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1.
《测量评论》2013,45(96):50-58
Abstract14. General. Except for one or two located by an auxiliary triangle or by ray and distance, every point is fixed by a fully observed triangle of which the base is a pair of pillars. To justify the larger and more expensive party required for this method a high rate of observation must be maintained. The two observing periods available each day in the northern Sudan are the 3–4 hours starting just before dawn, and the 2–3 hours which end with sunset. Since moveluent in the cultivation is generally slow and on foot or by donkey, the longer morning period is best used for observing the single angles at each of a series of points there. The shorter and hotter afternoon period may then be used for observing the rounds of angles at each of a pair of pillars, which can normally be reached or at least approached by car. Asfar as possible the points observed to from these pillars will be those occupied on either the preceding or following morning, so that the triangles can be closed as soon as possible. Up to nine triangles have been closed in a day. 相似文献
2.
《测量评论》2013,45(9):167-168
AbstractIn the reduction of geodetic triangulation the computation of the spherical excess of each triangle is of great importance; for unless the amount of spherical excess is known, the accuracy with which the angles have been observed cannot be assessed, nor can the triangle itself be computed by the simple formulae applicable to plane triangles. 相似文献
3.
《测量评论》2013,45(66):166-174
AbstractThe computation of geographical coordinates in a geodetic triangulation is usually carried out using Puissant's method, in which the assumption is made the sphere radius ν (the radius of curvature of the spheroid perpendicular to the meridian) not only touches the spheroid along the whole small circle of latitude ?,but also, since ρ (the radius of curvature in meridian) is very nearly equal to ν it makes such close contact with the spheroid that the lengths of sides and angles of a geodetic triangle may be considered identical on both sphere and spheroid. 相似文献
4.
《测量评论》2013,45(78):353-366
AbstractIT 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. 相似文献
5.
《测量评论》2013,45(83):219-223
AbstractMr. Rainsford's article on “Least Square Adjustments of Triangulation: Directions versus Angles” in the Empire Survey Review No. 78, Vol. x, October 1950, leads to many speculations and interesting results. I try to show here, how, by assuming artifices to simplify the results, weights may be assigned to angles derived from directions so that the results of adjustment by angles, with these weights, will be the same as the adjustment by directions, all of equal weight. 相似文献
6.
《测量评论》2013,45(36):364-368
AbstractThe method to be described consists of the measurement of a short base and the computation of the distances to various points, to which rays have been drawn on a plane table. The angles at the two ends of the base are observed with a theodolite. This method will be referred to as the “Short Base Method”. 相似文献
7.
《测量评论》2013,45(72):90-92
AbstractWhen developing the argument leading to the stereographic solution of the spherical triangle and its application to field astronomy (Empire Survey Review, Vol. 2, No. 10, October, 1933, p. 226) A. J. Potter rendered a very useful service in demonstrating how proofs of the two practically useful properties of the stereographic projection can be provided along lines that demand no more than simple geometry in their development. The proof advanced for the unique property that any circle on the. sphere remains a circle in projection is at once simple and complete; but in the attempt to prove that the projection is orthomorphic in the sense that angles everywhere remain true there is the difficulty that the argument was developed for what must be regarded as a special case in that the point was located on the great circle through the origin of the projection normal to the plane of the projection. Treatment of the problem along similar lines for other points away from the central meridian does not seem to admit of such ready solution and the alternative approach suggested here, while still not demanding. anything beyond simple geometry for its understanding, affords a proof for a general case. 相似文献
8.
《测量评论》2013,45(20)
AbstractThe usual method employed is to plot or to compute the traverse from each end; the poin t having the same coordinates in each route is the station where the gross angular error occurred. There is, however, a method of finding the error by plotting the traverse one way only. Let us consider the traverse having the known terminals A B (see Fig.). Suppose that the error occurred at the point P and that the final point obtained (plotting the traverse from A) was B′ in place of the correct point B. We can easily see that the triangle PBB′is isosceles, and that therefore a straight line bisecting BB′at right angles will meet the traverse in the required point P. 相似文献
9.
《测量评论》2013,45(54):311-314
AbstractThere has always been a marked difference of opinion on the relative merits of the methods of bearings and of angles as applied to triangulation, though it is probable that the majority of writers prefer the method of bearings for first-order work. The subject was mentioned in a recent issue of this Review (vii, 47, 19). 相似文献
10.
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. 相似文献
11.
YAO Jili XU Yufei XIAO Wei 《地球空间信息科学学报》2007,10(3):173-176
Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick. 相似文献
12.
《测量评论》2013,45(58):152-153
AbstractIn vol. iv, nos. 29 and 30, of the E.S.R., there appeared an article by Mr. D. R. Hendrikz on the “Adjustment of the Secondary Triangulation of South Africa”. He shows that, in applying the Schols method of orthomorphic transmission to the adjustment of a secondary net to a primary triangle, the secondary sides suffer small displacements. 相似文献
13.
《测量评论》2013,45(1):31-33
AbstractThe figure which follows shows the geometrical solution of Simple Resection by Cassini in 1669, two years before the Collins solution. It is clearly the geometrical illustration of the Delambre (1786) solution; for db = b cosec β, dc = c cosec γ and the angle QAR is known, being BAC + β + γ ? 180°. Hence the Delambre solution-that in most common use to-day—reduces to a triangle in which two sides and the contained angle are given, as has been mentioned elsewhere. 相似文献
14.
《测量评论》2013,45(9)
AbstractThe following method will be found better and quicker than the usual logarithmic process in computing the co-ordinates of intersected points in minor triangulation and traverse work. Let A and B be two stations whose co-ordinates (x 1 y 1), (x 2 y 2) are known. Let P be an intersected point whose co-ordinates (x, y) we wish to determine. Let α and β be the observed angles at A and B respectively. 相似文献
15.
《测量评论》2013,45(26):223-225
AbstractDURING the course of his work a surveyor often has to solve a right-angled triangle in which one side is very small in comparison with the two others. As the orders of magnitude of the sides in such a triangle differ so widely, a simplified formula can be substituted for that of Pythagoras. 相似文献
16.
《测量评论》2013,45(30):462-466
AbstractThe fixation of Minor Triangulation in a Primary system does not, in general, warrant rigorous adjustments of figures; less laborious methods are desirable. For Secondary work a least square adjustment to approximate coordinates is quite sufficient, while, for Tertiary, graphical solutions are amply accurate. Apart from that, cases may arise to which a figure adjustment is not applicable, as in the small net shown in Fig. 2, p. 464. The line BC cannot be equated to the line AB in the ordinary way since it is not the side of a triangle. In this case an adjustment to approxima te coordina tes will overcome the difficulty. 相似文献
17.
AbstractDuring the last few years a method of measuring accurately the lengths of lines of moderate length by means of high-frequency variations in the intensity of light emitted by a special transmitter, which promises to have many important applications in triangulation and precise traversing, has been devised by Mr. E. Bergstrand, of the Geographical Survey of Sweden. In principle, the method has certain resemblances to the apparatus invented and used by Fizeau for measuring the velocity of light, Bergstrand's instrument having been designed in the first place for the measurement of the same constant. In Fizeau's apparatus, it will be remembered, a ray of light was directed through the cogs of a revolving toothed wheel towards a distant mirror, and, when the wheel reached a certain angular velocity, the ray reflected from the mirror was intercepted by the cogs, so that an observer stationed on the same side of the wheel as the light source no longer saw the reflection of the light in the mirror. The angular velocity of the wheel being known or observed, the time taken for the cogs to obliterate the reflected image could be calculated, and twice the distance to the mirror divided by this time gave the velocity of light. In the Bergstrand apparatus, which is called the “geodimeter”, light pulses of known frequency and varying intensity are directed to the end station of the line whose distance is required, and, after reflection by a mirror at that station, are received back in a special receiving apparatus alongside the transmitter. Here they are converted into small electric currents, which, when the required distance is a certain function of the wave length of the transmitted and reflected pulses, can be made to give zero deflection on a sensitive galvanometer. In this way, the distance to be measured can be determined in terms of the wave length of the pulses. Experiments so far carried out with this apparatus have been successful up to distances of about 36 kilometres. Even with the latest model, however, as we shall see later, it is necessary to know the approximate distance to within 1½ km. 相似文献
18.
Michael R. Helfert Kamlesh P. Lulla Victor S. Whitehead M. Justin Wilkinson Donald E. Williams Michael J.. McCulley 《国际地球制图》2013,28(3):65-79
Abstract Although high‐resolution microwave synthetic aperture radar (SAR) sensors possess all‐weather capability for mapping soil moisture from spaceborne platforms, continuous temporal and spatial monitoring of this important hydrological parameter has been relatively limited. However, the recent launch of operational SAR sensors aboard various satellites have made possible synoptic soil moisture monitoring a reality. Such systems operate over a wide range of frequencies, look angles, and polarization combinations, and thus show synergistic advantages when combined for estimating soil moisture patterns. Two soil moisture inversion algorithms have been developed using as inputs radar backscattering data at L, S, and C bands in the microwave frequency range. These models have been tested using radar image simulation with speckle added. It is observed that the neural network algorithm yields superior results in mapping actual soil moisture patterns over the linear statistical inversion technique, although both models show comparable errors in soil moisture estimation. We infer that using statistical estimation errors alone for comparison purposes may lead to erroneous conclusions regarding the advantages of one soil moisture inversion algorithm over another. 相似文献
19.
《测量评论》2013,45(14):464-472
Abstract The Mythical Spheroid.—The preceding article dealt with the fact that the spheroid of reference is a myth and that, even if it were not, we could not get hold of it at any given place. In order to apply corrections to observed quantities or, more generally, to operate upon them mathematically, we must make some assumption such as that of the spheroidal level surface. Probably a lot of harm has been done by attaching the notion of too concrete a thing to the spheroid. Disputes and misconceptions have arisen. People talk of“putting the spheroid down at a point” and imagine that the obedient thing is still at their feet when they get to another point, perhaps distant, in their system of triangulation or what not. Actually the spheroid may be disobedient not only as regards the direction of the vertical but also because it is above their heads or below their feet. What happens is that at each point afresh the computer treats the observations as if they were made there on the surface of a spheroid. In the same way, but travelling still farther along the road of hypothesis, he may treat observations for astronomical positions as if the compensation for visible elevations were uniformly distributed as a deficiency of density down to a depth of 122·2 kilometres. That was the depth which happened to give the smallest sum of squares of residuals in a certain restricted area, but nobody imagines that it corresponds with a physical reality, especially the ·2! It was a convenient mathematical instrument which, once the theory was to be given a trial, had to be fashioned out of some assumption or another. All this has little to do with geodetic levelling but is meant to try to banish the spheroid out of the reader's mind or at least to the back of his mind. In what follows we shall be compelled to make a certain amount of use of the family of spheroids but always with the above strictures in view. 相似文献
20.
《测量评论》2013,45(62):300-311
AbstractChesterton did not, of course, intend this gibe to be taken literally. But the more we consider what he would doubtless have called the “Higher Geodetics”, the more we must conclude that there is some literal justification for it. Not only are straight lines straight. A sufficiently short part of a curved line may also be considered straight, provided that it is continuous (i.e. does not contain a sudden break or sharp corner), and provided we are not concerned with a measure of its curvature. Similarly a square mile or so on the curved surface of the conventionally spheroidal earth is to all intents and purposes flat. We shall achieve a considerable simplification, without any approximation, in the treatment of the present subject by getting back to these fundamental glimpses of the obvious, whether the formalists and conformalists accept them or not. 相似文献