Notes on Technical Proceedings

of the International Association of Geodesy and other Associated matters


B.P. Lambert

Director of National Mapping

Department of National Development, Canberra, A.C.T.


The Assembly was held at Helsinki, Finland, in July and August, 1960.

It was only possible for the writer to attend Sessions of the International Association of Geodesy and with­in that Association to concentrate on Geodetic Survey.


Distance Measurement

Techniques of measurement with Geodimeter and Tellurometer are well established and accepted as regular geodetic procedures (See Appendix 3). They have also been made the subject of an IUGG resolution. Several new types of equipment have been, or are at present in course of, development. However, the Tellurometer is still definitely the optimum geodetic distance and measuring instrument.


Specifications for Horizontal Control Survey

Tentative recommendations were made covering accuracy specifications (See Appendix 4). In discussion it was very clearly indicated that these applied to fundamental surveys (i.e. surveys giving overall coverage) and not to first order surveys.

From this it appeared that the primary chains were to be of a higher order of accuracy and the major fill in between these primary chains was to conform to the recommended specifications.

Generally, the specifications provide for linear and azimuthal accuracy of 10 parts per million between adjacent stations about 20 miles apart.

How long such a specification will last, when any survey agency can now measure a line with an accuracy of 4 parts per million, remains to be seen.

The writer considers that the present first order objective of the National Mapping Council, which seeks a precision of measurement characterised by a probable error of 4 parts per million in both in direct linear distance and azimuth displacement on lines between adjacent stations, should certainly be retained.


Precision Levelling

In the precision levelling field some countries are already using automatic levels for first order work.

There was a full report submitted on the adjustment of the European levelling net and extensive discussion of mean sea levels. The latter discussion arising primarily from the IUGG Liverpool Symposium 1959. These discussions certainly draw attention to the difficulties of finding a true value for mean sea level.

The writer once again came away with the impression that too high a degree of precision was being sought by conforming to the specification for levelling of Higher Precision and that the earlier IAG's specification for levelling of Precision was good enough for any national primary net.

These respective classification line up very closely with the National Mapping Council's first and second order classifications.

This matter was subsequently discussed with Professor Kneissel, Permanent Secretary German Geodetic Commission who thoroughly agreed that good second order levelling with automatic levels would be best for the primary levelling of a previously unlevelled country, the size of Australia.

This endorses the view expressed by members at the last meeting of the National Mapping Council.


Figure of Earth

It would appear that the best procedure at present for Australia would be to swing over to the figure being currently used by the National Aeronautical and Space Administration of the USA. In this figure a = 6,378,148 metres and f = 1/298.3. It is possible to convert successive lines of a traverse or triangulation from Clarke 1858 to this figure by simple semi-graphic techniques which should be adequate until a final result is obtained for the Figure.

The USSR is concentrating on continued astro-geodetic and gravimetric surveys for Figure determination and application of minor corrections to observed data.

Both USA and USSR are no doubt concentrating on the use of Satellites for Figure determination. No Russian works were presented but numerous American publications were available covering basic theory.



In the computation field there appears to be a move towards the application of the methods of mathematical statistics particularly in computations relating to Figure of Earth determination.

There was very little discussion on application of electronic computer techniques to geodetic survey calculations. Although from available reports it is obvious that they are being extensively used.

Hotine forwarded a paper on his Third dimension in Geodesy" and Levallois submitted a paper in which he claimed that the present techniques "specially astro-geodetic levelling, must give the same results as the tri-dimensional computations to build up the shape of the topographical surface when they are treated the right way.


Terrestrial Refraction

Some consideration was given to the problems of terrestrial refraction and experimental equipment has been developed for determining the coefficient of vertical refraction. This looks as though it might be cumbersome for field use. In connection with horizontal refraction in Australia, it is suggested that the technique of simultaneous reciprocal azimuth observations be given a thorough trial in the next few years.


Use of Satellites

Considerable interest was shown in Satellite techniques of geodetic survey and this obviously is the next most important development in the geodetic field. One speaker pointed out that if stellar photography only is used the problem is one of analytical photogrammetric triangulation in reverse and that the inherent errors are the same unless some supplementary measurements are obtained. It is understood that precise radio telemetric devices will be fitted in some future geodetic satellites and possibly flashing lights also.


Likely effect of future Satellite observations on current Australian Geodetic Survey Activities

It became apparent in the course of the proceedings that there is now a growing awareness of the great percentage of clear nights in Australia that are suitable for stellar observations. With the likely intensive future concentration on satellite observation, Australia will almost certainly be sought out as an observation area. It is therefore of the utmost importance that Australian Geodetic Surveys are of the highest practical order of accuracy. That accuracy is al­ready being achieved in respect of distance measurement on the earth's surface. It is suggested that serious consideration now be given to increasing azimuthal accuracy and to the determination of geoid contours.

The practical way to achieve this is by increasing the number of La Place Stations.

In this regard it should be noted that, because of the ameliorating influence of low latitudes, for most of the northern half of the continent second order La Place Stations will suffice. In the southern portion second order stations should be judiciously added to the normal pattern of first order stations.

Due notice should be taken of the IAG re­commendation that such stations should be in pairs and also to the desirability, previously mentioned, of observing simultaneous reciprocal azimuths.

It is thought not unlikely that some fairly simple method of determining longitude differences between closely adjoining stations might be evolved.

Where really bad horizontal refraction effects are evident it will be desirable to follow the proposal put forward by Major A Bomford RE and resulting from his Australian traversing experience, namely, that Almucantar position determinations be made at each traverse stations and that observation to Sigma Octantis be included in the rounds of horizontal angles at every such station.


Distributed Papers

The aspects most relevant to National Mapping are covered by the Appendices attached hereto :

Appendix 1 - Provisional Report on Triangulation and Trilateration.

Appendix 2 - General Report on Precise Levelling.

Appendix 3 - Report of Special Study Group No.13 - ­Electronic Distance Measurement Using Ground Instruments.

Appendix 4 - Report of Special Study Group No.14 - ­Specifications for Fundamental Geodetic Networks.


Summary of Recommendations

As a result of attendance at the above Assembly and subsequent discussions with various experts, it is recommended that :


Australian Geodetic Surveys be tentatively converted to the NASA (USA) Figure of the Earth (a = 6,378,148 metres, f = 1/298.3);


in Australian Geodetic Survey there generally be a doubling of the number of La Place positions, including appropriate use of second order determination and that as a general practice simultaneous re­ciprocal azimuth be observed;


the Primary levelling of Australia consist of good quality second order levelling and that in carrying out this levelling full use be made of suitable modern automatic levels.







Provisional Report on Triangulation and Trilateration 1957-1959

(Originally published in French)



This report has been prepared from extracts taken from the National Reports of the following 25 countries:

Argentine, Australia, Austria, Canada, Denmark, Spain, USA, Finland, France, UK, Greece, India, Eire, Israel, Italy, Japan, Norway, Poland, Portugal, Rhodesia and Nyasaland, Sweden, Switzerland, Czechoslovakia, Thailand, Turkey.

The report is divided in three main sections; measurement of distances, measurement of angles and adjust­ment of triangulation, trilateration and precision traverses.


Measurement of Distance

Distance measurements have been carried out almost exclusively by means of invar wires, the Vaisala inter­ferometer apparatus, the Geodimeter and the Tellurometer. In Italy a new type of radar equipment is in course of experimental development.

Hiran and Shoran have been used exclusively in the USA and Canada respectively.

The Geodimeter has been used to measure :

base lines (Australia, Austria, Canada, USA, Japan)

sides of base figures (Austria, Czechoslovakia) triangulation sides (Argentine, Spain, USA, Japan, Sweden, Czechoslovakia) with very high precision approximately 1 part per million. Spain considers that the mean of 20 sets of measurements has an error less than 1 centimetre.

The disadvantages enumerated in the use of the Geodimeter are principally the following :


the case with which the zero indicator can got out of order;


the need of a field device for checking frequency; (In Spain frequency checks have been made before and after operations using a RHODE-SCHWARTZ frequency standard);


instability of the reflected light ray caused by refraction if the line crosses a deep valley.


A new model of the Geodimeter (No. 4) has recently been built by the Swedish firm of AGA. It is a short distance instrument useful for distances between 15 metres and 6 kilometres (and under favourable conditions up to 15 kilometres). The precision expressed as a mean square error (mse) is ±10 millimetres ± 5 parts per million.

The Tellurometer in general has been found economical, convenient to use, robust, reliable, and readily capable gf precise measurement (1 part per million France; 2 parts per million UK; 4 parts per million Canada).

It is being used in all possible ways, for example :


base lines (Denmark, France, UK, Norway);


sides of traverses (Australia, Denmark, USA, France, British Overseas Territories);


sides of long, narrow quadrilaterals concurrent­ly with angular measurement (Canada) with the objective of obtaining higher precision than possible with geodetic traversing;


sides of triangulations (Denmark, USA, Great Britain, Norway, Portugal);


sides of trilateration (Denmark, USA, UK, Norway).


The capabilities of this instrument have brought about great changes in geodetic survey techniques in new countries; it has been found possible to carry out ex­tensive projects in very short time by adopting the method of precise traversing. The work in the field is diminished and the selection of routes greatly facilitated.

The greatest practical difficulty encountered is in the determination of meteorological conditions.

In particular, the precision with which the temperature can be determined varies inversely as the length of the line; in fact, the mean of the temperatures at extremities does not agree with the actual inter­mediate temperature and it is only by obtaining an estimate equal to or less than 0.2°C (France, Norway) can one hope to obtain a precision of measurement of 1 part per million for distances greater than 25 kilometres and then only with measurements extending over one week.

In the case of lines crossing the sea, measurements will result in great difficulties and uncertainties.

In one case (Norway) the frequency was standardiz­ed (before and after operations) by using a quartz frequency meter which in turn was controlled by radio signals. The resultant error in standardization was less than 1 part per ten million.

The Royal Institute of Technology of Stockholm has constructed a new instrument for electro-optical measure­ment of distances; it is known as the Terrameter. It can be used for distances smaller than 5 kilometres with a pre­cision of 10 parts per 10 thousand millionth of a second (i.e. 0.03 metres). They have also under development a transistorised model with a con­sumption of about 1 watt.


The following is a summary of the most important distance measurements carried out by various countries :


Argentine : has measured 8 bases each with 5 or 6 invar wires and totalling a distance of 71.2 kilometres. The wires are standardised by three comparisons with an underground base of 120 metres (measured with 4 metre invar bars pre­viously standardized at Paris) and by comparison with an open air base of 960 metres, previously standardised by means of the Vaisala interferometer method.

The Geodimeter has been used to measure 4 sides (each 2 to 3 times) of Cerro Puntalla (2476 metres above msl) and 4 other trig points at distances of 5 to 17 kilometres (2,000 to 3,000 metres above msl). The comparisons with sides of the network have given differences of -0.01 metres, +0.01 metres, +0.03 metres and +0.05 metres.


Australia : has only made limited use of the Geodimeter during the period but on the other hand there has been extensive use of Tellurometer, and it is being used to establish the geodetic network over all the continent, using the method of precision traversing for joining between the existing isolated triangulation networks. The total distance measured has been 18,000 kilometres of which only a small portion has been done by classical tri­angulation.


Austria : has collaborated with Germany and Switzerland to measure a base at Heerbrugg of about 7 kilometres length using invar wires. The Geodimeter has been used to measure two parts of the Vienna base line and 5 sides (8.3 to 17.6 kilometres) of two triangles of the Munich base extension network.


Canada : has measured a base approximately 16 kilometres long near Ottawa, with invar tapes, forming part of an experiment­al network of which some sides have been measured both by Geodimeter and Tellurometer. With the Geodimeter 10 bases have been measured varying in length between 20 and 30 kilometres and incorporating 30 measurements on each of 3 nights, mean errors are within 3 centimetres.

The Tellurometer has been used to measure 40 sides of a classical triangulation. The Tellurometer and theodolite have been used to measure long narrow net­works.

The shoran network of 502 sides which was commenced in 1949 is finished; it covers 2,500,000 square miles. in the northern portion, the mean length of sides is 230 miles.


Denmark : the Tellurometer has been used to measure 8 first order triangulation sides. Preliminary calculations in­dicate an accidental error of 10 parts per million with smaller systematic errors.

The Tellurometer has also been used in Greenland for base line measurement and precision traversing and also for connecting the first order network with the triangulation in the interior.


Spain : the Geodimeter has been used to measure 4 sides at the junction of meridional and latitudinal junctions of existing triangulation.

The four sides have been broken into 3 parts and the Geodimeter and reflector placed on masonry piles. The velocity recommended at Toronto was used.

Observations are planned to continue on this basis. unfortunately, the sides will have to be broken into sections as their length (approximately 50km) is too much for direct measurement with the Geodimeter.


United States of America : both the Geodimeter and Tellurometer are in current use.

In the USA, Alaska, Hawaii and the Virgin Islands some 7300 kilometres have been measured with the Tellurometer; in Ethiopia 7 bases totalling 77 kilometres have been measured.

Using the Geodimeter in cooperation with 17 Latin American countries 25 bases have been measured for unification of the north and South American networks. These have been measured at various elevations up to 4500 metres and under extremes of temperature without any unfavourable effect.

Hiran trilateration has been used to measure numerous networks, for connecting islands to brazil and others to Formosa, for the resurvey of the Marshall Islands and for connecting Cuba to central America.


Finland : one base 3742 metres long has been measured with 8 invar wires in Lapland and a mean square error of ±0.79 millimetres obtained. The wires were standardised before and after operations against the Nummela base.

The standard base at Nummela was measured 4 times in 1958 with the Vaisala interferometer comparator with a mean square error of ±0.06 millimeters.


France : experiments have been undertaken with the Tellurometer to determine the best mode of use and with this objective in view four bases and sides of geodetic triangles have been measured.


Great Britain : the Lough Foyle base has been remeasured with the Tellurometer. Since 1957 many sides of the first order triangulation have been measured with the Tellurometer. In general differences of 1 to 2 parts per million have been found but in some instances as low as 40 parts per million has been encountered.

The Tellurometer has been used on precision traversing in central and eastern Africa, Gambia, West Indies and for trilateration in Sierra Leone and in the isles of the West Indies.


Israel : a base 2.5 kilometres long has been measured 3 times at Esdod with an invar band standardised at the NPL England with a relative error 1:2,500,000.


Italy : a base of 12 kilometres (mse ±  0.012 metres) has been measured with invar wires for standardisation of radio/electric distance measuring equipment.

Radar instruments are under development for measur­ing lines up to 100 kilometres long; errors of ±0.5 metres have been obtained in comparison with triangulation.


Japan : 8 triangulation sides have been measured with the Geodimeter and differences of -0.63 to +0.14 metres on 36 to 20 kilometres respectively. It is planned to use the Geodimeter to measure sides at intervals of 200 kilometres in the existing network.


Norway : the Lista base has been measured with the Tellurometer, 20 triangulation sides remeasured and 23 new triangulation sides measured in the neighbourhood of Trondelag.

A triangulation side was measured in 1957 using Geodimeter on loan from Denmark, and has since been measured twice, (1958 and 1959) with the Tellurometer; the results referred to the provisional triangulation value are too large respectively by 41, 12 and 5 centimetres. per the Geodimeter V = 299793.1 was used and for the Tellurometer 299792.5 was used. Adjusting to the latter value reduces the difference of 41 to 35 centimetres.

Between triangulation and trilateration in the Trondelag area, there is a scale factor of 1:92,000. introduction of this factor reduces differences to less than 10 parts per million except for 2 sides crossing the Trondheim Fiord.


Portugal : measurement with invar wires is in hand of the 19 kilometre base at Vilar Formoso. The Tellurometer has been used on the high precision triangulation of Lisbon over sides of 1 to 9 kilometres. The differences with respect to trigonometric lengths are very strange and vary be­tween 1:140,000 and 1:20,000.


Rhodesia and Nyasaland : Tellurometer trilateration has been used for continuation of the geodetic survey in the north. A closed quadrilateral has been measured of which the sides form part of the geodetic triangulation; the results for one side forming part of a meridian arc are :

length by Tellurometer unadjusted

35918.088 metres

length adjusted as trilateration

35918.051 metres

length adjusted as trilateration & triangulation

35918.067 metres

length calculated in 1930

35918.289 metres

length calculated in 1950

35917.929 metres


Sweden : five first order sides have been measured with the Geodimeter (4 of 35 kilometres, 1 of 10 kilometres) forming part of a four sided traverse, a speed of light of 299,793.8 was used. The mse obtained was between ±0.01 metres and ±0.08 metres.


Switzerland : a base of 7254 metres was measured near Heerbrugg. The measurements were made by German, Austrian and Swiss operators.

Twenty different invar wires were used standardised by both the bureau of weights and measures, Paris, and the technical department at Braunschweig and by direct comparison with the Varsala base at Munich. Calculations are in progress.


Czechoslovakia : a Geodimeter was standardised on the Prague 960 metre base and then used to remeasure trigonometric sides of 21 kilometre maximum length and a geodetic base of 6.3 kilometers previously measured with invar wires. The result and precision is superior to 1:500,000.

The Geodimeter was also used for trilateration over a base extension network and the previously mentioned precision was confirmed.


Measurement of Directions

There is nothing significant on the types of signals and lamps used or on the techniques of usage.

Even theodolites used are habitual. Wild T3, Kern DKM3, Hildebrand Askania/Gigas with photographic registration, Bamberg etc.

On the other hand, there is a significant trend toward the use of radio for intercommunication in the field.

The principal methods of azimuth observation used are the well-known method of Schreiber (Argentine with repetition and reiteration on the micrometer dial, Japan, Greece, Sweden). Schreiber modified (Rhodesia and Nyasaland), method of sectors (Austria, Switzerland) and of directions (Finland, UK, Italy, Portugal).

The number of readings of a direction are not all uniform. Some adopt the following numbers :


for the base extension 24 (Argentine);


for the geodetic network 12 (Japan) or 16 (Canada, Rhodesia and Nyasaland) or 24 (Austria, Finland, Greece, Italy, Portugal) or 32 (Canada);


for the first order network 9 (Argentine).

Not every report mentions the mean error of a direction as a function of the observed values.

Some reports give details of the error after adjustment :


errors after adjustment with the formula of Ferrero









±0.56" to ±0.65"





Rhodesia and Nyasaland

±0.43" to ±0.72"


errors deduced from adjustment of survey






±0.62" to ±1.20"


four countries have indicated the errors of closure of triangles



less than ±2"



maximum ±2", mean ±0.63"


Rhodesia and Nyasaland

±0.59" to ±0.97"



approximately 0.2"


In all these matters; weights, errors before or after adjustment, errors of triangle closure, it is hoped that the 12th Assembly General will approve the worthwhile proposals of study Group No.14, in order to codify the expressions of precision and to establish the weights and tolerances to be adopted.

Many countries have finished their triangulation. Some have completed in the period under review (Italy, Poland, Switzerland, Czechoslovakia, Turkey), some have concentrated all their activity on linear measurements with the new instrument (Australia, Spain) some have stopped for different reasons (India, Ireland, Israel, Thailand). That is why mention is made here only of certain countries that have carried out work which in it­self constitutes an entity of importance in the field of angular measurement.


Argentine : continues with its well-known triangulation project. More than 144 geodetic network stations and 116 supplementary first order stations have been established, 15 of 51 proposed figures have been observed.


Austria : has reobserved 6 geodetic stations.


Canada : continues with triangulation observation - first order work of a length of 22,217 kilometres has been completed. Two large chains of triangulation, one in Saskatchewan and the other in Alberta have completed a very large loop in conjunction with previous work. 5,536 kilometres of second order triangulation has been completed.

A network of 7 stations near Ottawa has been measured for the purpose of checking radio/electric equipment; the sides are of variable length between 8 and 64 kilometres.


Denmark : has continued with triangulation in Greenland on the east side in order to continue the triangulation chain from Cape Farvel to the North.


United States of America : has dedicated much of its effort toward projects involving the launching of geodetic satellites in order to strengthen the whole triangulation of the country, for long distance connection between geodetic survey and for the general determination of the figure of the earth.

Trigonometric stations numbering approximately 4,000 have been connected to the first order network filling in the network in the USA. itself, in Alaska, in Hawaii and the survey of the borders of the Great Lakes etc.

In collaboration with the Ethiopian Government a first order triangulation over the basin of the Blue Nile was commenced in 1957.

This survey is tied to the African datum which in turn is connected to the European datum. To the end of 1959, 251 stations had been completed.

In collaboration with the Government of Iran a chain of triangles has been observed of the frontier with Turkey to that with Pakistan.

Astronomical stations for latitude and longitude have been observed along this chain at intervals of 30 miles.

With the consent of the Libyan Government a first order triangulation arc has been completed from Tunisia to Egypt for cartographic purposes.


Finland : has carried out triangulation in Lapland. At first long lines (up to 70 kilometres) were attempted but these proved unsatisfactory due to meteorological conditions and shorter distances (average 38.5 kilometres) were used. This will provide a long desired connection with the Norwegian triangulation.


France : in 1957 they completed the observations of its first order network by the additional first order work in Brittainy; the total being 950 first order points connected to 15 bases and 11 La Place Stations.


Great Britain : has extended first order observations to the Isle of St Kilda.

Overseas triangulation has been under­taken in Uganda, Kenya, Tanganyika, Nigeria, in the eastern portion of North Borneo and in other minor places.


Greece : has continued with revision for the purpose of reestablishing marks and assuring the precision necessary for the next European adjustment. 9 new points have been established and observations completed at 25 first order stations.


Japan : has reobserved 38 stations in their geodetic scheme.


Norway : has continued and is continuing with its geodetic network in the north-east - 11 stations were observed in the period.


Portugal : has occupied 12 out of the 36 points of the new fundamental triangulation and 20 first order points in the central region.

On the Isle of San Miguel (Azores) and the Isle of Madeira the old triangulation networks are being revised.


Rhodesia and Nyasaland : a first order geodetic network over the whole country is under way. In the period 1957-1960 83 new stations were established.


Switzerland : Their geodetic network was completed many years ago and complementary work on sub­sidiary control continues.


Connection between triangulation schemes of different countries have not been numerous in the period, but account should be taken of the fact that numbers of such connections were reported in the previous period.


Denmark and Sweden have extended their first order triangulation by 4 triangles north across the Kattegat, with 3 stations on the Danish side and 2 on the Swedish side;


the triangulation covering the basin of the Blue Nile in Ethiopia has been linked with the Sudan triangulation;


the chain of quadrilaterals at present underway in Iran is linked with the surveys of Turkey and Pakistan;


the USA in collaboration with 17 Latin American Countries has established 750 first and second order triangulation stations in continuance of the project of creating a common geodetic network for North and South America;


Germany, France and Switzerland have improved the international junction in the vicinity of Basle;


France, Italy and Switzerland have also improved the junctions in the region of Mont Blanc. Italy has established 7 stations;


Norway and Sweden will complete the junction of their triangulations in the next two years;


the now fundamental triangulation of Portugal will join with the Spanish geodetic survey following resolutions adopted at the Symposium on European Triangulation (Lisbon 1960);


the African Arc (30th meridian) is available in Rhodesia and Nyasaland. Junctions from this have been made to the Belgian Congo, Mozambique and Tanganyika.


The following information on La Place (LP) activity is taken from available reports.

Spain : has established a new LP point at Ponade Francia.


France : has established a new LP point near the Crozon base in Brittainy making a total of 11 points in the network.


Israel : has completed azimuth observations at 3 points spread equidistantly along the southern portion of the network. Probable errors were between 0.16 and 0.30".


Norway : has observed 2 new LP stations with probable errors in longitude of ±0.014" and latitude of ±0.022" respectively. Time was measured with a quartz clock.


Poland : has measured 20 LP points along the first order survey and at other points in the complementary triangulation.


Portugal : proposes 4 LP points in the new fundamental triangulation. For this purpose, a special study has been made of the accuracy of the circle of a Wild T4 theodolite.


Sweden : has a programme in hand for the measurement of new LP station to a very high precision.


Switzerland : has not measured any LP points as they consider the equation applies only at sea level and that no means exists whereby it can be applied to angles read among high mountains.


Turkey : has measured 7 LP points bringing their total to 106.



Adjustment of Triangulation, Trilateration and Precision Traverses

The activities of various countries in various types of adjustments have been grouped under that country's name but the various types of adjustment are grouped separately.

Classical triangulation adjustment has been under­taken by Argentine, Finland, France, Israel, Japan, Poland and Portugal.


Argentine : has adjusted 10 polygons (out of a total of 51) and some chains along parallels and meridians. For the solution of 1121 normal equations they used the method de las figuras de enlace already mentioned in the General Report 1954-56.


Canada : has completed preliminary adjustment on four first order triangulation areas.


Finland : has commenced in 1955 the adjustment of the triangulation of the whole country that was before completion of all the angular observations. For this purpose, they have fixed a chain along the 43rd parallel as a buffer zone between the adjustments of the northern and southern parts of the country. At present the adjustments of the northern portion and the buffer zone are under way.


France : has in hand the adjustment of the National first order network and also that of North Africa.


Israel : has the adjustment of the southern portion of its triangulation under way. It will be com­pleted when astronomic observations have been finished.


Japan : has adjusted two arcs to fit into the previous principal adjustment of 1956.


Poland : has finished the important calculations of a first order astro-geodetic network containing 13 base lines, 20 La Place points and 34 points of astronomic/gravimetric levelling.

The following conditions were applied, triangle closures, side equations (mean error of 30 in the 7th place of logarithms) bases (mean error ±0.9") and azimuth (mean error 0.5").

Before proceeding with the adjustment, corrections were applied for movement of the pole, speed of transmission of radio waves, azimuth observed at each end of control lines, for deviation of the vertical, for the length of the station and for the difference of direction of the geodesic line and the normal section.

The Krassowski ellipsoid was used. The angles were adjusted by a method of indirect observation.

The sides developed from base lines and La Place azimuths are treated as free of errors.

The adjustment was carried out on the Gauss-Kruger plan by the method of Prania-Praniewicz.


Portugal : for their adjustment of the geodetic network the system was broken up into blocks and the calculations were based on the Hayford Ellipsoid.

An adjustment of the primary network was carried out by the USA in 1956 using the ED 1950. The geodetic networks of the 5 Isles of the Central Group are being recalculated on the new datums.


Sweden : Their new network completed in 1953 will be strengthened by space triangulation.


Adjustment of pure trilateration has been carried out in Canada where it is reported that the adjustment of Shoran trilateration (carried out since 1955) and using a fixed position at Thule has been completed as a block adjustment using a UNIVAC calculator of the United States of America.

A method of adjustment using both angular and linear measurements has been developed and used in Canada.

The length equations are written in logarithms and the logarithms of distances corrected simultaneously with the directions, the corrections being determined as residuals of the adjustment.

This method has been applied to an experimental Tellurometer network near Ottawa in which two distances only at the ends of the net were measured with the Geodimeter and introduced without correction.

The results of 8 different adjustments of the net­work indicate that the Tellurometer distances are too large by 1:300,000.

The same method was used for the adjustment of the two arcs of triangulation previously mentioned in which case sides were measured with the Tellurometer.

The USA has developed methods for simultaneous adjustment of triangulation, trilateration and traverse. The formulae, techniques and methods were described at the Annual Reunion of the American Geophysical Union at Washington (1960). Adjustments with these methods have been carried out since 1958.

To the present 5,600 miles of figures have been adjusted with sides in the neighbourhood of 4.5 kilometres and with mean length corrections of 1:48,000 and angle corrections that have been within the tolerances acceptable for 2nd order work.


The calculation of geographical positions of points, calculation of projection coordinates, and the solution of great systems of linear equations are more and more being carried out by electronic calculators.

Canada : has used the IBM 650 for the solution of the following problems. For calculation of geographic position given the following data :

Geographic coordinates of two starting points, length and azimuth of the line joining those points, angles A and B for each triangle. Out­put is sines of the three plane angles of each triangle together with the relative differences of these sines for an angular difference of 1"; the lengths of the two unknown sides; the re­ciprocal azimuths of these lines; spherical excess; geographical coordinates of the un­known point. The time of calculation for each triangle is 5 seconds.

The calculation of plane coordinates in the stereographic projection, the input data being; geographical coordinates of point of origin of projection, distance from origin at which scale factor is unity, coordinates of the origin referred to the false origin, geographical coordinates of the point of transformation. The output is; distance and azimuth of the point from the origin, convergence of meridians, N and E coordinates in metres and X and Y in feet. The time to calculate each point is 7 seconds.

In order to facilitate the solution of systems of 100 linear equations, special punch cards have been prepared and special pneumatic accessory used.


United States of America : has carried out with a similar computer, for Great Britain, calculations for the application of three dimensional techniques to the adjustment of trilateration and triangulation.

The same machine has also been used for adjustment of aerial analytical triangulation and for the treatment of observations made to rockets and satellites.


France : has studied the propagation and solution of large linear systems for the IBM 704. At present it is possible to resolve in 15 minutes, linear systems with 200 unknowns corresponding to a geodetic network of one hundred points.

Use has also been made of a method of reducing stars to the day of observation, commencing from a fundamental catalogue say for example based on the year 1960. This method is easily adaptable to calculators in common usage such as BULL, or IBM 650.


Portugal : The electronic calculator ZEBRA has been used for adjustment of large geodetic systems; a programme of normalisation and of elimination has been developed permitting the treatment of 52 conditional equations.


Notes on other activities

The research and work completed in the fields of trigonometric levelling, horizontal refraction, horizontal displacements and of stellar triangulation are not numerous, but the latter are of very great importance.

Indirect levelling is nearly always carried out by the same techniques and is not a subject of particular research.


Portugal : elevations of trigonometric stations near to lines of precision levelling are derived from bench marks. Elevations of other points are obtained by trigonometric levelling.

Reciprocal vertical angles are generally made over very short distances, 2 to 6 kilometres at the maximum.


Switzerland : in high mountains in the neighbour­hood of Jungfrau many reciprocal vertical angles have been read between points of known coordinates. On some points, about 10 kilometres apart, astronomical observations have been made to determine components of the deviation of the vertical from which contours of the geoid have been deduced, orthometric altitudes have also been obtained.

For adjacent points, about 6 kilometres apart, it has been found that :

for geoid contours and orthometric heights a mean error of ±4 centimetres and a geoidal elevation of 24 metres at the central point (2575 metres elevation) of the zone studied;

for the deviation of the vertical mean errors of ±1.5" and values as high as 20 to 25".


Czechoslovakia : the adjustment of all angles measured in the altimetric network (trigonometric) have been made taking into account the configurat­ion of the geodetic network, the influence of deviations of the vertical, and variations in the coefficient of refraction for each point.


There has been very little interest in research into earth movement.

Japan has completed a 2nd and 3rd order survey of 1270 kilometers in the region of Tottori which subsided in the 1942 earthquake end in the mining zones of Kyushu, Scrachi and Hokkaido for the purpose of watching local deformation of the terrain.

On the other hand, in the neighbourhood of Nilgala horizontal displacement is determine by measuring base lines with 25 metre invar wires and observing the angles between these. Operations are repeated every 2 years.


Finland : to diminish the effects of lateral refraction in flat areas always constructs wooden towers at least 5 metres high.


Switzerland : horizontal refraction is encountered in the plains country but is extremely rare in mountainous regions.

It goes without saying that in high mountains a constant lateral refraction is difficult to determine because it merges into the influence of the deflections of the vertical.

Some research is underway to clear up the phenomenon over one line of 20 kilometres where lateral refraction reached a value of 2".


Finally, it is important to stress the technique of Professor Vaisala for photographing a light flash against a stellar background. The lights are set off automatically at a high altitude and are attached to a balloon.

Experiments have been conducted between the observatories at Turku and at Helsinki.

Adopting a three dimensional system of coordinates referred to known terrestrial points, the intersection of the separate planes containing the observation points and the various light flashes enables resection of the extremities of line joining two un­known observation points.

The results of this experiment have been positive, errors as compared with triangulation have been -1.8 metres in horizontal distance and -0.9 metres in the vertical over a distance of 153 kilometres.

Measurable distances can be lengthened and precision improved, this will be the objective of further programmed experiments.

This type of triangulation should diminish the effect of lateral refraction, increase the length of sides, control extended geodetic determinations without reference to the direction of the vertical and permit a new system of geodetic triangulation in three dimensions.

In future methods based on the studies of Marussi, the calculation procedures of Hotine and the experiments of Vaisala should permit entry into a new phase involving large extensions and contributing to the completion of triangulation schemes with sides greater even than 150 to 200 kilometres.

The hope is expressed that at the 12th Assembly at Helsinki there will eventuate a recommendation along those lines.







General Report on Precise Levelling 1957 – 1959

by A. Waalewilln.


This report has been compiled from the information received from 31 countries in reply to a questionnaire, sent by the Central Bureau on February 1, 1960. The answers received after June 25, 1960 could not be inserted in this preliminary form of the report.


General Information

The total length, levelled by the reporting countries during the period 1957-1959 is about 100,000 kilometres of levelling of high precision and about 60,000 kilometres of levelling of second order. In some cases, the reported levelling of the first to be accomplished but mostly the levelling is carried out along lines that have been measured once or even twice before. This relevelling is necessary in areas with strong tectonic movements, but even in stable areas relevelling cannot be avoided because many benchmarks along the line will disappear in the course of time.

First levellings were completed in Madagascar, French Equatorial Africa and French West Africa. Relevelling of the national network was finished in DDR, Scotland, Northern Ireland and the Netherlands, while the relevellings in Austria and Norway will be finished soon.

A specification of the levellings carried out in this period will be found in the national reports.



Nearly all countries report the use of the well-known first order dumpy levels Wild N III and Zeiss A and the reversible level Zeiss III together with invar staves. Some countries are using the instrument of Cooke, Troughton and Simms (Great Britain, Ireland and New Zealand) or the Fischer level (Coast and Geodetic Survey Level) (United States and Thailand).

In the Deutsche Demokratische Republik the Ni 004 of Zeiss Jena is used, in France the instrument IGN 50. In the Nether­lands the Fennel Plani is used besides Wild and Zeiss levels; New Zealand reports also the use of a Watts level. In Chili the level III (without parallel plate micrometer) is used, with staves of the Coast and Geodetic Survey model.

Various countries report their intention to make use of the new automatic instruments even for first order work. In particular, the Zeiss Ni 2 equipped with parallel plate micrometer, a rigid tripod and invar staves is considered successful.

Some countries use it as an experiment only (Australia, the Netherlands, Portugal, Czechoslovakia) others mention it as their standard equipment (Belgium from 1960, Spain, Rhodesia and Nyasaland).

It is to be expected that this tendency will continue; the instrument of Filotecnica Salmoiraghi 5190 is used in Denmark. In France the Zeiss Ni 2 and Ertel are used in 4th order levellings.

New instruments are reported by only very few countries: the DDR reports an automatic level Koni 007, developed by Zeiss Jena. We know however that similar instruments are being constructed by, for instance, Askania, Cooke, Troughton and Simms and Hilger and Watts.

DDR reports also on a comparator for invar staves to be used in the field. In Sweden such a device has been constructed, using a military range finder. Sweden developed also an equipment for measuring the temperature gradient.



The methods of the various countries are in general the conventional ones. Some countries give detail referring to special Publication 239 of the US Coast and Geodetic Survey (Chili, USA, Thailand) the Cholesky method (Spain) or the improved method IG Merlin (Tunisia).

The maximum length of sight diverges for various countries :

         40 metres - Ghana, Poland and Tunisia

         45 metres - New Zeeland

         50 metres - Portugal

         60 metres - the Netherlands and Union of South Africa

         70 metres - occasionally in Finland.

The maximum allowed discrepancy (forward minus backward measurement) as given by some countries is :

2.5mm√D (D in km) - the Netherlands

3.0mm√D (D in km) - Rhodesia and Nyasaland, Union of South Africa

4.0mm√D (D in km) - Congo, Ghana, Thailand

1.5mm√D (D in km) - Portugal

3.2mm√D (D in km) - Australia



Large countries give Mean Sea Level (MSL) as their datum; the levelling network is adjusted to a number of tide gauges along the coast (Chili, USA, Canada).

Other countries have only one tide gauge as their datum which enables them to define their MSL in terms referring to that particular tide gauge. In these cases, determination of MSL must be repeated at regular intervals if the land is rising or sinking with respect to MSL (Norway, Sweden). In contrast some countries maintain the once established height of a certain benchmark as their datum point (Austria, Belgium, Japan, the Netherlands, Portugal, Tunisia).

The levelling nets of DDR, Poland and Czechoslovakia are now referred to the same datum point, viz. The zero of the maregraph at Kronstadt, which is also the Soviet Union's datum point.

The nets of Ireland and Northern Ireland will be referred to a common datum point, which is MSL observed at the new tide gauge at Malin Head.


Adjustment and corrections

In various countries new first order measurements are adjusted to existing heights of stable benchmarks, to avoid diffi­culties in general use (Austria, France, Great Britain, the Netherlands). Besides, so-called scientific heights are obtained from a free adjustment of the new levelling net.

In nearly all countries a correction for gravity is applied; about half of them are measuring the acceleration of gravity (at intervals from 1 kilometre in mountainous areas to 10 kilometres in flat areas). In the remaining countries a theoretical value of g is used, but some of these countries are considering to measure R.

Correction for refraction is applied in only two countries (Finland and Sweden) whereas it is applied only in special cases in Chili and in Portugal.

Corrections for the attraction of sun and moon were reported only by Sweden. In Japan a secondary level net was improved by applying corrections for deformations of the earth's surface; the mean error decreased from 2.7 mm/km to 1.8 mm/km.

It is difficult to compare the figures of precision given by different countries. Some are using the formulas of 1912, others the 1936 or 1948 formulae. Moreover, it is not always clear whether a probable or a mean square error is given. In general, the mean square total limiting error per kilometer is somewhat more than 1 mm, but in some cases a value of 2.5 mm is reached.

In only one case, for one line, it was possible to deter­mine the limit z (Portugal; z = 60 km). Sweden did not apply the formulas because it is considered they should be replaced by more convenient ones. Your General Reporter believes that only repeated
measuring of the same levelling line will provide the material to obtain a better insight into levelling precision and accuracy by statistical analysis. Any other attempt to replace the present formulas by new ones will be fruitless.

Several countries are using electronic computers in solving sets of equations in the adjustment of levelling nets (USA, France in 1960, the Netherlands, Sweden in 1960). Canada has prepared a program for computation of orthometric elevations and dynamic numbers on the IBM 650. This program is now being modified to distribute misclosures. In Great Britain punched aids are used for routine computations.



The information concerning junctions was not always clear so that it could not in every case be decided whether the junction was new or already reported before. Moreover, the data furnished by two neighbouring countries were frequently in disagreement; the same phenomenon appeared in the previous General Report. Probably this results from the fact that many junctions are not measured simultaneously by both countries concerned.

The junctions as far as they are not mentioned in the previous report are :


Number of Junction points

Reporting country

Neighbouring country


Other periods




? before 1940




? before 1940


Northern Ireland


1 near future








3 in UELN

7 in Southern Norway

The Netherlands



















4, 1946 in UELN

2, 1946










No details











Republic du Congo




Republic Centrafricaine





no details





no details




no details




various 1929








no details




no details




1 in 1937

Rhodesia and Nyasaland 

Union of South Africa



Rhodesia and Nyasaland 



1 near future




3 near future

North Africa

West and Equatorial Africa


3 near future


Water crossings

The transfer of levels across wide water gaps is reported by various countries. By far the widest is the Japanese crossing with triangulation methods of the Tsugaru Strait in its western part, the distance being 20 kilometres. Together with the crossing in the eastern part of the Tsugaru Strait a circuit is closed, but no details about the misclosure of this circuit are available.

In France a measuring across a 10 kilometre wide gap south of Marseilles is in preparation; it will be carried out with Wild T3 theodolites.

Crossings of 5 kilometres are reported by Japan (m.59 error 5.9mm) and by Norway. Further 2 crossings of 3 kilometres were carried out in the United States of America, another one of 3 kilometres in Scotland. Smaller water crossings are reported by DDR (2150 metres, mse 1.6 mm), Congo, Chile, USA. France, Ghana, Great Britain, Iran, Ireland, Japan (2.3 kilometres with mse 3.0mm and one of 0.6 kilometres with mse 0.7 mm), Norway, Poland, Rhodesia and Nyasaland. In the Netherlands 12 transfers were accomplished by hydrostatic levelling after the example of Norland.

The widest gap was 6700 metres closing a circuit around the Shallows. The misclosure of this 250 kilometre circuit, containing 3 hydrostatic levellings of about 3 kilometres, one of 6.7 kilometres and a 7 kilometre long stretch through the tidal marsh was 6.2mm. In Sweden successful experiments were made to carry out hydrostatic levelling in winter putting the pipe on the ice.

A level connection between England and France will be made by reading tide gauges on either side of the Channel and applying a correction for the effect of wind, current and barometric pressure.


Seasonal and diurnal oscillations of the earth's surface

In Belgium 4 levels and a set of horizontal pendulums were used in investigations into the influence of the sun's heating on a patch of ground. Observations were carried out for at least 48 hours continuously. The measurements are not yet finished.

In the Netherlands small movements between marks in piles about one kilometre offshore and marks on the coast were revealed by hydrostatic levellings. The movements are closely related to the tide; the sea bottom was apparently low at high tide, with an ampli­tude of maximum 12mm (tidal amplitude about 3m).


Secular and sudden movement of the earth's surface

Preliminary studies were carried out in Israel and Sweden. Local movements of the earth's surface were found in Austria, Czechoslovakia, and in the Netherlands. Vertical movements in Poland are about 1mm/year, with a maximum of 2mm/year.

In some countries earth movements caused by the removal of water, oil and gas were determined (United States of America, Japan, New Zealand, the Netherlands). In Japan the most severe sinking by this cause in 50cm/year in Niigata. In the United States of America, a settlement of 18.86feet (about 5.75m) was measured after an earthquake in the region of Hebgen Lake (Montana).

The survey of vertical deformations in Japan was extended. The land uplift in Norway was investigated from the results of tide gauges. The land upheaval at Oslo was 3.6mm/year, at Bergen zero.


Special investigations

In Israel preliminary investigations into the systematic effect of refraction along a continuous slope were carried out. Poland reports a study on refraction and the effect of temperature variations on the precision of levelling.

The systematic effect of the illumination on certain types of staves was investigated in Finland and in the Netherlands. In Finland this phenomenon was studied for normal painted staves, but no effect has been found, neither by artificial lighting nor in field observations. In the Netherlands a pair of engraved staves were investigated with artificial lighting. It was found that most of the lines of the investigated staves were elevated above the surface of the invar ribbon so that direct lighting from above will cast a shadow under the line.

The result will be an increase of the staff reading so that the northern end of a levelling line will be estimated too low, which is in contradiction with the results found in Great Britain.






Report of IAG Special Study Group No.19

Electronic Distance Measurement Using Ground Instruments






Special Study Group No.19, dealing with Electronic distance measurement using ground instruments was set up at the end of 1956, with Col. RCA Edge as President and PH Kenny as Secretary. It has taken several months to enroll the members of the group, and it was not until mid-1959 that it was fully formed. The time available for the study necessary to complete this report has been short.


Scope of the Study

The group is concerned only with the study of instruments set up on the earth's surface to measure distance for geodetic purposes by means of electromagnetic waves. It is not concerned with airborne instruments (SHORAN, HIRAN or airborne Tellurometer) or instruments in­tended for hydrographic and topographic survey or navigation. It is concerned with actual measurements and their calculation, not with the incorporation of these measurements into triangulation, trilateration or traverse nets. This last is the province of SSG No.14.



It has not been possible to arrange a meeting of the SSG as such, but a number of members attended the Symposium on Distance Measurement at Washington on May 6 - 12, 1959. There was also an informal meeting of certain members during the Commonwealth Survey Officers Conference at Cambridge, England, in September, 1959. The subject was also discussed at the Lisbon meeting on the European triangulation adjust­ment in May, 1960. Reports of these meetings have been made available. For the rest this report is based on the study of a number of papers etc which were made available to the Group (See References).


Scope of this Report

The study has been carried out under the following main headings :


Design and construction of instruments.


Operating methods (including special precautions necessary).


Practical results and accuracy attainable.


Connected scientific questions (speed of light, refractive index etc).


Owing to the shortage of time, however, it has been necessary in this report to concentrate mainly on items (b) and (c) above.



Techniques considered

The techniques and systems considered by the group have been of four types :


Systems depending upon the phase comparison of continuous radio waves


Three such systems were briefly studied Decca, Lorac, and Raydist. These systems have been adapted and used with success for distance measurement and position fixation for topographic and hydrographic purposes, but it does not appear that they, or other systems of this type, can be used for geodetic work in normal conditions since, except when they are used over absolutely homogeneous surfaces such as water, their accuracy is seriously impaired by uncertainty as to the speed of radio ground waves over varying types of terrain. These methods are not therefore further considered in this report.


Light interferometry


This method depends on the observation of interference between light reflected several times over a short distance with light from the same source reflected once over a longer distance when the latter is an exact multiple of the former. The technique was originally used in the laboratory for the measurement of short lengths and it has been adapted for much longer distances in the Vaisala apparatus which has been successfully used to measure lengths up to 864 metres in Finland, Argentina, the Netherlands and Germany.

Very great accuracy (of the order of 1 part in 10 million) is obtainable, but the distance measurable is severely limited because of the necessity for a very high degree of atmospheric stability along the path. Moreover, elaborate vibration ­free, stable mountings are required for the light source and reflecting surfaces. The method is therefore to be regarded more as a laboratory method, especially applicable to the standardisation of measuring tapes and the calibration of other distance measuring instruments. In the context of this report it is not regarded as a geodetic method and is not, therefore, considered further.


Instruments using modulated light waves


These instruments all work by means of a comparison of outgoing and returning modulated light waves reflected from a distant mirror. The following instruments, of which some details are known, have been considered :

Geodimeter, Models NASM 1,2,3 & 4;


Munich prototype electronic distance meter;    

Federal German Institute of Applied Geodesy Electronic Distance Meter; and

Russian Light Range Finder SVV 1.


Instruments using modulated microwave signals


These instruments use a phase comparison technique to measure the transit time of crystal modulated microwave signals transmitted from a master station and instantaneously retransmitted from a remote station. The following instruments have been studied :

Tellurometer, MRA 1 and MRA 2; and

Cubic Microdist.


Basic physical questions relevant to the Study 


Speed of light in vacuo (Co)

Various light velocities have been used in the past for distance measurements with electromagnetic waves. The velocity now accepted by the IUSR and IUGG is :

299,792.5 ± 0.4 kilometres per second (km/s).

This has been used throughout this report, all results received having been reduced to this value unless otherwise stated. It is obviously desirable to refine this value further if possible, although the measure­ments included in this report do not suggest that it is incorrect. The Geodimeter measurements tend to indicate that it is 0.2km/s too low whilst the Tellurometer measurements suggest that it is too high by 0.4km/s. These opposite tendencies are curious, but they have little significance and are most likely to be due to refractive index errors.


Refractive index of air (light waves)

No standardised formula for the refractive index in air of light waves has been laid down by the IUGG or IAG. It appears desirable to do so in order that all results obtained may be immediately comparable. The currently accepted value for the refractive index (n) of standard air at optical frequencies is understood to be that given by Edlen's formula :

(n-1) * 100,000,000 = 6432.8

+ 2949810 ((146 – (O^2))^-1)

      + 25540 ((41 – (O^2))^-1)

where O is the vacuum wave number expressed as the reciprocal of the vacuum wavelength measured in microns.

Standard air is dry air at 15°C, 760mm Hg with 0.03% carbon dioxide by volume. However, the formula believed to have been used for all Geodimeter measurements quoted in this report is that due to Barrell & Sears

(nG-1) * 10,000,000 = 2876.04

+ 16.288/(O^2)  

                                              + 0.136/(O^4)

         where O is the light group wavelength in microns. These formulae agree to 1 part in 100 million over the visible spectrum, and are both accurate to better than 1 part in 10 million.

The refractive index in ambient conditions is obtained by the following approximate formula based on the assumption that dry air and water vapour behave as ideal gases, and upon as assumed mean value for water vapour over the group of wave lengths transmitted.

         nL     = 1 + [(nG – 1/1 + æ*t) * (p/760)] – (0.000,000,005/1 + æ*t)^e

         where nL    = refractive index in ambient conditions

nG    = refractive index in dry air with 0.03% carbon dioxide at NTP (0°C, 760 mm Hg) for light of the group wavelength employed, calculated as above

t       = temp in °C (=T° K - 273)

p       = atmospheric pressure in mm Hg

æ      = coefficient of expansion of air (0.00367)

e       = partial vapour pressure in mm Hg

Although the Barrell & Sears formula reduced to ambient conditions as above is theoretically slightly less accurate than the best available, its error appears to be negligible for geodetic purposes and since it has been so widely used in the past, it is recommended that it be adopted as standard for distance measurements using light waves.


Refractive index (microwaves)

A number of slightly different formulae for the refractive index of microwaves have been used in the past. Aslakson initially developed his own formula for SHORAN work. Later a formula was developed by Smith and Weintraub which was used by Wadley and others for early Tellurometer measurements. It would appear that the best formula avail­able at present is that first published by Essen and Froome. This is as follows (neglecting the effect of partial pressure of carbon dioxide) :

(nR - 1) * 1,000,000 = 103.49 (p - e)/T + (86.26/T)*(1 + 5748/T)e

 where T = Temp in °K

p = Atmospheric pressure in mm Hg and

e = partial pressure of water vapour in mm Hg

This formula has an accuracy of ±1 part in 10 million in normal conditions and is better than ±1 part in a million in extreme conditions. It has been pre­ferred by Wadley and others for their more recent work. It is recommended that it be adopted as standard. The simplified form in which it has been used by Wadley and others for most Tellurometer measurements is the following :

N= (nR - 1) * 1,000,000 = (4730/(459.5 + t))*(p + (8540 e/(459.5 + t)))

where        nR = the refractive index of radio microwaves

t = the dry bulb temperature in °F

p = atmospheric pressure in inches of mercury

e = partial water vapour pressure in inches of mercury

This form is satisfactory for normal conditions but becomes inaccurate in extreme conditions. The complete form is therefore to be preferred.


Conclusions and Recommendations

The instruments that have been established to have the required characteristics of high order geodetic instruments as regards convenience in use, range and accuracy, are the following :


Using light waves

Geodimeter NASM 1



Geodimeter NASM 2


Using microwaves

Tellurometer MRA 1



Tellurometer MRA 2


The Geodimeter NASM 3 and 4 can also be used for certain geodetic purposes but are excluded because of their more re­stricted application. Not enough is known about the Russian Light Range Finder SVV 1 to include it with (a) above, although it seems to have geodetic capabilities. The Cubic Microdist is also claimed to have the required characteristics for a microwave instrument, but as no results have yet been received this cannot be confirmed.

Accuracy (when used as recommended – see be­low)

Geodimeter NASM 1

Probable (50%)

±3.0cm ±0.7 parts per million


Limiting (95%)

±9.0cm ±2 parts per million

Geodimeter NASM 2

Probable (50%)

±1.5cm ±0.7 parts per million


Limiting (95%)

±4.5cm ±2 parts per million

Tellurometer (MRA 1 & 2)

Probable (50%)

±2.0cm ±2 parts per million


Limiting (95%)

±6.0cm ±6 parts per million







Geodimeter NASM 1 & 2

up to 40 kilometres in good conditions; normally up to 30 kilometres.

Tellurometer (MRA 1 & 2)

up to 80 kilometres in good conditions; normally up to 50 kilometres


Recommendations for Use


Electronic distance measurements, especially using microwaves, are more subject to un­detectable systematic errors peculiar to the particular line measured than are non‑electronic measurements; viz conditions of refraction, ground reflection and propagation, and electrical interference. Those errors cannot be wholly eliminated even by frequent repetition in widely varying weather conditions. Therefore, especially with microwave methods, it is better to measure with reasonable pre­cision a number of different lines (e.g. the sides of a triangle or braced quadrilateral) in the area where scale control is required, than to attempt to measure a single line with very high precision.



Weather : By night; best when conditions are uniform and stable; preferably over­cast weather with fair wind.

Met observations : Must be very carefully taken at both terminals, especially air temperature which should be taken using the dry bulb of a mechanically aspirated psychrometer and should be correct to 0.1°C.

Siting of bases : Ideally the entire light path should be a few metres clear of the ground. Grazing rays and excessively elevated rays should be avoided as they increase uncertainty as to refraction.

Observing programme : Not less than 12 complete measurements spread over at least 2 nights in favourable met conditions, more if un­favourable. Each measurement to consist of mirror and light conductor readings on all frequencies in all phase positions.

Calibration : Frequency to be checked in working conditions before and after observations. Zero correction to be calibrated on a short base, say 50 - 200 metres. Calibration to be repeated before and after observations.



Weather : As for Geodimeter. Extreme heat, mist, fog, rain, snow and dust to be avoided.

Time of day : Although there is some indication that the periods between 1100hrs and 1600hrs and between 2100hrs and 0400hrs are best, this is not consistently so, and it is of much greater importance to observe during suitable weather what­ever time of the day it may occur.

Met observations : To be taken with extreme care especially wet and dry bulb temperatures which should be measured with a mechanically aspirated psychrometer.

Recommended tolerances : Barometric  Pressure ±0.2mb (0.15 mm Hg); Temperature ±0.1°C.

Siting of lines : Ideally the entire signal path should be a few metres clear of the ground to secure optimum refraction and ground swing conditions. Grazing rays passing through unstable atmosphere and rays considerably elevated over highly reflective bare and smooth surfaces to be avoided e.g. sea, waterlogged plain. Rays should be kept well clear of metal girders etc. (e.g. of observing towers) and lines should never be sited near likely sources of electrical interference, e.g. transmitters, HT cables etc.

Observing programme : Not less than 6 sets of observations spread over not less than 2 days in favourable met conditions and 3 days in unfavourable. Each set to cover the whole carrier frequency range.

Ground swing : Not to exceed 6mμs (90cm). If exceeding 4mμs, to be reduced if possible by varying the standpoint of the instrument. If exceeding 2mμs care to be taken that a whole cycle is developed, the mean being taken for one or more cycles, discarding incomplete cycles.

Calibration : Frequency to be checked in operation­al conditions before and after measurement. Zero correction to be calibrated on a short base 150 metres - 1000 metres (accuracy ±1mm). Calibration to be checked before and after measurement.

Ambiguity : Repeat coarse readings at different carrier frequencies during each measure­ment. Independently check lengths if possible. Scrutinise possibly ambiguous results carefully in the field. Periodically check B, C & D frequencies.


Calculation of Refractive Index

It is recommended that the Barrell & Sears formula, and the Essen & Froome formula, given above, be adopted as standard when calculating the refractive index for distance measurement purposes of light waves and microwaves respectively.


Future Studies

Future study should be concentrated mainly on the question of obtaining representative meteorological measure­ments especially for temperature in the case of the Geodimeter and temperature and humidity in the case of the Tellurometer.

The following points should be covered :


Best position for met instruments;


Best configuration of line;


Best weather conditions;


Best time of day or night for observations.


Study of the following is also recommended :


Further refinement of Co value;


Ground reflection and ground propagation of microwaves;


Electronic delay in instruments;


Optimum microwave length for measurement purposes;


Path curvature of microwaves and its effect on refractive index.






Report on the work of Special Study Group No.14

Specifications for Fundamental Geodetic Networks

by Lars Aselund


The Study Group was finally established in the beginning of 1960, though some preparatory discussions were held in 1959.


The members of the group are:

E Andersen, Denmark

L Asplund, Sweden

W Baarda, Netherlands

P Bencini, Italy

H Dufour, France

BCA Edge, UK

LA Gale, Canada

AA Isotov, USSR

M Kaeisel, Germany

R Koronowski, Poland

BK Meade, USA

S K S Mudaliar, India

H Negri, Argentine

VR Olander, Finland

OG Reitz, Rhodesia and Nyassaland

GRL Rimington, Australia

A Tarczy-Hornech, Hungary

H Wolf, Germany


The task of the group has been to study the question of specifications for fundamental geodetic networks and to present proposals of such specifications. It was desirable that at least some tentative results could be presented already to the Helsinki Assembly.

The work has been carried out by correspondence, and in addition, some of the group members had an opportunity to meet in connection with the Lisbon Symposium on the European triangulation adjustment. On this occasion also a general discussion on the subject was held, open to the participants of the symposium.

The question of specifications is very much a practical matter, the goal being to secure a reasonably high accuracy, especially over long distances, with a reasonable demand for labour and costs. On the other hand, it was clear from the beginning that the group could not reach a final proposal of specifications without making rather extensive in­vestigations with test computations in order to study the propagation of errors in very large geodetic networks. The need of investigations has been stressed by the fact that where modern distance measurements have been used in check­ing old classical networks, it is a frequent experience, that much larger discrepancies have been found than was expected.

The following proposal of specifications and standards, based on existing practical experience, thus definitely are not to be regarded as final, but may serve as a basis for the discussion at the Helsinki Assembly, and possibly with the changes which are found desirable, may be recommended by the Association to serve tentatively as a guide until specifications can be finally accepted.


Draft proposals


General specification

A geodetic network is accepted as fundamental when in the adjusted not the mean square error of the relative position of neighbouring stations never exceeds 1:100,000 √S/30 where S denotes the distance between the stations in kilometres.

Comments : Every network forming international links or else being of interest for scientific investigations on an international basis, for instance as regards the determination of the dimensions of the earth, should in principle be established as fundamental and thus be subject to the given accuracy criterion. It is evident, however, that for a long time to come many parts, which from the accuracy point of view cannot be accepted as fundamental, will have to be included in any computations in order to get reasonable extension of the network. It is important that the specifications given also are applicable on the work of strengthening old networks to bring them to fulfil the standards of a fundamental net.

It certainly is not satisfactory, as has been done here, to give an accuracy criterion only as regards neighbouring stations (forming triangulation, trilateration or traverse sides), since the accuracy over longer distances actually is still more important. The criterion thus will have to be revised, but the study group is not prepared to propose a rule before having carried out more investigations into the subject. The expression 1:100 000 √S/30 might tentatively be used also over longer distances, but is by no means ideal, being too rigorous on medium distances. An empirical formula 1:100 000 3√S/30 (cubed root of S/30) has been discussed, but it does not seem to be useful on very long distances.

A fundamental network should be formed in such a way that proper checks are at hand through geometrical conditions. Thus, in triangulation and trilateration single chains should not be allowed, but the network should be built up by double chains, chains in polygons or preferably as area nets. Traverses should always be arranged in systems of polygons.

Where the scale of the network is determined by means of tapes or wires, calibration of these instruments on the international meter standard must be carried out, preferably by using a reference base line adequately standardised. Where the scale of the network is determined by electro-optic or radar-type methods the value of the velocity of light and formulae for refractive index should be used as accepted by the Association.


Recommendations of standards for various measurement methods

Horizontal angle measurements

The measurements of a horizontal angle should be distributed on at least three different days. In triangulation work the accuracy as computed by the Ferrero formula should give a mse of station adjusted direction less than 0.4". Triangle closures larger than 2.5" should be rejected. In traverse work and in connection with trilateration work, where the Ferrero formula is not applicable the mse of station adjusted directions as computed from the station adjustments should average loss than 0.35".


Base measurements with base extension nets

Base measurements should be arranged in a way to exclude as far as possible uncheckable systematic sources of errors. Tapes or wires should be calibrated before and after the base measurement. At least three different measures should be used in each direction. Base nets should be given a configuration which with regard to the local circumstances as far as possible exclude dangerous systematic effects due for instance to refraction. It is recommended to plan these measurements to give a mse less than 1:400,000 of the triangle side (the extended base). The mse should never exceed 1:200,000.


Distance measurements

The measurements should be distributed in at least two different days. The type of equipment used should have been accepted as capable of an accuracy (mse) of 1:300,000 when used for measurements substituting bases and base nets, and of 1:150,000 in traverse and trilateration work. The meteorological observations during the measurement period should be arranged in a way to secure a corresponding accuracy in the determination of the refractive index.

Comments : Special precautions, which will depend on the type of instrument used, will have to be taken in order to reach the required accuracy. Moreover, measurements substituting bases and base nets should preferably be arranged in such a way that independent checks can be had for instance by measuring the sides and the angles of a triangle or some other closed figure. Unless the distance measurement equipment is extremely accurate, a trilateration net should be strengthened by suitable angle measurements for in­stance along traverses joining the La Place stations.

Astronomic measurements of azimuth and longitude at La Place Stations should be arranged to exclude as far as possible systematic influences. The determinations of azimuth as well as longitude should be distributed in at least three different nights. Longitude should be determined as the difference of longitude from a longitude central, where corresponding measurements have to be made in such a way that systematic effects as far as possible are eliminated in the difference. The measurements should have such an accuracy, that the mse of the expression A - LsinB (A denoting azimuth, L longitude and B latitude) as computed out of the station measurement data is less than 1". La Place stations should preferably be observed by pairs with the azimuth side in common.


Distribution of bases in triangulation nets

The density of length determined sides has to be deduced from the specification that the accuracy of side lengths in the weakest part of the net has to be better than some 1:100,000. Since this accuracy will be influenced by many factors such as accuracy of the different measurements in­troduced in the network and of the local figure of the net, no very simple rule for determination of this density can be expressed. It is recommended, that the side which is estimated to be the weakest one in between two bases, as those have been planned, be tested by approximate computation of the weight the side length will get in the adjusted net, making it possible to estimate the mse to be expected. Such a determination is very easy in a triangulation chain. In an area net the calculation may for the sake of simplicity be restricted to include only a narrow part of the net between the two bases.

Comments : Since however a simpler procedure is very desirable some empirical formulas are under consideration. A reasonable estimate can be had by means of the well-known strength of figure expression with regard to the inaccuracy in the bases. The criterion might be expressed as :


80 >  R1 + 40 +  40

--      --

2       2

Na     Nb

Where R1 is the strength of figure value computed between two proposed bases, the mse of which are estimated to be 1:100,000 Na and 1:100,000 Nb respectively.


Distribution of La Place stations

The general accuracy demand indicates that no side of the network should have a mse in azimuth exceeding some 2". Using an estimate of the accuracy, which is kept in the various measurements introduced in the network, a test of the azimuth accuracy of the weakest side between two pro­posed La Place stations can be made in a similar way as described in above.

Comments : However, in traverse and triangulation nets a simpler rule probably would prove sufficient, giving the permissible number of azimuth transporting angles between two La Place stations as a function of the accur­acy of horizontal angle measurements and astronomic measurements. A trilateration net is a little more com­plicated in this respect. If, however as suggested in the comments above the network is strengthened by angle measurements along traverses joining the La Place Stations, the distribution rule could be used as for traverses.

It seems to be a common experience, however, that the La Place stations preferably should be more frequent than what would theoretically lead to the mentioned accuracy of 2". This question will have to studied further. As a reasonable approach, corresponding to the accuracy rules above, the permissible number of azimuth transporting angles between La Place stations might be put as 8 to 10 in triangulation and 6 to 8 in traverse work.

Old networks, which are found too weak, may frequently be reinforced to meet the accuracy requirements given above by introducing additional distance measurements and La Place stations. It is however necessary to make perfectly sure that the stations involved in such additional measurements are unchanged since they were used in the original triangulation. Usually this will demand a check by remeasurement of a suitable part of the net including the stations in question and by comparison with the previous results.