GEODETIC LEVELLING IN KENYA

Abstract

Kenya-Topography. Kenya lies astride the Equator between latitudes 4°N and 4°S and extends from Lake Victoria to the Indian Ocean (34°E to 42°E). Between long. 36° and 36½°E it is traversed from north to south by the great Rift Valley, the surface of which is generally 2000-3000ft. lower than the level of the plateau on each side. The plateau culminates in the Aberdare Range (13,000 ft.) east of the Rift, and the Mau Forest (10,000 ft.) and Cherangani Hills (11,000ft.) west of the Rift. Together with the isolated mountain masses of Elgon (14,000 ft.), Kenya (17,000ft.) and Kilimanjaro (19,500ft.), this topography may be expected to cause considerable local distortion in the shape of the geoid. Gravity surveys in 1933-4 indicated a negative anomaly below the floor of the Rift Valley, suggesting that it had been forced down by over-riding pressure from both sides.     

IMPLICIT CONDITION EQUATIONS IN THE ADJUSTMENT OF TRIANGULATION FIGURES

Abstract

In adjusting a triangulation network it may happen that certain condition equations, of the existence of which we know a priori (by formulæ or by plotting the network point by point), cannot be established by simple inspection of the figure. This usually happens when some of the observations are missing in the otherwise continuous network. Such equations, not readily identifiable from the diagram, may be called “implicit” condition equations.     

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.     

THE GEODIMETER: AN INSTRUMENT FOR THE ACCURATE MEASUREMENT OF DISTANCES BY HIGH-FREQUENCY LIGHT VARIATIONS

Abstract

The 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.     

THE VARIATION OF THE ATMOSPHERIC COEFFICIENT OF REFRACTION WITH THE NATURE OF THE SOURCE OF LIGHT

Abstract

In working out vertical heights on the Akuse-Kete Krachi chain of triangulation in the Gold Coast a fairly considerable difference was found between values of the coefficient of refraction obtained from observations taken during the day and those taken at night, the mean values being 0.069 for daylight observations to heliographs and 0.087 for night observations to lamps. This difference no doubt is due mainly to the condition of the atmosphere during the day differing from its condition during the night rather than to any effect due to different sources of light. A new chain has recently been observed in Western Ashanti, and the index of refraction for the daylight observations again gave a lower value than that obtained from the night observations, the figures being 0.073 and 0.099 respectively. For the night work three different sources of light were used, hurricane lamps for short lines, Tilley vapour-pressure lamps for lines of intermediate length, and McCaw acetylene signalling lamps by Watts for long lines. It occurred, therefore, to the writer to examine the results to see if the mean values of the index of refraction showed any variations for the different light sources, since it seemed reasonable to suppose that the constitution of the light emitted from each source would be different and hence that the coefficient of refraction might vary.     

THE USE OF THE MAGNETIC NEEDLE ON SURVEYS IN TRINIDAD

Abstract

In Trinidad the magnetic needle is used on all secondary surveys. The term “compass surveys” was given, unfortunately, to these secondary surveys in order to distinguish them from surveys carried out in open country in the ordinary manner with the theodolite oriented by means of solar observations or by bearings obtained direct from the trigonometrical framework.     

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.     

SOLUTION OF PROBLEM IN THE SUBDIVISION OF A TRIANGLE

Abstract

The division of a triangle into three lots of equal area by lines, drawn from a point within it perpendicular to the sides, appears at first sight to be a very simple problem, in which an average surveyor would experience no difficulty in performing the necessary computations for the determination of the position of the required point where the division lines meet.     

THE SURVEY FRAMEWORK OF NIGERIA

Abstract

The vertical framework of Nigeria comprises a network of primary instrumental levels and trigonometrical heights. The primary levels consist at present of (1) a network in the South-western Provinces, (2) a continuous line of levels from Lagos through Ibadan, Ilesha, Akure, Benin, Onitsha, Awka, Okigwi, Aba, and Port Harcourt to Bende in Calabar Province, and (3) a further line from Ilesha to Oshogbo and thence along the railway to Minna, where it is connected to L41, the south terminal of the Minna base. The total mileage of double levelling is 1,128 miles. Trigonometrical heights have been determined by reciprocal observations over all the primary chains.     

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.     

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.     

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.     

ON THE CLASSIFICATION OF MAP PROJECTIONS

Abstract

1. Classes and Varieties. A map projection can be considered from different points of view, each such point of view representing a “class” of projections. The classes, in their turn, are subdivided into “varieties”.     

A MACHINE METHOD OF RESECTION

Abstract

With the modern calculating machine in easy reach of every computer, the problem of determining the position of an occupied point from which direction observations have been made to three or more known points has become quite simple. The method outlined below is quite elegant in form and exceedingly simple on the machine. Let A, B, C be the three points whose co-ordinates (X₁Y₁), (X₂Y₂), (X₃Y₃) are known, and let (XY) be the co-ordinates of the point P which we wish to fix.     

APPLICATIONS OF REMOTE SENSING IN THE STUDY OF THE MOUNTAINOUS TERRAIN OF DAGESTAN

The authors explore a wide range of applications of remote sensing methods in the study of natural hazards posed by exogenous geomorphologic processes in areas of predominantly calcareous and shale-based rock in mountainous portions of Dagestan. Space imagery, air photographs, and ground truth established from field observations provides the basis for the mapping of environmental conditions with an emphasis on the extent to which mass movements and other exogenous geomorphologic processes pose natural hazards to human residence and economic activity. Translated by Elliott B. Urdang, Providence, RI 02906 from: Geomorfologiya, 1993, No. 4, pp. 26-35.     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. 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”.     

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.     

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.     

THE TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID

Abstract

In January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method.     

THE ORTHOMORPHISM OF THE STEREOGRAPHIC PROJECTION

Abstract

When 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.