must be more correct theoretically to perform the least-square adjustments by directions rather than by angles. It is fairly obvious that an adjustment of the same figure by directions will not give the same result as an adjustment by angles: the unknowns in each case are different and the number of directions is usually about 25 per cent. greater than the number of angles for the same figure. Strictly, the least square method is only applicable to observations from which all systematic errors have been eliminated, and in which the remaining errors are truly accidental. It is generally safe to assume that most survey errOlS consist of a random and a systematic part. Rarely, if ever, is it possible to state that all systematic error has been eliminated, strive how we may to take all precautions against it.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION: DIRECTIONS VERSUS ANGLES

Abstract

This paper continues the discussion started in an article of the same title (E.S.R., ×, 78, :353-66), on which a further letter was written in October, 1952. The amount of computation required originally was very considerable, and it was obviously impossible to publish it all. The recent letter was necessary to answer the suggestion that the agreement between errors put in and corrections obtained from the L.S. solution was not very close. It seemed sufficient to give the list of errors and corrections, leaving readers to judge for themselves. The correlation coefficient from the two sets of figures was 0.78, which looked quiteg90d. Unfortunately, it was not realized before that corrections from a L.S. solution cannot, legitimately, be compared with errors put in on directions unless a station correction is first applied to the errors to make the sum of the errors at each station equal to zero. This is one of the points about the direction method of adjustment which is not very easy to understand.     

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.     

TRIANGULATION BEACONS

Abstract

Reports, appearing from time to time on the results of completed triangulation, show a variety of methods of construction of beacons. These range from temporary brushwood and calico signals to something of a more permanent nature. No doubt the purpose of the work, the type of country, local conditions, methods of observing, and finance, all enter into a decision as regards the necessity for the type of beacon to be used.     

MINOR TRIANGULATION

Abstract

When Clarke had written finis to his account of the Principal Triangulation he and O'Farrell (his famous chief computer) framed those simple methods of computation which were to be characteristic of the work of the “tertiary computers”. The tertiary triangulation, resting upon an adjusted primary and a rather poor-class secondary, covered the country at distances of a little over a mile between points. Points were chosen not so much for visibility as for convenience of chaining.     

TRIANGULATION IN TANGANYIKA TERRITORY

Abstract

This is a résumé of the triangulation work completed within the Mandated Territory of Tanganyika, formerly German East Africa. The period covered includes the German Occupation down to 1915 and also the Colonial Office Administration from 1919 to the present day.     

AERIAL RECONNAISSANCE FOR TRIANGULATION

Abstract

Since 1929 much of the primary triangulation carried out by the Geodetic Service of Canada has been preceded by an aerial reconnaissance of the areas: during this reconnaissance a tentative selection is made of station sites, and likely lines of sight are indicated. Varied types of topography have been covered—mountainous, rolling, flat wooded, mountain valleys. In most cases there were three common factors: the areas were well watered with lakes and rivers which permitted low flying in safety with pontoonor skii-equipped planes, ground transportation was difficult, and no contour maps existed. In some of the areas existing maps were very incomplete; of a few, reconnaissance aerial maps were available in which the planimetry was good; the better the map the easier the aerial reconnaissance. In all cases it was considered necessary that the air operations be checked by ground visits to the tentatively selected stations.     

THE EARLIEST GEODETIC TRIANGULATION

Abstract

WILLEBRORD SNEL VAN ROIEN, the “learned Snellius,” was born in 1580 at Leyden, where his father Rudolf was Professor of Science. He naturally proceeded to the university, and made such rapid progress under his tutor, L. van Ceulen, that he was already in 1600 delivering lectures on Ptolemy's “Almagest.” With his mind developed by travel in Europe, including a residence of some duration at Prague, where he was associated with Tycho Brahe before that great observer's death in 1601 and with the still more eminent Kepler as another of Brahe's pupils, he had acquired such scholarship as to publish in 1608 a daring reconstruction of the defective work, “De sectione determinata,” by Apollonius of Tyana. This was the year of his marriage to Maria de Lange, daughter of the Burgomaster of Schoon.     

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.     

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.     

A TRIANGULATION SYSTEM FOR NEWFOUNDLAND

Abstract

Following a request from the Commission of Government of Newfoundland, the Canadian Government has consented to an arrangement whereby the Geodetic Survey of the Department of the Interior will assist the Island Government in laying down two main nets of triangulation as the basis for the survey development of Newfoundland. The completion of the final practical details was reached in Ottawa recently, and the work, it is expected, will extend over a period of five years.     

AERIAL TRIANGULATION FOR CONTROL PROVISION

The author has been involved in aerial triangulation, in various capacities, for some 27 years. This period has seen some very significant changes worthy of remark. This essay is a general review of that period; it does not go into detail and no formulae are quoted. The idea has been to look at the more notable developments, skipping the earlier and well documented period in favour of more recent times, particularly as regards the references. The objective will have been achieved if it provides a starting point, indicating further reading, for those who wish to study the subject in greater depth.     

THE YELL AERIAL TRIANGULATION EXPERIMENT

The paper considers the experimental comparison of a method of aerial triangulation in previous experimental use by Eden and the standard Ordnance Survey method using stereocomparators. The accuracy of plan fixations was high by both methods, with Eden's method providing the better result. A comparison is made of the times taken under experimental conditions for both methods.