A PNEUMATIC APPARATUS FOR MEASURING THE FLATNESS OF PHOTOGRAPHIC PLATES

Abstract

The paper describes a simple pneuluatic apparatus, working at a pressure of about ½lb./in.², which enahles the flatness of photographic plates to be checked rapidly prior to their use in the camera. The errors of flatness are shown directly by the levels of coloured water columns in parallel manometer tubes; the magnification is 2,500 and the linear range is ±15μ (±0.0006 in.). The apparatus essentially measures departures from a prescribed form and has therefore other applications.     

EXAMPLES OF CURVATURE AND REFRACTION CORRECTIONS TO VERTICAL ANGLES

Abstract

The correction to observed vertical angles for curvature and refraction can be found by adding a log factor to the log distance, which gives the log of the correction in seconds. This factor is 8·144 for metres and 7·628 for feet. The examples will make this clear. For machine computation, the correction in seconds can be obtained by multiplying the length in metres by 0.0139 or the length in feet by 0·00425. Alternatively, this can be done on the slide. rule by dividing the distance in metres by 72 or in feet by 235. The mean coefficient of refraction is taken as 0·07.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

THE CALCULATION OF THE HEIGHT OF KILIMANJARO

Abstract

The observations to height Kilimanjaro were made from two ground stations, Domberg (5,081·6 ft.) and Lelatema (5,323.1 ft.) and from a point called Kibo near Kaiser Wilhelm Spitze which is regarded as the highest point on the crater rim. It was originally intended to include a third ground station, Kifaru, but it was discovered that the ice cap obstructed observations between this point and the top.     

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.     

Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic

We present software for spherical harmonic analysis (SHA) and spherical harmonic synthesis (SHS), which can be used for essentially arbitrary degrees and all co-latitudes in the interval (0°, 180°). The routines use extended-range floating-point arithmetic, in particular for the computation of the associated Legendre functions. The price to be paid is an increased computation time; for degree 3,000, the extended-range arithmetic SHS program takes 49 times longer than its standard arithmetic counterpart. The extended-range SHS and SHA routines allow us to test existing routines for SHA and SHS. A comparison with the publicly available SHS routine GEOGFG18 by Wenzel and HARMONIC SYNTH by Holmes and Pavlis confirms what is known about the stability of these programs. GEOGFG18 gives errors <1 mm for latitudes [-89°57.5′, 89°57.5′] and maximum degree 1,800. Higher degrees significantly limit the range of acceptable latitudes for a given accuracy. HARMONIC SYNTH gives good results up to degree 2,700 for almost the whole latitude range. The errors increase towards the North pole and exceed 1 mm at latitude 82° for degree 2,700. For a maximum degree 3,000, HARMONIC SYNTH produces errors exceeding 1 mm at latitudes of about 60°, whereas GEOGFG18 is limited to latitudes below 45°. Further extending the latitudinal band towards the poles may produce errors of several metres for both programs. A SHA of a uniform random signal on the sphere shows significant errors beyond degree 1,700 for the SHA program SHA by Heck and Seitz.     

The geopotential to (14, 14) from a combination of satellite and gravimetric data

A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γ_E=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γ_E withf=1/298.25, KM=3.9860122·10 ²² cm ³ /sec ² , the consistent equatorial radius was found to be6378143 m.     

TESTING A THEODOLITE FOR ACCURACY

Abstract

When a theodolite is used to measure an angle, the result will be subjected to certain instrumental and personal errors which affect the measurement. Such errors may be accidental or systematic. Those of the former type, which follow no law and which may with equal probability occur at any graduation, are more easily eliminated, since, if a very large number of readings is taken, it is probable that the errors will cancel out and that the mean will approximate very closely to the correct figure. Systematic errors are usually due to instrumental defects and rnay be expressed as a function of the reading itself; it is the object of the manufacturer to eliminate these as far as possible, since cancellation by reiteration or by repetition is not to be expected wholly.     

Books

Abstract

This is a summary of the problems which are involved in the apparently trivial task of measuring the length of a sinuous line on a map. It represents an extended review of the publication Cartometric Measurements, by H. Kishimoto. It is concerned with three basic problems: (1) the sorts of errors which may result from using different instruments and methods of measurement and how these may be corrected: (2) the sorts of errors which may occur in the map and how these may be corrected: 3) the fundamental problem of what is 'length'. Extensive use is made of East European literature on these subjects.     

SOME DIFFICULTIES EXPERIENCED IN USING MULTIPLEX PLOTTING EQUIPMENT

Abstract

The discussion herein relates to the use of Multiplex equipment in India. It is possible, though improbable, that the difficulties referred to may not be found in equipment produced by all manufacturers.     

Improvement of the geoid in local areas by satellite-to-satellite tracking

Summary The concept of satellite-to-satellite tracking measuring the relative velocity of two orbiting satellites spaced some hundreds kilometers on a close orbit, provides now possibilities for the investigation of the Earth’s gravity field. In the paper only medium and short wave length effects affecting the measured relative velocity have been considered. Collocation is used in such an analysis of local geoid improvement, because this method allows to combine heterogeneous data in a consistent way. Covariance functions relevant for the particular case of a circular equatorial orbit are given. Two kinds of observation equations have been formulated. The choice of observation equation with regard to satellites configuration is discussed. It is found that it is sufficient to have a limited number of satellite-to-satellite observations in a 7^o×7^o area around the estimation point with distances between profiles of about 1^o.5 and between the two satellites forming the pair of 200+350 km; the altitude of satellite-to-satellite observations should be as low as possible. The accuracy of the geoid determination strongly depends on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with an assumed reference field of (40,40). The influence of measuring errors is discussed and it is shown that only satellite-to-satellite observations with accuracy better then 0.1 mm/sec will give an improvement of the geoid. Finally, some results on the combination of low-low satellite-to-satellite tracking and terrestrial gravity data are given. The proposed method seems to be especially interesting for unsurveyed areas. Furthermore, it has the practical advantage that only a local coverage data is needed.     

Statistical analysis of discrepancies in high precision levelling

An investigation was made of the behaviour of the variable (where ρ_ij are the discrepancies between the direct and reverse measurements of the height of consecutive bench marks and theR _ij are their distance apart) in a partial net of the Italian high precision levelling of a total length of about1.400 km. The methods of analysis employed were in general non-parametric individual and cumulative tests; in particular randomness, normality and asymmetry tests were carried out. The computers employed wereIBM/7094/7040. From the results evidence was obtained of the existence of an asymmetry in respect to zero of thex _ij confirming the well-known results given firstly by Lallemand. A new result was obtained from the tests of randomness which put in evidence trends of the mean values of thex _ij and explained some anomalous behaviours of the cumulative discrepancy curves. The extension of this investigation to a broader net possibly covering other national nets would be very useful to get a deeper insight into the behaviour of the errors in high precision levelling. Ad hoc programs for electronic computers are available to accomplish this job quickly. Presented at the 14^th International Assembly of Geodesy (Lucerne, 1967).     

A METHOD FOR THE DETERMINATION OF THE DISTORTIONS OF THE IMAGE FORMED BY A MULTIPLEX PROJECTOR

Abstract

A Method is described for the determination of the resultant of the radial and tangential components of the distortion of the image produced by a Multiplex projector.     

LOCAL ERRORS IN RELATION TO ANALYTICAL METHODS OF AIR TRIANGULATION

Abstract

In view of the limitations of the use of plotting machines in air triangulation a detailed investigation of the practical possibilities of the analytical methods has become necessary, especially now that inexpensive means of reducing the labour of calculation is in course of realisation.

In analytical methods it is practically possible to correct the measured photographic coordinates for determinable errors. Also, the use of a reseau as developed by the Ordnance Survey facilitates the reduction of several distortions. It is however argued and demonstrated that some errors of a local character remain without effective checking.

A discussion of the nature of local errors shows that the number of points usually employed for relative setting is too small to be effective in disclosing them. An increase of the number of observed points is therefore suggested, and should be expected to improve the accuracy in the meanwhile.

An assessment of the value of doubling the number of minor control points and of the improvement resulting from the use of reseau is made from a statistical analysis of data kindly provided by the Ordnance Survey.

Comparison of 89 overlaps carrying one centimetre reseau and 100 overlaps without the reseau shows that the use of reseau reduced the root mean square error of evaluation of want of correspondence by 13 per cent., which just passes the 10 per cent. point of significance. The use of double minor control on the reseau overlaps gave an improvement which is about equal to that due to the use of the reseau. Doubling the number of minor control points is shown to increase the effective number of degrees of freedom from one to an average of four, which should reduce effectively the chances of large errors passing unnoticed through the stages of relative setting.

Work on the frequency of local errors of various sources is in hand, and will probably be published in later issues of the Review.     

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

On the night errors in astronomical determinations

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.     

SOME NOTES ON THE ADJUSTMENT OF TRAVERSES

Abstract

It has now become a truism that angles in traverses are observed with a far greater accuracy than the sides, and this applies to all categories of traverse work: precise, transit-and-tape, tacheometric traverses, etc. The result of this is that the effect of angular errors on misclosures in co-ordinates is sometimes so small when compared with that of linear errors that it may be considered as negligible.     

THE USE OF “EVEN ANGLES” IN STADIA SURVEYING

Abstract

While there is no standard method in stadia surveying of taking a set of readings for distance and altitude, the following may be regarded as the conventional, text-book method. The telescope is directed at the staff and the apparent lower hair brought to bear exactly on some convenient foot-mark. The readings of all three hairs are then taken and recorded (4.00, 5.41, and 6·83). Finally the vertical circle is read—to the nearest minute or to a fraction of a minute according to circumstances—and the result entered in the field-book (6° 31′ or 6° 31′ 20″). This method has its merits. It is straightforward and flexible and there is a simple (numerical) check on the accuracy of the staff-readings. Nevertheless it is by no means a perfect method.     

THE SURVEYOR'S LEVEL YESTERDAY AND TO-DAY

Abstract

The last twenty-five years have been remarkable for the progress made in the application of science to instrument design and manufacture. Certain instruments such as the Surveyor's Level appeared twenty-five years ago to have almost reached finality of design; but during the intervening period the improvements made have been of so radical a nature that the progress made has been greater than during any corresponding period. In short, the modern level is a more efficient instrument than its prototype and in spite of reductions in size and weight is, capable of yielding more accurate results with a less expenditure of time and energy. In order to appreciate fully how radical these changes have been, a direct comparison may be made between a first-class level as made twenty-five years ago and a similar instrument as made to-day. Twenty-five years ago it was not possible to obtain a level that could be relied upon to remain in adjustment; one that could be quickly checked and easily corrected offered distinct advantages. The Reversible Level was designed with this end in view; and it is proposed to select such an instrument having an objective aperture of 1·65 inches and to compare it with a modern instrument of the same aperture. The focal length of the telescope of the Reversible Level was 16 inches, and the weight of the instrument with its box was 21½ lbs. (Plate VIII, fig. 1). Many surveyors with long experience of this type still speak highly of its reliability and accuracy; it certainly compared very favourably with other instruments of its period.