EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In a previous article on this subject (Empire Survey Review, January 1937) the writer sought to show that for trigonometrical observations of vertical angles made near noon in the Tropics the coefficient of refraction depends chiefly on height above ground level in the case of stations sited within a few hundred feet above the general level of the ground surface. Indeed, the computed values of the coefficient K show a definite and appreciable increase with “h”, the height of the observing station above ground level; it is usually assumed that K decreases with increase in height above the Mean-Sea-Level surface. From analysis of the results obtained by varying h but holding the heights above Mean Sea Level fixed the writer came to the conclusion that the variations in K could only be due to abnormal values of dt/dh and d²t/dh², “t” denoting the air temperature. Now it is generally recognized by meteorologists that abnormal lapse-rates of temperature do frequently occur in the lower air layers in the Tropics; but up to the present time no temperature soundings in Nigeria are available. Recently, however, the writer came across the results of the aerological soundings made by an expedition in East Africa during the year 1908. The results of many of the soundings were of no use for the purpose of this paper; many of the observations were not taken at or near noon, and in others counterlapses of temperature in the lower layers indicated that conditions were not normal. A set of observations taken at Mombasa between 10 and 11 a.m. were eventually chosen as offering an example of what might reasonably occur in the lower layers of the atmosphere.     

ON THE ELIMINATION OF THE ERRORS OF PAIRING AZIMUTH OBSERVATIONS

Abstract

The 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.     

CORRECTION OF PLANE-TABLE HEIGHTS FOR CURVATURE OF THE EARTH AND ATMOSPHERIC REFRACTION

Abstract

Most text-books on surveying limit their discussion of the correction of vertical angles for curvature of the earth and atmospheric refraction to the correction of angles taken with a theodolite during triangulation and omit any reference to those taken with a clinometer. This is rather illogical, as in well-observed triangulation, with all vertical angles measured in both directions, no correction for these effects is necessary, whilst in plane-tabling on small scales where sketching at considerable distances is frequently employed the application of corrections for these effects is essential.     

THE RE-TRIANGULATION OF GREAT BRITAIN-II

Abstract

Reconnaissance.—It has been possible to draw up a “paper scheme” for most of the primary triangulation by examination of large-scale topographic maps for possible obstructions to the proposed rays (after due allowance for curvature and refraction along the ray); the fact that certain of the proposed lines had been definitely observed in the existing primary or secondary triangulation was of course of material assistance. Since, however, all observations were to be to luminous beacons, requiring a close organization, it would have been unsound to draw up an observing programme on the strength of this paper scheme alone. The omission of a few key rays, subsequently found to be obstructed by timber, whose height cannot be appreciated from maps, or by local features which had grown up since the last triangulation, would have entailed some confusion in the observing programme, the establishment of additional stations for occupation during a later season, and the reoccupation of stations surrounding such additional points; in short, the probability of a year's delay in obtaining sufficient material for adjustment, and a considerable loss of economy. Arrangements were accordingly made for the paper scheme of the English main chain to be verified and amended on the ground by special reconnaissance parties in 1935, when in fact no instruments or beacons were available to commence observing in any case. In the same way, field reconnaissance of the Scottish main chain and of the Western figure (Wales and the S.W. peninsula) was completed in 1936 and a start made on the Eastern figure (East Anglia and S.E. England), so as to get the reconnaissance and station preparation well ahead of observing. Experimental reconnnaissance of a few secondary blocks—for which, as also for the primary reconnaissance of the flat enclosed East Anglian country, paper schemes are practically useless—was also commenced in 1936 and is being pushed ahead rapidly in 1937.     

THE ADJUSTMENT OF TRIGONOMETRICAL LEVELS AND THE EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

This paper is written primarily with the object of ascertaining how other Colonies and Dominions deal. with the adjustment of their trigonometricallevels; further, since the greater part of Nigeria is now covered by a framework of levels of primary accuracy it is of interest to examine the results. Moreover, the evaluation of the coefficient of refraction, and from it the temperature lapse-rate, is of some importance in view of the recent publication of the War Office Aneroid Tables. These tables are based on a standard lapse-rate of temperature.     

NOTES ON THE BASE LINES OF THE CEYLON TRIANGULATION

Abstract

The triangulation of Ceylon depends for its scale upon two bases, each about 5½ miles long, situated at Negombo on the West Coast (latitude 7° 10′) and at Batticaloa on the East Coast (latitude 7° 40′). Both bases are in low, flat country; brick towers up to 70 feet high had to be built over the terminals to enable observations to be taken to surrounding points. These lines have recently been re-measured.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

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.     

ELIMINATION OF ERRORS OF LATITUDE AND REFRACTION IN THE PAIRING OF AZIMUTH OBSERVATIONS

Abstract

In 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.     

TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject.     

THE HEIGHT DETERMINATION OF MOUNT KILIMANJARO TANGANYIKA,EAST AFRICA

Abstract

The following account of the expedition which succeeded in fixing a new height for Mount Kilimanjaro is taken in the main from the diary of the party that made the necessary observations, but, for the sake of clarity, it is as well to set out here a very brief statement of the position.     

On the path curvature of electromagnetic waves

To facilitate the calculation of atmospheric refraction from radiometeorological sounding observations, the coefficients of refraction for light and microwaves have been expressed in the general form k=A.p+B.U+(C·p+D·U) dt/dz+E·dU/dz where p is total pressure, U is relative humidity and A, B, C, D and E are tabulated functions of temperature t. Three-place tables are given in metric units for the temperature range −10°C to +30°C. The paper includes a general discussion of the variation of refraction with weather, and outlines computation procedures for electromagnetic measurement of long lines on the basis of radiosonde data.     

On the refraction coefficient of microwaves

New formulae are developed for the evaluation of the refraction coefficient of microwaves, which is the key factor for the curvature correction of microwave EDM. These new formulae are based on two distinct humidity distributions which often characterize the atmosphere during daytime. The first case assumes that the relative humidity is constant with height. For this distribution the new formulae are based on a revised form of the Robitzsch formula which enables also the evaluation of the microwave refraction coefficient from a known refraction coefficient of light. The second case assumes that the specific humidity is constant with height.     

OBSERVING POLARIS IN DAYLIGHT

Abstract

For azimuth and latitude it is a great advantage to observe Polaris in daylight as it eliminates torches and lamps. The following describes a rule of thumb method of finding the hour angle and a diagram to find the, altitude from the R.A. The altitude is then set on the vertical circle and, by moving the telescope a few degrees about the meridian (by compass), Polaris can easily be spotted near the centre of the field. The telescope must be focussed at infinity. After finding the star, the rigorous observations must be carriéd out.     

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.     

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.     

Crop Evapotranspiration Estimation for Wheat (<Emphasis Type="Italic">Triticum aestivum</Emphasis> L.) Using Remote Sensing Data in Semi-Arid Region of Maharashtra

Penman–Monteith method adapted to satellite data was used for the estimation of wheat crop evapotranspiration during the entire growth period using satellite data together with ground meteorological measurements. The IRS-1D/IRS-P6 LISS-III sensor data at 23.5 m spatial resolution for path 096 and row 059 covering the study area were used to derive, albedo, normalized difference vegetation index, leaf area index and crop height and then to estimate wheat crop evapotranspiration referred to as actual evapotranspiration (ETact). The ETact varied from 0.86 to 3.41 mm/day during the crop growth period. These values are on an average 16.40 % lower than wheat crop potential evapotranspiration (ETc) estimated as product of reference crop evapotranspiration estimated by Penman–Monteith method and lysimetric crop coefficient (Kc). The deviation of ETact from ETc is significant, when both the values were compared with t test for paired two sample means. Though the observations on ETact were taken from well maintained unstressed experimental plot of 120 × 120 m size, there was significant deviation. This deviation could be attributed to, the satellite images representing the actual crop evapotranspiration as function crop canopy biophysical parameters, condition of the crop stand, climatic and soil conditions and the microclimate variation over area of one hectare. However, Penman–Monteith method represents a flat rate of specific growth stage of the crop.     

THE EFFECTS OF ECCENTRICITY AND MISPLACED INDICES OF DIVIDED CIRCLES

Abstract

Special precautions are taken in the workshop to ensure that divided circles are so mounted that the point from which the circle graduations radiate lies accurately on the axis about which rotation of the circle and reading index or indices takes place. If, through some accident, eccentricity is present, it is still possible to obtain accurate readings if the instrument is used to the best advantage, and the object of the following notes is to assist the surveyor to this end. It will be found that errors arising from eccentricity can be made to cancel out, except in the case of a vertical circle fitted with a single reading index.     

中性大气对非差伪距定位的影响及其模型改正分析

中性大气包括对流层和平流层,它们对GPS信号造成的延迟影响是GPS定位的一个主要误差源。与电离层的影响相比,消除中性大气的延迟影响更复杂,只能用经验模型进行改正。本文就中性大气对GPS定位的影响进行详细地分析和说明,对中性大气改正模型及其相关问题进行明确地论述。最后以中国IGS跟踪站一年中不同季节的观测数据为基础,通过对相同的数据采用不同的中性大气改正模型分别进行相同的定位解算,并对不同模型的定位结果进行分析,得出有关中性大气模型改正与GPS定位之间及改正模型间的定性和定量的关系。     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

The Stereographic Projection, owing to the ease and accuracy with which it can be drawn on a small scale, offers natural attractiveness for the treatment of spherical geometry upon a plane surface. It would therefore be rash for a present-day writer to claim as novel what may well be an infringement of patent rights morally belonging to Hipparchus, who possibly knew most of what is worth knowing about the matter 2,000 years ago. However, since a fairly extensive delving into writings upon the subject has not brought to light anything quite on the lines here put forward, it may be worth while to systematize in this paper some processes which the present writer has found practically useful for some time past.