THE GEODETIC LEVELLING OF CEYLON (1926–1929)

Abstract

The Net.—The total length of the lines of the level-net is roughly 2400 miles. The net comprises 27 circuits with perimeters varying between 74 and 268 miles, and is generally closer in the wet zone than in the sparsely populated and undeveloped dry zones. In 12 circuits there are differences of level exceeding 1000 feet. The highest point reached in the net is 6572 feet, and a branch line runs from Nuwara Eliya to the summit of Pidurutalagala, the highest mountain in the island (8282 feet).     

LONG LINES ON THE EARTH : VARIOUS FORMULAE

Abstract

The use of radar has already begun to revolutionise the science of surveying. It requires the computation of lines on the earth between a hundred and a thousand miles long for the fixation of topographic control.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In 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.     

THE APPLICATION OF RADAR TO SURVEYING

Abstract

Radar can be applied to surveying for precise measuren1ent of long lines, and as a navigational aid and position-fixing device for an aircraft performing a photographic survey. Trials of the radar method have recently been carried out in Australia using a modified “Shoran” equipment. The results of a large number of radar measurements of six distances, varying from 160 to 310 miles in length, indicate that an accuracy of 7 parts in 10⁵ can be achieved. Equipment errors constitute the immediate limit to accuracy, but reasonable modifications would yield a figure of 2 parts in 10⁵. Radar measurements can be completed in a fraction of the time required by normal ground survey methods, since a measurement of upwards of a hundred miles is made in a single step.

As an aid to photographic surveying a straight-line track indicator actuated by data from the “Shoran” equipment has been designed and flight tested. Its performance enabled a pilot taking aerial photographs to keep the aircraft to within an average departure of less than 0.02 mile from any desired straight-line flight path.     

A MODIFICATION OF BOWDITCH'S RULE,TO PRESERVE THE BEARING OF THE DATUM LINE IN A CLOSED TRAVERSE

Abstract

The article derives formulae for adjusting the lengths and bearings of a traverse so as to obtain an exact closure, whilst obeying the Least Squares condition and an added condition that the original bearing of one of the traverse lines is to remain unaltered.     

A TRIGONOMETRICAL UPSET

Abstract

If 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.     

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.     

SILTING AND ISLAND GROWTH IN THE ZAMBEZI NEAR LIVINGSTONE

Abstract

The Northern Rhodesia Survey Department recently carried out a series of measurements of certain cross-sections of the Zambezi in the vicinity of Livingstone. The stretch of river over which the above were made is that known as the Regatta Course and extends between the top of Loando or Long Island downstream to the mouth of the Maramba River. This stretch is about three and a half miles southwest of Livingstone and two to four miles upstream from the Victoria Falls.     

LENGTH AND AZIMUTH OF LONG LINES ON THE EARTH

Abstract

In the E.S.R., viii, 59, 191–194 (January 1946), J.H. Cole gives a very simple formula for finding the length of long lines on the spheroid (normal section arcs), given the coordinates of the end points. In the course of the computation the approximate azimuth of one end of the line is found, the error over a 500-mile line being of the order of 3″ or 4″. If the formula is amended so that the azimuth at the other end of the line is used in computing the length of the arc, the error is then less than 0″·1 over such a distance. An extra term is now given which makes this azimuth virtually correct over any distance. Numerical tests show that Cole's formula for length and the new one for azimuth are very accurate and convenient in all azimuths and latitudes.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION-I

Abstract

“A Well-Defined mountain, though miles inland and never visited by the surveyors, will often prove the very keystone of a chart which cannot be regularly and theoretically triangulated” (“Hydrographic Surveying”, by Rear-Adm. Sir Wm J. L. Wharton, K.C.B., and Rear-Adm. Mostyn Field, F.R.S. 3rd Ed. 1909, p. 128). To many the reasons prohibiting the occupation of inland stations may be unknown; it may suffice to state that, in the past, British hydrographers have mapped many coastal waters where penetration of the land was at least inadvisable. Since the charts so made were in general sold to the world, seamen of all nations have benefited from the surveys.     

TRANSVERSE MERCATOR FORMULAE

Abstract

The Transverse Mercator Projection, now in use for the new O.S. triangulation and mapping of Great Britain, has been the subject of several recent articles in the “Empire Surpey Review. The formulae of the projection itself have been given by various writers, from Gauss, Schreiber and Jordan to Hristow, Tardi, Lee, Hotine and others—not, it is to be regretted, with complete agreement, in all cases. For the purpose for which these formulae have hitherto been employed, in zones of restricted width and in relatively low latitudes, the completeness with which they were given was adequate, and the omission of certain smaller terms, in the fourth and higher powers of the eccentricity, was of no practical importance. In the case of the British grid, however, we have to cover a zone which must be considered as having a total width of some ten to twelve degrees of longitude at least, and extending to latitude 61 °north. This means, firstly, that terms which have as their initial co-efficients the fourth and sixth powers of the longitude ω (or of y) will be of greater magnitude than usual, and secondly that tan² ? and tan⁴ ? are likewise greatly increased. Lastly, an inspection of the formulae (as hitherto available) shows a definite tendency for the numerical co-efficients of terms to increase as the terms themselves decrease—e.g. terms in η⁴, η⁶, etc.     

FIRST-ORDER TRAVERSES IN CEYLON

Abstract

In the last three years about 250 miles of “precise” traverse have been surveyed in this country to provide control for detail surveys. A brief account of the results may be of general interest. The traverses are situated where trig. points are far apart, and the cost of subsidiary triangulation would have been excessive on account of the flat nature of the country.     

THE UGANDA MAlLO SYSTEM

Abstract

The survey of “mailos” or native estates in the Kingdom of Buganda has taken a prominent place in the annual programme of the Survey Department of Uganda for over 30 years past. The survey, which has covered some 17,000 square miles and is now practically complete, has some unusual features, and although it has no claims to refinement or to great precision, a short account of its history and workings may be of general interest. The system of land settlement introduced by Sir Harry Johnston has already been described in the Empire Survey Review (“The Surveyor and the Politician”, by H. B. Thomas, vol. ii, p. 28).     

THE YEAR 1931 IN NORTHERN RHODESIA

Abstract

In the survey world of Northern Rhodesia the most notable event in 1931 (apart, of course, from the birth of this Review) has been the completion of the aerial survey contracts undertaken for the Government by the Aircraft Operating Company. The results have justified expectations particularly with regard to the mapping of 63,000 square miles of the Territory on a scale of 1/250,000. Used in conjunction with the information obtained by ground methods by the Mining Companies, who have kindly consented to put their information at our disposal, a really reliable detailed map of a considerable portion of the Territory should be obtained. The mosaics of the six principal townships are also proving of value and contain a wealth of detail which would be difficult to obtain so accurately by ground survey except at great expense. On the other hand it is obvious that it would be a costly business involving a very large amount of ground control to prepare a closely contoured plan such as is required for detail purposes in connection with township lay-outs.     

PHOTOGRAPHIC SURVEYING OF FLAT COUNTRY

Abstract

THE mapping of flat country from the ground always entails much more work than the mapping of hilly country for the obvious reason that the nearness of the horizon, coupled with the obstruction of trees, buildings, and vegetation, restricts the view, and long lines are not possible. In contrast to this, mapping from air-photographs becomes much more simple when the country is flat, for the photographic projection is not complicated by height distortions, and it is only necessary to correct for distortions caused by the impossibility of keeping the camera perfectly horizontal at the instant of exposure. During the past four years in Bengal and the United Provinces, where the alluvial plains scarcely vary a foot from monotonous flatness, many thousands of square miles have been surveyed photographically, and excellent maps have been made on a scale of 16 inches to 1 mile and are being used by Settlement Officers for purposes of land assessment.     

THE ORTHOMORPHIC PROJECTION OF THE SPHEROID–III

Abstract

In the last instalment we were able to obtain most of the surveyor's projections in common use by applying simple scale conditions to the meridians and parallels. This method of approach naturally suggests that results of some value might be obtained by applying similar conditions to the plane co-ordinate lines. If we do so, we are immediately led to consider curves on the surface known as geodesics, which are the nearest approach to straight lines it is possible to draw on a curved surface. Accordingly, we give some account of these curves for the benefit of surveyors who have not hitherto made their acquaintance.     

LONG LINES ON THE EARTH: THE DIRECT PROBLEM

Abstract

19. 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.     

GEOGRAPHICAL NAMES IN UNINHABITED REGIONS AND THE CONTROVERSY OVER THE MOUNT EVEREST MAP

Abstract

(I) The deserts of India and Baluchistan.—In the eastern half of the Great Indian Desert there are rock-outcrops projecting above the sand at in tervals averaging twenty miles; these have been landmarks for travellers for centuries, and consequently they all have native names. In the western desert there are no outcrops and no objects to name; but the desert nomads and the camel-breeders do have names for vague undefined areas, which seem to move as the sandhills move. The rock-outcrops in Baluchistan are larger and more numerous, and many are consequently without Baluchi names. Nothing would have been gained from inventing names; names are for use, not for show, and the desert people know their own requirements. It is better on a map to limit the nomenclature to the names that have been born of the people and that have stood the test of time than to supplement them with fictitious names. Survey stations on unnamed hills are therefore generally designated by symbols such as B45.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION—II

Abstract

There are numerous possibilities in a Six-point Countersection. The example exhibited in Fig. 5 shows no more than one such concatenation. Here two stations, A and B, are the, only known positions in the neighbourhood; but they are over 29 miles apart and are not mutually visible.     

MAPPING OUT OF CROWN LANDS IN CEYLON

Abstract

The Island of Ceylon has an extent of 25,332 square miles, and a population of nearly seven millions; the range of latitude is from 5° 55′ to 9° 50′ North and of longitude 79° 42′ to 81° 53′ East.