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1.
《测量评论》2013,45(56):53-68
AbstractThis extremely simple and elegant method of computing geographical co-ordinates, given the initial azimuth and length of line from the standpoint, was published by Col. A. R. Clarke in 1880. There is no other known method giving the same degree of accuracy with the use of only three tabulated spheroidal factors. Clarke himself regarded this as an approximate formula (vide his remark in section 5, p. 109, “Geodesy”); but as this article demonstrates, it is capable of a high degree of precision in all occupied lati tudes when certain corrections are applied to the various terms. These corrections are comparatively easy to compute, require no further spheroidal factors, and some of them may be tabulated directly once and for all. 相似文献
2.
AbstractThe constant K in equation (12) represents distance expended through time lags in the instrument itself, and, although the value of K can be calculated from electrical data, this would not be very satisfactory and it would be better to determine it directly by means of observations over a line of known length. In addition, the point from which K would be reckoned is not a convenient one for actual field measurements. Instead of this, it is more convenient to choose an index mark on the instrument itself and referall measurements to this and thence to the mark over which the instrument is set up. 相似文献
3.
Abstract19. Formulae.—In Nos. 6, vol. i, and 9, vol. ii, pp. 259 and 156, there has been described a new method for dealing with long geodesics on the earth's surface. There the so-called “inverse” problem has claimed first attention: given the latitudes and longitudes of the extremities of a geodesic, to find its length and terminal azimuths. It remains to discuss the “direct” problem : a geodesic of given length starts on a given azimuth from a station of known latitude and longitude; to find the latitude and longitude of its extremity and the azimuth thereat. The solution of this direct problem demands a certain recasting of the formulae previously given. In order of working the several expressions now assume the forms below. 相似文献
4.
Abstract The Arc of the Geodesic.—In the first part of this paper a method was given for computing the azimuth of a geodesic. The method gives the convergence of the geodesic correctly up to the second power of e the eccentricity. The formula (9), however, also depends on the assumption that σ, the arc-length of the geodesic, can be obtained with sufficient accuracy from the Supplemental Dalby Theorem, that is to say, by a purely spherical computation. It is, therefore, needful to show that this supposition is justifiable; a means must in fact be indicated for verifying the assumption. 相似文献
5.
Summary The discrepancy between precision and accuracy in astronomical determinations is usually explained in two ways: on the one
hand by ostensible large refraction anomalies and on the other hand by variable instrumental errors which are systematic over
a certain interval of time and which are mainly influenced by temperature.In view of the research of several other persons and the author’s own investigations, the authors are of the opinion that
the large night-errors of astronomical determinations are caused by variable, systematic instrumental errors dependent on
temperature. The influence of refraction anomalies is estimated to be smaller than 0″.1 for most of the field stations.
The possibility of determining the anomalous refraction from the observations by the programme given by Prof. Pavlov and Anderson
has also been investigated. The precision of the determination of the anomalous refraction is good as long as no other systematic
error working in a similar way is present.The results, which are interpreted as an effect of the anomalous refraction by Pavlov and Sergijenko, could also be interpreted
as a systematic instrumental error.
It is furthermore maintained thatthe latitude and longitude of a field station can be determined in a few hours of one night if the premisses given in [3, p.68]are kept.
It has been deplored that the determination of the azimuth has not been given the necessary attention. It is therefore proposed
to intensify the research on this problem.
The profession has been called upon to acquaint itself better with the valuable possibilities of astronomical determinations
and to apply them in a useful and appropriate manner. At the same time, attention has been called to the possibility of improving
astronomical determinations with regard to accuracy as well as effectiveness. 相似文献
6.
Error analysis in length measurements is an important problem in geographic information system and cartographic operations. The distance between two random points—i.e., the length of a random line segment—may be viewed as a nonlinear mapping of the coordinates of the two points. In real-world applications, an unbiased length statistic may be expected in high-precision contexts, but the variance of the unbiased statistic is of concern in assessing the quality. This paper suggesting the use of a k-order bias correction formula and a nonlinear error propagation approach to the distance equation provides a useful way to describe the length of a line. The study shows that the bias is determined by the relative precision of the random line segment, and that the use of the higher-order bias correction is only needed for short-distance applications. 相似文献
7.
《测量评论》2013,45(85):319-325
AbstractIn 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). 相似文献
8.
《测量评论》2013,45(57):102-114
Abstract25. A very complete exposition of the Clarke formulæ has been made in a paper entitled “Latitudes, Longitudes and Azimuths—Clarke's Method”, by G. T. McCaw, which was cyclostyled by the G.S.G.S. in 1922. In the present article the writer carries the theme a step further by indicating more fully the maximum possible values of the various small errors, tabulating them when possible, and also giving examples of the computation of long lines which require the inclusion of the various corrective terms. The formulæ for these corrective terms have been expanded to include higher power terms for investigational purposes. References are given to the page and formula number from McCaw's paper: his notation has been slightly altered, but this is fully explained in the present text. The azimuth used in the Clarke formulæ is that of the geodesic and not that of the plane curve. 相似文献
9.
The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary 总被引：1，自引：1，他引：0
In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding
average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as
many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources.
This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary,
where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling
line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is
investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results
show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if
the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the
normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10−3mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which
is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated
along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line. 相似文献
10.
11.
《测量评论》2013,45(11):287-291
AbstractThe perfect pairing of east and west observations for azimuth, put briefly, should consist of combinations of simultaneous observations of stars of the same altitude and of the same declination. Needless to say, this is a counsel of perfection, and in practice the surveyor has usually to rely on some sort of an approximation to this ideal. It is only on very rare occasions that the necessary time is available and the atmospheric conditions favourable enough to obtain this perfect harmony of observations. Assuming that the latitude of the azimuth station and the atmospheric refraction are accurately known, the necessity of pairing would not arise, and the grouping of the observations into two sets of east and west stars with a varying discrepancy between the members of the individual pairs would be quite unnecessary. In general one might say, when an azimuth observation is taken, neither the latitude nor the atmospheric refraction is known accurately, and the question arises as to whether there is any simple method of eliminating or reducing these two causes of error. 相似文献
12.
《测量评论》2013,45(43):274-284
AbstractRecently the writer of this article became interested in the conical orthomorphic projection and wanted to see a simple proof of the formula for the modified meridian distance for the projection on the sphere. Owing to the exigencies of the war, however, he has been separated from the bulk of his books, and, consequently, has had to evolve a proof for himself. Later, this proof was shown to a friend who told him that he had some memory of a mistake in the sign of the spheroidal term in m4given in “Survey Computations”, perhaps the first edition. Curiosity therefore suggested an attempt to verify this sign, which meant extending his work to the spheroid. This has now been done, with the result that the formula given in “Survey Computations”, up to the terms of the fourth order at any rate, is found correct after all. 相似文献
13.
《测量评论》2013,45(25):153-156
AbstractIn a previous Article (Empire Survey Review, ii, II) I described a simple graphical method for the elimination of latitude error in observations for azimuth. It was pointed out that the ideal method of adjustment of azimuths would be a simultaneous elimination of both latitude and refraction errors and, with that in view, a purely theoretical method of such an adjustment was demonstrated in the last paragraph of the article. It has now occurred to me that a fairly simple mathematical solution is possible. 相似文献
14.
AbstractIf the geographical co-ordinates, Φ0, L 0, and the azimuth A 0 at a station O of a triangulation undergo corrections, ?Φ0, ?L 0 and ?A 0, the geographical co-ordinates, Φ, L, and the azimuth A have to be re-computed for all the vertices throughout the whole triangulation. This is a tedious operation. It may be vastly simplified, however, by the employment of differential formulae. The derivation of these formulae would consume considerable space, so that the results alone are given here. 相似文献
15.
S. H. Laurila 《Journal of Geodesy》1969,43(2):139-153
The main environmental problem in tracking a satellite through the atmosphere is in finding the most probable value of the
mean refractive index. In this paper, the mean refractive index is computed as a four-part model. The troposphere is treated
as one altitude range from sea level to 9 kilometers, and the stratosphere is divided into three altitude ranges, 9 to 18,
18 to 27, and 27 to 36 kilometers. At 36 kilometers, the N-value is approximately equal to two and reduces rapidly to zero.
By the use of theEssen formula in radio wave application and the modifiedKohlrausch formula in light wave application, point-to-point values of the refractive index are computed through these altitude ranges.
The polynomial expansion of second order from the basic exponential function is selected as the model, and the curve-fitting
adjustments of the computed values are established separately to each altitude range to obtain coefficients A, B, and C.
A model based on the U. S. Standard Atmosphere, 1962, is used as the reference to which four sets of actual soundings made
in Lihue, Hawaii and Fairbanks, Alaska on February 3 and July 2, 1966, are compared. The results show that the parabolic adjustment
has a very high reliability. In the use of standard atmosphere, the standard error of the refractive index through the total
altitude range of 0 to 36 kilometers, and at the 70° zenith distance, equal only ±7 millimeters when radio waves are utilized,
and ±3 millimeters when light waves are utilized.
Paper presented at Conference on Refraction Effects in Geodesy and Electronic Distance Measurement, University of New South
Wales, 5–8 November 1968. Hawaii Institute of Geophysics Contribution No. 239. 相似文献
16.
《测量评论》2013,45(89):121-126
AbstractThe purpose of this note is twofold; first, to criticize the “azimuth” section of the paper “Some Notes on Astronomy as Applied to Surveying”, by R. W. Pring (E.S.R., July 1952, xi, 85, 309–318),and secondly, out of these criticisms to develop an alternative method of making observations for azimuth. It will be apparent that this method owes much to the ideas put forward by Mr. Pring. 相似文献
17.
J. C. Owens 《Journal of Geodesy》1968,42(3):277-291
The development of lasers, new electro-optic light modulation methods, and improved electronic techniques have made possible
significant improvements in the range and accuracy of optical distance measurements, thus providing not only improved geodetic
tools but also useful techniques for the study of other geophysical, meteorological, and astronomical problems. One of the
main limitations, at present, to the accuracy of geodetic measurements is the uncertainty in the average propagation velocity
of the radiation due to inhomogeneity of the atmosphere. Accuracies of a few parts in ten million or even better now appear
feasible, however, through the use of the dispersion method, in which simultaneous measurements of optical path length at
two widely separated wavelengths are used to determine the average refractive index over the path and hence the true geodetic
distance. The design of a new instrument based on this method, which utilizes wavelengths of6328 ? and3681 ? and3 GHz polarization modulation of the light, is summarized. Preliminary measurements over a5.3 km path with this instrument have demonstrated a sensitivity of3×10
−9
in detecting changes in optical path length for either wavelength using1-second averaging, and a standard deviation of3×10
−7
in corrected length. The principal remaining sources of error are summarized, as is progress in other laboratories using
the dispersion method or other approaches to the problem of refractivity correction. 相似文献
18.
《测量评论》2013,45(55):26-27
AbstractEvery student of Close and Winterbotham's “Text Book of Topographical Surveying” learns that rewebbing diaphragms is a simple job. Unfortunately, when circumstances compel a surveyor to reweb a micrometer diaphragm in the field, he is liable to find, after some years in the tropics, that fever (and one thing and another) have played havoc with the steadiness of hand and eye. Under present conditions young surveyors who have been trained on optical micrometers may find themselves using 5″ micrometer theodolites with over a dozen webs, anyone of which is liable to sag, break or develop whiskers, while even a “Tavi” may conceivably remind the user that it has one web. 相似文献
19.
《测量评论》2013,45(20):334-336
AbstractIn a tale, delightfully told in vol. ii, no. 8, pp. 121–2 of this Review, Mr. Kitching revealed how he was called upon to assist in determining the length of an Arab mile. In the notes following the story a reference was made to measurements of arc carried out in the ninth century A.D. The following notes add some more details to those already given. The full table of the Arab units of length is given below; in the reference above, one step was left out. 相似文献