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1.
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
2.
《测量评论》2013,45(30):457-462
AbstractIn the original geodetic series in Southern Rhodesia—completed by Mr Alexander Simms in 1901—the geographical coordinates of all stations were referred to the point SALISBURYas origin. The coordinates of SALISBURY were fixed by interchange of telegraphic signals with the Royal Observatory at the Cape for longitude, combined with astronomical determinations of time, latitude, and azimuth (see Vol. III, “Geodetic Survey of South Africa”). 相似文献
3.
《测量评论》2013,45(30):450-457
Abstract Malaya.—The geographical positions of points in the “Primary Triangulation of Malaya”, published in 1917, depend upon latitude and azimuth determinations at Bukit Asa and on the longitude of Fort Cornwallis Flagstaff, Penang, the latter being supposed to be 100° 20′ 44″.4 E. This value was obtained by Commander (later Admiral) Mostyn Field in H.M.S. Egeria 1893, by the exchange of telegraphic signals with Mr Angus Sutherland at Singapore, Old Transit Circle. The longitude, 103° 51′ 15″.75 E., accepted for Singa- pore in order to arrive at this determination of Fort Cornwallis Flagstaff, was based upon that of an Observation Spot, 103° 51′ 15″.00 E., fixed in 1881 by Lieutenant Commander Green, United States Navy, by meridian distance from the transit circle ofMadras Observatory, the corresponding longitude of the latter being taken as 80° 14′ 51″.51 E. 相似文献
4.
AbstractWhen computing and adjusting traverses or secondary and tertiary triangulation in countries to which the Transverse Mercator projection has been applied, it is often more convenient to work directly in terms of rectangular co-ordinates on the projection system than it is to work in terms of geographical coordinates and then convert these later on into rectangulars. The Transverse Mercator projection is designed in the first place to cover a country whose principal extent is in latitude and hence work on it is generally confined to a belt, or helts, in which the extent of longitude on either side of the central meridian is so limited as seldom to exceed a width of much more than about 200 miles. 相似文献
5.
《测量评论》2013,45(56):68-72
AbstractI. 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. 相似文献
6.
Luc M. A. Jeudy 《Journal of Geodesy》1988,62(2):113-124
Standard formulae overlook the contribution of a number of terms in the derivation of variance-covariance matrices for parameters
in nonlinear least squares adjustment. In a large class of nonlinear mathematical models, these terms can contribute to an
important error in the estimation of parameter variances. Improved formulae are derived. A numerical example is given and
the use of our improved formula in the case of least-squares adjustment in the explicit case (L=F(X)) is fully documented. 相似文献
7.
Summary
The standard Mollweide projection of the sphere S
R
2
which is of type pseudocylindrical — equiareal is generalized to the biaxial ellipsoid
E
A,B
2
.Within the class of pseudocylindrical mapping equations (1.8) of
E
A,B
2
(semimajor axis A, semiminor axis B) it is shown by solving the general eigenvalue problem (Tissot analysis) that only equiareal mappings, no conformal mappings exist. The mapping equations (2.1) which generalize those from S
R
2
to
E
A,B
2
lead under the equiareal postulate to a generalized Kepler equation (2.21) which is solved by Newton iteration, for instance (Table 1). Two variants of the ellipsoidal Mollweide projection in particular (2.16), (2.17) versus (2.19), (2.20) are presented which guarantee that parallel circles (coordinate lines of constant ellipsoidal latitude) are mapped onto straight lines in the plane while meridians (coordinate lines of constant ellipsoidal longitude) are mapped onto ellipses of variable axes. The theorem collects the basic results. Six computer graphical examples illustrate the first pseudocylindrical map projection of
E
A,B
2
of generalized Mollweide type. 相似文献
8.
《测量评论》2013,45(65):131-134
Abstract1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”. 相似文献
9.
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial
derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding
formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘ and the estimations of truncation error are given in this article.
Received: 26 January 1996 / Accepted: 11 June 1997 相似文献
10.
《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
11.
《测量评论》2013,45(60):217-219
AbstractMap Projections.—A matter that should have been mentioned in the original article under this title (E.S.R., vii, 51, 190) is the definition of a map projection. In the list of carefully worded “Definitions of Terms used in Surveying and Mapping” prepared by the American Society of Photogrammetry (Photogrammetrie Engineering, vol. 8,1942, pp. 247–283), a map projection is defined as “a systematic drawing of lines on a plane surface to represent the parallels of latitude and the meridians of longitude of the earth or a section of the earth”, and most other published works in which a definition appears employ a somewhat similar wording. This, however, is an unnecessary limitation of the term. Many projections are (and all projections can be) plotted from rectangular grid co-ordinates, and meridians and parallels need not be drawn at all; but a map is still on a projection even when a graticule is not shown. Objection could be raised also to the limitation to “plane surface”, since we may speak of the projection of the spheroid upon a sphere, or of the sphere upon a hemisphere. Hence, it is suggested that “any systematic method of representing the whole or a part of the curved surface of the Earth upon another (usually plane) surface” is an adequate definition of a map projection. 相似文献
12.
R. H. Rapp 《Journal of Geodesy》1967,41(1):55-65
In support of requirements for the U.S. Air Force Cambridge Research Laboratories, gravity anomalies have been upward continued
to several elevations in different areas of the United States. One area was 340 to 400 N in latitude and 960 to 1030 W in longitude, generally called the Oklahoma area. The computations proceeded from 26, 032 point anomalies to the prediction
of mean anomalies in 14, 704, 2.5′×2.5′ blocks and 9,284, 5′×5′ blocks. These anomalies were upward continued along 28 profiles
at 5′ intervals for every 30′ in latitude and longitude. These anomalies at elevations were meaned in various patterns to
form mean 30′×30″, 10×10, 50×50 blocks. Comparisons were then made to the corresponding ground values. The results of these comparisons lead to practical
recommendations on the arrangement of flight profiles in airborne gravimetry. 相似文献
13.
《测量评论》2013,45(94):372-376
AbstractIn the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour. 相似文献
14.
J. Feltens 《Journal of Geodesy》2008,82(8):493-504
Vector-based algorithms for the computation of azimuth, elevation and the ellipsoidal normal unit vector from 3D Cartesian
coordinates are presented. As a by-product, the formulae for the ellipsoidal normal vector can also be used to iteratively
transform rectangular Cartesian coordinates (X, Y, Z) into geodetic coordinates (φ, λ, h) for a height range from −5600 km to 108 km. Comparisons with existing methods indicate that the new transformation can compete with them. 相似文献
15.
《测量评论》2013,45(9):130-137
Abstract The International Map of the World.—Officially known as the Carte du Monde au Millionième, this undertaking has the following history. At the International Geographical Congress which was held at Bern in 1891, Professor Dr. Albrecht Penck proposed the construction, by all the nations of the world, of an International Map on the scale of 1 to 1 million. This idea was unanimously approved, and a very sketchy outline was roughed out for its prosecution. Of this outline the chief item that has survived is the size of the sheets, which were to be six degrees in longitude by four in latitude. Well, time passed and nothing much happened. Year after year there were a few murmurs at congresses about the map, and a few, a very few, sheets were printed, some by Section “F” of the British War Office. There was no general organization to look after the prosecution of the map, and there were no adequate regulations for its construction. Generally speaking, the official map-making institutions were out of touch with the scheme, and geographical societies and congresses had no money and no power to carry it out. 相似文献
16.
Global mean sea surface heights (SSHs) and gravity anomalies on a 2′×2′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and
GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0∘–360∘ longitude and –80∘–80∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters
of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting
heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then
computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was
added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface
and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary
grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square
(RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences
between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans.
Received: 26 September 2001 / Accepted: 3 April 2002
Correspondence to: C. Hwang
Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095.
This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively.
The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively.
Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided
very detailed reviews that improved the quality of this paper. 相似文献
17.
《测量评论》2013,45(63):20-24
AbstractThe shutter eyepiece is a device for eliminating the effects of personality in observations involving the timing of a moving star crossing graticule lines. It is of importance in longitude observations and in any mixed observations involving timing of star passages over cross-lines—vertical, horizontal or oblique. 相似文献
18.
Least-squares by observation equations is applied to the solution of geodetic boundary value problems (g.b.v.p.). The procedure is explained solving the vectorial Stokes problem in spherical and constant radius approximation. The results
are Stokes and Vening-Meinesz integrals and, in addition, the respective a posteriori variance-covariances.
Employing the same procedure the overdeterminedg.b.v.p. has been solved for observable functions potential, scalar gravity, astronomical latitude and longitude, gravity gradients
Гxz, Гyz, and Гzz and three-dimensional geocentric positions. The solutions of a large variety of uniquely and overdeterminedg.b.v.p.'s can be obtained from it by specializing weights. Interesting is that the anomalous potential can be determined—up to a
constant—from astronomical latitude and longitude in combination with either {Гxz,Гyz} or horizontal coordinate corrections Δx and Δy, or both. Dual to the formulation in terms of observation equations the overdeterminedg.b.v.p.'s can as well be solved by condition equations.
Constant radius approximation can be overcome in an iterative approach. For the Stokes problem this results in the solution
of the “simple” Molodenskii problem. Finally defining an error covariance model with a Krarup-type kernel first results were
obtained for a posteriori variance-covariance and reliability analysis. 相似文献
19.
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
20.
《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