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1.
《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
2.
《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
3.
AbstractAbout sixteen years ago an apparent need of the time led the writer to consider the construction of a small-scale map of the British Empire. It was immediately obvious that such a sheet, prepared in a manner to reduce the errors of scale and bearing to figures approaching the minimum, would have to extend from the Yukon and across the Eastern Hemisphere to New Zealand_ Accordingly, it would involve an oblique projection, cutting the Equator at some angle to be investigated. Moreover, the depth of the map would necessarily be the least possible in order to conform with the desiderata above. 相似文献
4.
《测量评论》2013,45(27):269-272
AbstractThe last issue (No. 26) of the Review contained an article on “Observing with the Zeiss and Wild Theodolites”, making reference among other matters to the errors of the parallel-plate micrometer. The statement was made that the error was due to the difference in travel between the two plates. This is not strictly correct but could not be better expressed without additional explanation, out of place in an already overlong article. 相似文献
5.
《测量评论》2013,45(77):306-314
AbstractLieut.-Col. Browne's interesting method of combii1ing radial line plots (“The Application of Transformation Factors to the Adjustment of Air Photographs”, E.S.R., x, 73, 119-130) depends for its success on the basic accuracy of the radial line plots of the individual air photo strips. It therefore poses the very interesting question: What accuracy can we expect in a graphical radial line plot? 相似文献
6.
《测量评论》2013,45(89):134-140
AbstractThe formulae given in this paper can be used for a station adjustment at a trigonometric station and also for the adjustment of errors in a level survey. As applied to levelling, the problem consists in finding the most probable values of the reduced levels of a number of points where the observed level differences between the points are not consistent with each other. It can be shown that the required values of the reduced levels are those which reduce the sum of the squares of the residual errors to a minimum, where the residual error is defined as the difference between the calculated and observed levels. 相似文献
7.
《测量评论》2013,45(20):354-358
Abstract 6. Further Expansions.—Equations (4.3) and (5.5) enable a computer to transform coordinates from the Cassini projection to the Gauss projection without recourse to geographical coordinates. If applied to one or two points, no doubt these equations would be quite satisfactory; but if applied to 100,000 points their use would be laborious and it would be difficult to adapt them to machine computing. 相似文献
8.
《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
9.
《测量评论》2013,45(32):85-89
AbstractThe necessity of transforming rectangular co-ordinates from one system of projection to another may arise from, various causes, One case, for example, with which the present writer is concerned involves the transformation, to the standard belt now in use, of the co-ordinates of some hundreds of points of a long existing triangulation projected a quarter of a, century ago on a, belt of Transverse Mercator projection, In this case conversion is complicated by the fact that the spheroid used in the original computation differs from that now adopted, and, also, the geodetic datums are not the same, The case in fact approaches the most general that can occur in practice, One step in one solution of this problem, however, is of perhaps wider Interest: that is, the transformation from one belt of Transverse Mercator projection to another when the spheroids and datums are identical. It is this special case which will be discussed here. 相似文献
10.
《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
11.
Abstract Introductory Remarks.—A line of constant bearing was known as a Rhumb line. Later Snel invented the name Loxodrome for the same line. The drawing of this line on a curvilinear graticule was naturally difficult and attempts at graphical working in the chart-house were not very successfuL Consequently, according to Germain, in 1318 Petrus Vesconte de Janua devised the Plate Carree projection (“Plane” Chart). This had a rectilinear graticule and parallel meridians, and distances on the meridians were made true. The projection gave a rectilinear rhumb line; but the bearing of this rhumb line was in general far from true and the representation of the earth's surface was greatly distorted in high latitudes. For the former reason it offered no real solution of the problem of the navigator, who required a chart on which any straight line would be a line not alone of constant bearing but also of true bearing; the first condition necessarily postulated a chart with rectilinear meridians, since a meridian is itself a rhumb line, and for the same reason it postulated rectilinear parallels. It follows, therefore, that the meridians also must be parallel inter se, like the parallels of latitude. The remaining desideratum—that for a true bearing—was attained in I569 by Gerhard Kramer, usually known by his Latin name of Mercator, in early life a pupil of Gemma Frisius of Louvain, who was the first to teach triangulation as a means for surveying a country. Let us consider, then, that a chart is required to show a straight line as a rhumb line of true bearing and let us consider the Mercator projection from this point of view. 相似文献
12.
13.
《测量评论》2013,45(70):357-363
AbstractThere are no proper projections for use in geodetic work in a country which has great extensions both in latitude and longitude. For, if a single projection of any kind be applied in such a case, the linear and angular distortions would be so great at the boundary that it is very difficult or even impossible to apply the corrections to them. In order to render it possible for any projection to be applied, the area in question should be divided either into strips bounded by meridians or into zones bounded by parallels. In the former case the Transverse Mercator or Gauss’ projection may be used, while in the latter, the Lambert conformal projection is the most suitable. China is such a country as that mentioned above. It covers an area extending from 16°N. to 53°N. in latitude and of no less than sixty-five degrees in longitude. The problem of choosing a projection for geodetic work depends only on how the area is to be divided. It has been decided by the Central Land Survey of China to adopt the Lambert conformal projection as the basis for the co-ordinate system, and, in order to meet the requirements of geodetic work, the whole country is subdivided into eleven zones bounded by parallels including a spacing of 3½ degrees in latitude-difference. To each of these zones is applied a Lambert projection, properly chosen so as to fit it best. The two standard parallels of the projection are situated at one-seventh of the latitude-difference of the zone from the top and bottom. Thus, the spacing between the standard parallels is 2½ degrees. This gives a maximum value of the scale factor of less than one part in four thousand, thus reducing the distortions of any kind to a reasonable amount. The area between these parallels belongs to the zone proper, while those outside are the overlapping regions with the adjacent ones. All the zones can be extended indefinitely both eastwards and westwards to include the boundaries of the country. 相似文献
14.
Abstract Introductory.—From time to time the question of the relation between the metre and the foot is raised, most frequently perhaps from Africa. Had there been no more than a single metre to consider the question would no doubt arise but seldom: the most recent authoritative comparsion would be generally accepted. But actually it is the existence of two metres—the “ legal” and the “international”—which complicates the question, so much indeed that there is no metrological factor which has influenced survey, British and foreign, more than the relation between these two metres. The question was discussed in this Review (I, 6, 277, 1932), but memories grow shorter, attention is more diffused, and besides there is required a more explicit statement of the situation as it affects British surveyors, especially in Africa, whence the question has been raised anew. To illuminate it, unfortunately the need recurs to repeat some well-known facts. 相似文献
15.
《测量评论》2013,45(61):267-271
AbstractSome publications that have dealt with the question of convergence of meridians seem, to the present writer, to be clouded with misconception, and these notes are intended to clarify some points of apparent obscurity. For instance, A. E. Young, in “Some Investigations in the Theory of Map Projections”, I920, devoted a short chapter to the subject, and appeared surprised to find that the convergence on the Transverse Mercator projection differs from the spheroidal convergence; the explanation which he advanced can be shown to be faulty. Captain G. T. McCaw, in E.S.R., v, 35, 285, derived an expression for the Transverse Mercator convergence which is equal to the spheroidal convergence, and described this as “a result which might be expected in an orthomorphic system”. Perhaps McCaw did not intend his remark to be so interpreted, but it seems to imply that the convergence on any orthomorphic projection should be equal to the spheroidal convergence, and it is easily demonstrated that this is not so. Also, in the second edition of “Survey Computations” there is given a formula for the convergence on the Cassini projection which is identical, as far as it goes, with that given for the Transverse Mercator, while the Cassini convergence as given by Young is actually the spheroidal convergence. Obviously, there is some confusion somewhere, and it is small wonder that Young prefaced his remarks with the admission that the subject had always presented some difficulty to him. 相似文献
16.
《测量评论》2013,45(3):109-115
AbstractWheatstone in 1838 published for the first time his remarkable discovery of Stereoscopy. To himself he had put the question, “What would be the visual effect of simultaneously presenting to each eye instead of the object itself its projection on a plane surface as it appears to that eye?” A preliminary experiment in which four objects were combined to form two resultant images at once sufficed to confirm his expectation and to demonstrate the phenomenon of synthetic solidity, to which he gave the name Stereoscopy He then proceeded to explain his discovery by means of a diagram based upon a more elementary experiment involving the formation of a single resultant image. Hitherto this experiment has been universally accepted, not only on account of the plausibility of its application, but because the movements described by Wheatstone can generally be readily seen when the experiment is repeated. These movements were regarded by Wheatstone as being of a stereoscopic character. It is the purpose of this discussion to show that the second experiment in no way represents the phenomenon of Stereoscopy, and that any diagram based upon this second experiment cannot afford a correct explanation of the stereoscopic principle. 相似文献
17.
《测量评论》2013,45(12):330-335
AbstractI. These notes are the results of following up in some detail the well-known fact that the horizontal distance between two points at altitude h is greater, by an amount proportional to h, than the distance between the corresponding points at sea-level. Traverses based on rectangular coordinates are considered, with special reference to the residual errors left after adjusting the misclosures of such traverses without first eliminating errors due to altitude. 相似文献
18.
AbstractIn two papers on this subject (v, 34, 236, and vi, 40, 85) some difficulties were examined and missing evidence explored. Reference was made to the past existence of divers acres in the British Isles. In a lecture by Professor A. E. Snape, M.SC., on “Our Units of Measurement”, delivered at the University of Cape Town and printed in the South African Survey Journal (III, Part viii, 24, 340, 1930), some other units are considered and additional evidence adduced. For example, the Cheshire acre is given as 2.11 statute acres. 相似文献
19.
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