DIVISION OF NATIONAL MAPPING
DEPARTMENT OF NATIONAL DEVELOPMENT

 

Training Notes for National Mapping Field Survey Staff

Compiled by RA (Reg) Ford 1974

 

 

CONTENTS

 

 

1.           CHAINING AND LEVELLING.

1.1.        Chaining.

1.2.        Use of the plumbob.

1.3.        Care of the tape.

1.4.        Step chaining.

1.5.        Slope chaining.

1.6.        The Abney Level.

1.7.        Errors in chaining.

1.8.        Use of the spring balance & thermometer.

1.9.        Clearing of lines for chaining.

1.10.      Reading the chain.

1.11.      Third order traversing with chain and theodolite.

1.12.      Accuracy standard of third order traversing.

1.13.      Marking the traverse.

1.14.      Location of the traverse.                   

1.15.      The traversing party.

1.16.      Distance between stations.

1.17.      Pickets and targets.

1.18.      Field chaining.

1.19.      Odd lengths in field chaining.

1.20.      Corrections to chained distances.

1.21.      Summary of chaining corrections and errors.

1.22.      Algebraic signs of errors.

1.23.      Errors of a full chain length.

1.24.      Check measurements.

1.25.      Angular measurements.

1.26.      The Surveyors' Level.

       The Tilting Level.

The Automatic Level

The Level tripod.

The Levelling Staff.

Testing and adjusting the level.

1.27.      Level Traversing - Hints.

Extracts from "Specifications, Third Order Levelling."

Field Book -   Rise and Fall Method.

Field Book -   Collimation Method.

 

2.           THEODOLITE, GENERAL DESCRIPTION, ITS USE IN ALL TYPES OF OBSERVATIONS.

2.1.        General Description.

 

3.           THEODOLITE, WILD T2, OBSERVING METHODS, TASKS AT TRAVERSE STATIONS.

3.1.        General preparations includes T2 manual.

3.2.        Setting up, screens, levelling, etc.

3.3.        Horizontal and vertical scales, description and reading.

3.4.        Observing horizontal and vertical angles, double pointing system, scale settings, and booking.

3.5.        Measuring and recording RM's, Eccentric Stations, Recovery Marks, Computation of RM distances.

3.6.        Eccentric corrections, all types. Formula, computations & example.

3.7.        Plumbing towers and beacons, with theodolites.

3.8.        Sigma Octantis azimuth determinations, method and booking.

3.9.        Hints on Ex-Meridian sun azimuth determinations, method and booking.

3.10.      Meridian transit observation for Latitgde and Longitude, Rimington's Method.

3.11.      Tacheometry, or Stadia Surveying.

Theory.

Reduction of stadia observations.

A tacheometric traverse to gather detail.

Field Book - layout and finalization.

Stadia Tables.

Accuracy - distance and heighting.

Curvature and refraction.

3.12       Almucantar observation for Longitude with Wild T3 Theodolite and stopwatch.

3.13       Latitude observations with the Wild T3 Theodolite – Meridian or Circum-Meridian Altitudes.

 

 

4.           TELLUROMETER, MRA2.

4.0.        Setting up.

4.1.        Description of the operating panel.

Use of the controls.

Pre-operational checking.

4.2.        Operation under usual conditions.

Pattern of operation.

Sequence of measuring.    

Operation over land.

Operation over water.

Atmospheric effects.

4.3.        Field computation of the measurement.

Atmospheric readings required.

Explanation of the "Coarse" figure.

Simple explanation of the tellurometer system.

Field book example of the computation.

4.4.        Fault finding procedure.

Faults common to the Master and Remote instruments.

Faults peculiar to the Master instrument.

Faults peculiar to the Remote instrument.

Anomalous CRT displays.

Trouble shooting charts.

 

4.5.        TELLUROMETER, MRA3.

General principles

Simplified theory of measurement

Conversion of time to distance

Zero error

The control panel

Dial readout unit

Making contact, preliminary arrangements

Sequential method of operation

 

4.6.        TELLUROMETER, MRA4 – MANUAL.

 

5.           THE COMPASS.

How to read the prismatic compass.

Magnetic declination.

Compass error.

Protracting bearings from maps.

 

6.           MIRRORS AND HELIOGRAPHS.

Use of the mirror for proving intervisibility.

Description of the heliograph.

Setting up the helio for "Simpler," operation.

Setting up the helio for "Duplex" operation.

 

7.           STATION MARKS AND MARKING.

Description of types of station marks.

Standard mark for one degree and half degree Control Stations.

Reference Marks, Witness Posts, etc.

Types of marks previously used.

How to build cairns.

Tripod and quadrupod beacons.

 

8.           ERECTION OF TOWERS AND MILLS SCAFFOLDING OBSERVING PLATFORMS.

8.1.        Stand point for the tower; dimensions of concrete blocks.

Assembling and erecting the tower.

List of tower parts.

8.2.        Necessary tower attachments.

8.3.        Erecting the Mills scaffolding observing platform.

Sequence of erection.

List of parts required.  Weight of one complete scaffolding.

 

9.           ACCESS NOTES AND SKETCHES.

9.1.        General.

9.2.        Field notes of the speedo and compass traverse.

9.3.        Drawing the access sketch; conventional signs.

9.4.        Helicopter access.

 

10.         MAP READING INCLUDING ELEMENTARY AERIAL NAVIGATION, USE OF THE PLANE TABLE.

10.1.      Objects of Map Reading.

10.2.      Understanding maps.

Marginal information.

Mapping terms.

True, Magnetic & Grid bearings. Protracting bearings.

Scales, Map Symbols, Relief & Contours.

Australian Map Grids. Use and reading Grid (Map) References.

10.3.      Hints on Map Reading.

10.4.      Elementary Aerial Navigation.

10.5.      The use of the Plane Table.

 

11.         ELEMENTARY ALGEBRA, LOGARITHMS, PLANE GEOMETRY & TRIGONOMETRY

Algebra, Logarithms, Plane Geometry and Trigonometry.

 

12.         SURVEY COMPUTATIONS.

12.1       Closed Surveys (Chain & Theodolite traverses).

Bearings, Latitudes & Departures.

Misclosures, computing the closed traverse.

Computing missing bearings and distances.

Use of Eastings & Northings instead of Latitudes & Departures.

12.2.      Spherical Excess & closure of triangles.

Formulae, figures used in triangulation.

Calculation of sides, spherical excess. Triangle miscloures.

12.3       Field computation, Latitude, Longitude & Reverse Azimuth.

Definitions and formulae.

Sequence of computation.

Tables used; example of computation.

12.4.      Heights from Simultaneous Reciprocal Vertical Angles.

Obtaining the Curvature and Refractive (C&R) index from Single Ray Vertical angles.

Applying the Curvature and Refractive (C&R) index to single ray vertical angles.

12.5.      Astronomical Terms used in Observations and Computations.

12.6.      Time and Time conversions, Hour angle.

12.7.      Computation of Ex-Meridian Sun Observation for Azimuth.

12.8.      Computation of Azimuth from a close circum-polar star.

Plate bubble corrections in Azimuth observations.

Interpolation of Right Ascencion and Declination of Sigma Octantis.

Time curvature correction between FL & FR pointings.

12.9.      Barometric heighting with Mechanism Barometers (Field computation).

Examples of various machine computations and Table of Temperature Constants.

Examples of computation using Log formula,

Table of Temperature Constants for use with Log formula.

12.10.    Computation, meridian transit observation for Latitude and Longitude, Rimington's method.

12.11     Almucantar observation for Longitude computation.

12.12     Latitude by Circum-Meridian Altitudes computation.

 

______________________________________________________________

 

 

 

1          Chaining

 

 

1.1.1           The direct measurement of distance with a steel band is referred to as "chaining”, from the use of the original Günter’s chain of 100 links. Modern steel bands are generally about 3.18mm wide and 0.25mm thick. The length now being used within the Division is 50 metres. The bands are graduated with stamped brass rivets or sleeves.

 

 

1.2         Plumbob

 

1.2.1      This is used for testing the verticality of beacon poles, transferring to ground the end marks of steel bands, setting the theodolite over fixed points and step chaining.

 

1.2.2      To hold the plumbob cord on the tape, the cord and tape are pinched together by the thumb and forefinger, at the points shown by the arrows in Figure 1.2.2.

 

Figure 1.2.2.

 

1.2.3      The two extreme positions likely to be encountered when using the plumbob to transfer the position on the tape to a ground point, or vice versa, are:-

 

(a)        shoulder height. This is the limit without losing accuracy;

 

(b)  peg height.

 

1.2.4      When using the plumbob, there will be slight movement of the bob, due to vibrations from the tape, wind, etc. This movement can be reduced to a minimum by gently tapping the ground with the point of the plumbob.

 

1.2.5      When the line of sight from the theodolite to a point is obstructed, it is possible to use the plumbob as a target. In order to minimise the error due to the movement of the plumbob, the string should be held as close as possible to the top of the plumbob. The point of the plumbob should be kept as close as possible to the point being plumbed. The correct method of holding the plumbob is shown in Figure 1.2.5.

 

Figure 1.2.5.

 

1.2.6      In order to mark a point with the plumbob, the tip of the bob should be about 13mm above the ground, and when the order to mark is given, the assistant settles the plumbob and a clearly defined hole is made with the point. If the ground is too hard for the point to mark, the plumbob is kept in the position shown in Fig. 1.2.6 until a chaining arrow is inserted.

 

Figure 1.2.6.

 

 

1.3         Care of the tape

 

1.3.1      When unrolling the band, 1 assistant takes the free end of the tape and walks slowly forward, while the other assistant holds the arrow on which the cross revolves, or the strap of the reel, so that the band comes off freely and easily, without jerks. The man at the cross or reel end also sees that the band does come off too quickly, and that it does not get caught on obstacles. As his end of the band comes in sight, he warns the man at the other end to be prepared to stop, at, the same time preparing to give a little at his end, in case of a sudden jerk. When the end of the band is reached, he gives the signal to stop, and both men lay the ends of the band on the ground, ready to start work.

 

1.3.2      In rolling up, the band is first laid out straight on the ground and one end is fastened to the cross or reel. The man working the latter, now starts to walk slowly towards the other end of the band, at the same time winding it up. In doing this he sees that it is not caught on any obstruction and is wound firmly and tightly without any sudden jerks taking place. When the end is reached, it is fastened to the cross or reel by means of a strap or leather lace.

 

Although most steel tapes used for surveying will withstand a direct tension of 36 Kilograms (about 80 lbs.) it is very easy to break them by misuse.

 

When a tape is allowed to lie on the ground, unless it is kept extended so that there is no slack it has a tendency to form small loops like that shown in Fig. 1.3.3. When tension is later applied, the loops become smaller either it jumps out straight or the tape breaks, as shown. If a tuft of grass or any object is caught by the loop, the tape almost always breaks or at least develops a permanent "kink". To avoid this, the tape must be handled so that no slack can occur. For measurements of less than a full tape length, the tape should be kept on the reel. It should be reeled out to the necessary length, and reeled in as soon as possible. The assistant, who handles the reel, must reel in any slack that might occur between the two assistants, while the tape is being handled. For measurements greater than the tape length, when the tape is off the reel, the tape should be kept fully extended in a straight line along the direction of measurements. When it is to be moved, it must be dragged from one end only.

 

            

Figure 1.3.3.

 

If it is necessary to raise the tape off the ground, the two assistants must lift the tape simultaneously and keep it in tension between them. Except for this operation, the rear assistant must not touch the tape while it is being moved. If he picks up the rear end, and moves forward faster than the other assistant le will form a "U" in the tape, which usually causes a loop to form when the tape is pulled taut. This may break the tape.

 

1.3.4      When the end of the measurement is reached, where a less-than-tape-length measurement is required, the assistant must not pull in the tape hand over hand as this creates a pile of loose tape on the ground. Instead, he must do one of three things:-

 

(i)      Carry the end of the tape, beyond the point, lay it on the ground, and walk back.

 

(ii)     Reel in the tape, the requisite amount.

 

(iii)    Take in the tape, forming figure-eight loops hanging from the hand. Each length of tape must be laid in the hand flat on the previous length and never allowed to change. Later, to extend the tape, lay it out carefully as he walks forward, by releasing one loop at a time. This method requires care and practise and should not be attempted until the required skill has been obtained by practise.

 

1.3.5      No vehicle should be allowed to run over the tape. Only in the case where the tape is across a smoothly paved street can a pneumatic tyred vehicle pass over the tape without damaging it. The tape must be held flat, and tightly pressed against the street surface by the two assistants.

 

1.3.6      When a tape is wet, it should be carefully cleaned, one oiled immediately after use.

 

1.3.7      In general, it is well to remember that a tape is easily damaged but, with care and thought, damage seldom occurs, keeping the following in mind:-

 

(a)     Keep the chain straight. If, for any reason it is necessary to pull it back do so from the end, rather than let it lie in a series of loops at an intermediate point from which it is pulled.

 

(b)    If pulling the chain around a corner see that it is pulled around a curve of large radius, and have an assistant watching it to see that the sleeves do not catch in a splinter or a piece of barbed wire or anything else which might break the chain.

 

(c)     If the chain is caught do not attempt to free it by jerking but go back and release it where it happens to be caught.

 

(d)    In running out a Box Tape from its case see that it runs out tangentially and is not bent back where it leaves the case. The tape should always be kept bright and clean.

 

If it gets wet, dry it at once, and if it becomes muddy, wash the mud away with clean water then dry the tape. It should never be wound up into the case when wet, but while drying it should be hung in a series of wide loops, which will allow it to dry quickly.

 

If it becomes dirty or rusty it should cleaned with kerosene, oil, or some non-abrasive such as "Brasso".

 

 

1.4         Step chaining

 

1.4.1      Measurements are carried forward by holding the tape in a horizontal position, and the plumb line is used by either or at times, by both assistants for projecting from tape to ground. Figure 1.4.1. shows an example of "Step chaining".

Figure 1.4.1.

 

1.4.2      It requires some practise to judge when the tape is horizontal. The best way is to pull sufficiently to eliminate sag and hold the stretched tape so that the angle between it and the plumb line is a right angle. It is impossible to judge horizontality from the uphill end of the tape.

 

1.4.3      In step chaining the length of the step will depend upon the angle of slope, and should not be so long that the height of the plumbed end above the ground exceeds 1.5 metres.

 

1.4.4      It should be noted that holding one end of a 50metre tape 1 metre above or below the true horizontal line will cause an error in the result of 8mm. Hence the need for a very close approximation to the level line, at the instant of plumbing.

 

 

1.5         Slope Chaining

 

1.5.1      The tape is held on a slope and the angle of slope read so that the measurements can be reduced to the horizontal.

 

1.5.2      The chain may be held at any convenient height at both ends however it is usual practise to hold waist high, the rear assistant reading the slope.

 

 

1.5.3      For slopes up to 4° the Abney Level (See 1.6.) is used to read the angle of slope. For slopes above 4° a theodolite should be used to read the vertical or slope angle. The theodolite is set accurately over the chained point, and the angle of slope read, to the assistants hand as he releases the plumbob at the "mark" signal.

 

 

1.6         The Abney Level

 

1.6.1      This is one of the popular instruments of the surveyor's kit. It is not a precise instrument by any means, angles of slope are read to within two minutes, in the larger size, and to within ten minutes in the smaller size. There is no magnification in the sighting tube through which the bubble and target are viewed at the one time. Below is shown, the method of using the Abney Level for chaining. A 4° slope is being read which is the allowable limit for the Abney Level.

 

  

Figure 1.6.1(a)

 

Figure 1.6.1(b)

 

Figure 1.6.1(c)

 

The graduated circle is divided into degrees, and the vernier to read to 5 minutes = 11 divisions of graduated circle divided into 12. Reading either side of index to 5¢.

   

1.6.2      Adjustment of the Abney Level

 

By taking the mean of back & fore sights. Two points of different elevation are selected, and the vertical angle between them is observed from both.

 

The angle of elevation observed from the lower station should equal the angle of depression from the higher. If not, the mean is the correct reading and the instrument is made to record this by the adjusting screws on the level.

 

Alternative to (b), the index error can be used :-

 

If the reciprocal observation gives 15° elevation and 17° depression, the index error is half the difference, i.e. 1° to be deducted from all depression angles and added to all elevation angles.

 

The following is probably a better method of recording and using, an Abney Level correction:-

 

With a theodolite determine the altitude of a well defined object some 500 metres away. Set this angle on the Abney Level, sight on the object with the Abney Level. Observe, carefully, where the sighting mark "cuts" the bubble reflection. It may be half or quarter way down from the top, etc. In future determinations of slope bring the bubble to this same position, relative to the sighting mark. When continuous use of the Abney Level is being made, it should be tested, as described, every 2 or 3-days.

 

 

1.7         Errors in chaining

 

1.7.1      Even experienced assistants have difficulty in preventing the tape and the plumbobs from moving, during measurements. The error from this source is, between 1:5,000 and 1:10,000. Variations in tension of 2.27kilogrammes (about 5 lb) introduce an error of 1:10,000 with a tape of average cross section, 50 metres long, and supported at the ends. Temperature may introduce an error of up to 1:5,000 so that, all in all, this type of measurement has an accuracy seldom better than 1:2,500. Using spring balance handles will improve the accuracy to 1:3,000. With temperature correction, as well, an accuracy of 1:5,000 can be attained.

   

1.7.2      If more accurate results are required then special equipment­ is necessary.

 

1.7.3      A distinction should be made between errors and blunders. Errors result from such things as:-

 

Incorrect alignment of the chain.

Temperature variations.

Tension variations.

             Tape not straight.

 

Blunders are usually due to:-.

 

Miscounting of chain lengths.

Misreading the chain.

Erroneous booking.

Misplacement of a chainage point.

 

 

1.8         Use of Spring Balance and Thermometer

 

1.8.1      It should be noted that a 50 metre tape will expand or contract 1mm for every 2°C change in temperature, or 8mm for every 15° C. It is very difficult to read an exact temperature of the tape.

 

In general, the thermometer should be held as close to the tape as possible, while taping is taking place. The ideal situation would be to have the thermometer clipped onto the band, with the bulb in contact with the steel.

 

1.8.2      The spring balance is simply attached to one and of the band and tension is applied, until the tension, at which the tape has been standardised, is reached. This is generally about 3.630 kilograms (about 8 lb) to 4.600 kilograms (about 10 lbs), when using the 50 metre band for chaining.

 

Tension should not be applied quickly, but as a gentle pull, applied by the leading assistant; this will reduce jerking, etc.

 

 

1.9         Clearing lines for chaining

 

1.9.1      Prior to commencing chaining, the line should be cleared of all obstacles which may tangle or bend the tape. Grass, scrub and trees, should be cut down as low as possible, and where chaining is to take place, with the tape resting on the ground, the line should be scraped free of all vegetation, rocks, etc. The principal problem in clearing vegetation from a survey line is maintaining a straight line.

 

If this is done, the effort involved is kept to a minimum, and work progresses more rapidly and systematically. Quite often, large trees have been felled only to find later that they were well off line. It is far better to take some trouble to locate the correct line. This is best done by using "sighting sticks" or "boning rods".

 

The first stick is set on the required line by theodolite or compass, at some convenient distance from the station. The axeman can then walk "on line" by looking back and aligning himself with this stick, and the theodolite. Before he loses sight of the back mark, in this case, the theodolite, the axeman should cut another bush stick, an inch or so, in diameter, driving it into the ground, on line with the previous marks. He then maintains direction by aligning himself with the two closest marks. This process is carried on for as far as necessary. Shorter sticks are used when clearing over a ridge; and longer ones when crossing a depression. If carefully executed, straight lines can be maintained for considerable distances, say about 1 kilometre, with an error of about half a metre, depending on the terrain.

 

 

1.10       Reading the chain

 

1.10.1    Steel bands, now in use in the Division of National Mapping comprise a 50 metre steel section, marked with brass studs each metre. Attached to the zero end of the band is a leader 1 metre plus long. The leader is graduated to millimetres.

 

1.10.2    In order to measure an uneven distance, the leader is held roughly over the forward station, by the forward assistant. The rear assistant then holds the nearest graduation on the band over the previous chainage mark. At the "read' signal given by the rear assistant, the reading on the "leader" is noted by the forward assistant, and the rear assistant reads, the whole metre on the band. To minimise the possibility of misreading, the two assistants now change position, and the procedure is repeated. See Figure 1.10.2.

 

Figure 1.10.2.

 

Rear assistant reads           04.000 metres.

Forward assistant reads        0.732      "

Distance                            04.732 metres

 

 

1.11        Third Order Traversing      

 

1.11.1    Theodolite and chain traverse

 

This is the method by which cadastral survey work is carried out, and boundaries of properties, measured and marked, or re-established, on the ground.

 

In mapping, 1st and 2nd order traverses are now carried out with electronic distance measuring equipment, taking the place of the chain. However, there is still a need for traversing of 3rd or 4th order standard. The latter is often a short connection to a photo reference point, etc., where a spring balance and accurate slope corrections are a needless refinement.

 

It is envisaged that traversing similar to the third order traverses would be required to connect mapping control points to distant satellite stations, or short traverses to get mapping control into timbered flat, terrain, unsuitable for electronic measuring equipment.

 

 

1.12       Accuracy Standards for Third Order Traversing

 

1.12.1    Error between traverse control points and adjacent control

 

The traverse control points should be determined with sufficient accuracy so that, after adjustment, it will be unlikely that the computed distance between a 3rd order control point and any adjacent 3rd or higher order, control point, will be in error by more than 1 part in 5,000.

 

1.12.2    Errors of standardisation, and between adjoining stations of the traverse.

 

The probable error of standardisation of the field tape should not exceed 1 part in 50,000 (i.e. an error of 1mm in the 50 metre tape) and the linear distance between adjoining stations on the same traverse, should be within 1 part in 25,000.

 

1.12.3    Angular error

 

The angles of the traverse should be measured to a uniform degree of accuracy, and the maximum misclosure at an azimuth station, or trigonometrical station should not be greater than 12 Ö n seconds where "n" is the number of traverse stations between azimuth control, thus, with 25 stations the misclosure should be 12Ö25 = 60 seconds or less. The angular adjustment per station should never exceed 5 seconds and seldom exceed 3 seconds.

 

1.12.4    Heights carried through traverse

 

Heights carried through the traverse by vertical angles should be correct to 1.5 metres after closure adjustments have been made.

 

1.12.5    Terminal control and azimuth control

 

Third order traverses must start and finish at third or higher order control points; and at intervals of 20 to 30 stations along the traverse; at permanently marked stations an azimuth check should be made. The probable error of this azimuth observation should not exceed 5².

 

Azimuth observations should also be made at junction stations. At first sight, the above standards may seem rather high, but, provided the chain is standardised accurately, they should present no problem to experienced personnel. Angles will usually be read with a Wild T2 theodolite, and the chaining will normally be along the ground, not in catenary or suspension.

 

It will be found that the initial linear surround is likely to be within 1 part in 12,000 to 15,000 or better.

 

 

1.13       Marking the Traverse

 

1.13.1    Permanently marked stations

 

These should be established at intervals of not more than 3kms along the traverse, with an average distance of about 1.5 kms. Two reference marks, one of which could be a reference tree, should be established at each station.

 

1.13.2    Marking of intermediate stations

 

These stations should be marked by temporary wooden pegs, about 25mm x 25mm x 200mm

 

 

1.14       Location

 

1.14.1    Access

 

Roads and fences will usually greatly expedite the work, if one proceeds in the right direction, and if the road does not carry heavy traffic or raise dust, to hinder the work. The traverse should run just off the road edge, and about half to one metre from the fence.

 

 

1.15       Traversing Party

 

1.15.1    Make up of party

 

If trained personnel are available and an efficient, economical party is required in fairly open country, the four man party is suggested.

 

(a)     A theodolite observer who reads and records angle and bearings in a field book.

 

(b)    A senior assistant who holds the back end of the chain, and records field notes in respect to chainage measurements, Abney Level slopes, and laid distances, references, etc. Notes taken in this second field book will require transcription later on, into the field book which records the angular work.

 

(c)     An assistant who takes the front end of the chain, applies the required tension, and usually reads the "reader", for any references required.

 

(d)    Another assistant nominated as the "axeman", who clears the line, and sets the pickets. If a vehicle can be taken near the line, and there is little cutting, the axeman may be able to bring the vehicle along.

 

However, there are many variations, even in the 4 man party. If the clearing is heavy, the axeman and assistant may both cut, and the senior assistant may take the front one of the chain, where he does the booking, leaving the theodolite observer on the back end of the chain.

 

Or the observer may do the booking of both angles and chainage, with the senior assistant setting pickets, driving the vehicle forward, and taking the front end of the chain. This will require a certain amount of walking by the senior assistant.

 

Again, in easy country, a 3 man party (axeman-picket setter; assistant; theodolite observer) can make good progress.

 

A 5 man party, if available, may also be economically employed, (2 men clearing, picket, setting and bringing on transport; one senior assistant; one assistant; one theodolite observer.

 

A party of 2 experienced, energetic men (observer and assistant) will also make good progress where there is no cutting to be done.

 

All the above work presupposes that the traverse stations are selected and located, as the traverse proceeds, and that chaining is not done in catenary, but along the ground. Reference marks on trees or corner posts should be observed and measured as the work proceeds, but it must be decided whether it is economical to emplace concrete blocks, and concrete reference marks, at selected stations as the traverse is run, or at a later stage, this depends on the going, and the availability of personnel.

 


1.16       Distance between Stations

      

1.16.1    This depends on the terrain, and on the observing conditions. Along straight roads or fences, in gently undulating country, 1.5 km legs are possible, in conditions of good observing. In hilly, heavily timbered country, where a road is being traversed, it may be difficult to see 100metres, on occasions, and special care in centring the instrument becomes essential, to hold the azimuth.

 

On open plains, in hot weather, it may be necessary to read the angles in the early morning, and late afternoon, though the chain­ing can be carried out during the day. These, decisions must be made by the party leader, depending on conditions prevailing at the time. Work will usually be expedited by the use of the longest legs which can be observed; if someone has to be sent to show up the forward or back pickets for the observer, much time will be lost.

 

Assistants should be trained to keep slightly off line, except when they are actually laying the chain, and so allow the theodolite observer to read his directions, once the forward picket is plumbed. With long straights, under open conditions, where the forward picket cannot be seen with the unaided eye, it is the responsibility of the rear assistant, and the observer to see that the chain is laid on line, or within 0.30m. Generally, in flattish, open timbered, country, legs from 350 to 500 metres will give best observing conditions and results.

 

 

1.17        Pickets or Targets

 

1.17.1    Pickets

 

Traversing in bush country is likely to be carried out by observ­ing to pickets cut from saplings or branches, as work proceeds.

 

Such pickets may be from 1 to 2 metres long, and 50mm to 75mm in diameter, sharpened at the bottom for driving into the ground, and with a "step" cut in the side 300mm to 450mm from the bottom, to assist such driving. The top 100mm to 150mm, should he cut to a straight four-sided, tapering point, or to a four-sided squared top with 25mm wide sides.

 

A 40mm x 50mm rectangular, or 40mm square, piece of white folded paper placed carefully, and centrally on the pointed picket, leaving about 13mm to 25mm showing, makes a good sight, however distance and visibility govern the size.

 

On occasions, the point may not be seen and the paper will then need to be bisected; it should therefore be carefully centred by the picket setter. If, for some reason (such as stock in paddocks or along roads) the squared top picket is adopted, a white papered top may assist visibility, and a strip of paper about 150mm x 50mm wrapped near the top makes a good sight for bisection. Spitting on the last few millimetres, of the strip of paper, when wrapping it around the pickets, is a crude but effective method of holding it.

 

A pointed picket is an extremely dangerous object to be left standing in open grazing country, on a road, or wherever animals could impale themselves. They must not be left standing.

 

In bushy country, it may be advisable to use pickets about as high as the telescope of the theodolite. This will ensure that the observer will always see his back picket after moving forward. Along roads, or in open country, the observer will probably prefer to use pickets about 1 metre high, over which he can set his instrument. The temporary wooden pegs, under each picket are often more safely hit in by the observer, after he has set his instrument over the picket. To counteract accidental bumps to the pickets before the instrument is set up, the pickets should be accurately plumbed by the picket setter, and a match (or hole made by the plumbob point) left to indicate the plumbed position.

 

1.17.2    Targets

 

Special traversing equipment is made by several firms. Instead of sighting to a picket, a metal target in black and white is used, which may be screwed to the theodolite tripod, and levelled with footscrews. For quickest results, the theodolite tripod and target tripods are interchangeable. The tripods are set up firmly, the targets levelled, and angles read with the theodolite the head of which is then unscrewed and transferred to one of the tripods from which the levelled target has been removed.

 

It will be realised that with four sets of tripods, three targets and one theodolite, a continuous series of steps can be undertaken with no hold-up. Work of the highest quality is possible with such sets.

 

 

1.18        Field Chaining

 

1.18.1    Chains

 

Most third order chaining has been done with the 300 foot steel band. However, future chaining will be done with metric bands, probably the 50 metre band. The characteristics of the 50 metre bands currently in use within the Division are:-

 

Width                   3mm

Thickness             0.05mm

Weight, approx.    0.680kg (1 metre = 0.013607kg.)

 

These characteristics agree closely with those of the 300 foot band previously in use: ‑

 

Width                   1/8²       (0.125")

Thickness             1/50"     (0.02")

Weight approx.     2.51b.    (1 ft = 0.0083 lb.)

 

It should be mentioned at this stage that the 15lb tension applied to the 300 foot band of approximately the same characteristics will probably be too great for the much shorter 50 metre band, and would tend to pull the assistant "off balance". A tension of 4.600kg (10.14lb) will probably be satisfactory for the 50 metre band; however this could be the subject for further investigation.

   

1.18.2    Chaining with the 50 metre band

 

Chaining in catenary, i.e. with the tape fully suspended, or with one, two, or three supports, is the recognised method of accurate chaining. The number of men required, in a party engaged on such measuring, and the effect of wind, (nearly always prevalent in the open areas of Australia) on the suspended steel band, are the drawbacks to this method.

 

If the ground chaining surface was perfectly flat, such as along a straight bitumen road, along the rail of a railway line, or on a claypan, the tape could be laid on the surface; with the correct tension applied, each end could then be marked by a fine scratch or pencil line. However such conditions are exceptional, and even under conditions with little or no undergrowth, it will be found that rocks, grass tufts, etc., prevent the band from lying flat enough to give an accurate horizontal distance. Also with the band completely along the surface, accurate temperatures are much harder to obtain.

 

Thus for normal field conditions with a small party it can be considered impractical to either chain in full catenary or completely along the ground, therefore it is necessary to adopt a compromise between the two methods.

 

Figure 1.18.2(a)

 

Each end of the band is held 450mm (approx. 18" or knee high) above the general level of the ground, or of the vegetation which supports the tape. A "pull" of 4.600 kg (approx 10 lb) is applied to one end of the band. Under this tension the effect is for about one third of the band at each end to be elevated with the central third supported a few millimetres above the ground on low bushes, grass tufts, etc. This method of chaining counteracts slight ground irregularities and obviates excessive low clearing. See figure 1.18.2(a).

   

When using this method, a standard "sag" correction for each 50 metres is determined at the time of standardization before the chaining task is undertaken. See paragraph, "Check against standardized steel band."

 

If high grass undergrowth supports the chain at a fairly regular height, the senior assistant will estimate this general supporting height and have the band held at the normal 450mm above this general height.

 

In all cases temperatures should be taken at the general height of the band, not with the thermometer lying on the ground, as this yields a highly inaccurate temperature for a band held as described.

 

Use of plumbobs

 

The skill needed to accurately use the above method is all in the use of the plumbobs, and can only be acquired by plenty of practise. Sixteen ounce plumbobs of the "conical" type, which enables easier viewing of the mark from directly above, should be used in preference to the "pear shaped" type.

 

The rear assistant has the most difficult task, he should double the surplus plumbob string through the brass loop in the end of the band, holding this string in the palm of the right hand, and using his right leg as a lever to keep his right arm and hand steady, (the reverse for a left-handed person, in all cases). The left hand should keep the plumbob string both at the right, height and against the outer edge of the brass loop on the end of the band. While waiting for the forward assistant to take up the tension, the plumbob's swing should be continually "dampened" by tapping its point on the ground, a few millimetres to the right of the mark. As the forward assistant takes up the tension on the spring balance, the rear assistant allows this tension to draw his plumbob directly over the mark; once there and steady, he calls loudly "Mark" If this system is practised, and adopted, it will obviate the "tug of war" so often seen with inexperienced assistants. See Figures, 1.18.2(b) and 1.18.2(c).

 

Figures, 1.18.2(c) and 1.18.2(b)

 

Check against standardized band

 

One 50 metre band should be properly standardized and held solely for the purpose of standardizing field bands. Ideally, this band should be of "invar"; also all steel bands should have the same characteristics. A suitable tension for field use should be adopted for standardization; this saves the calculation of a correction for tension and the need to apply it to every length laid in the field.

 

The field bands should be checked against the standard band in two ways, i.e.:‑

 

(a)     On a perfectly flat surface, in the shade, lay out an exact 50 metres with the standardised band. Use the correct tension and apply a temperature correction, if necessary.

 

Each field band is checked against this base at the same tension, and the temperature recorded. The difference in measurement gives the error of that particular 50 metre band at that temperature. This difference would only be used to correct any 50 metre length which may be chained along the ground.

 

(b)    Using the exact method to be employed in the field task, a full 50 metre length is laid out against the exact 50 metre base, the temperature is taken and the difference in measurement is noted. This difference will be a set correction covering "sag", "tension", and "error in length" for each 50 metre length laid at a corresponding temperature. Thus only temperature corrections need to be calculated for each length laid in the field. It is unlikely that many lengths will be laid completely along the ground, however it is a simple matter to make the check outlined in (a) above in case some lengths are more conveniently laid on the ground.

 

The usual procedure in laying the chain is briefly:-

 

(a)     The forward assistant pulls the chain ahead, taking care that it does not go under bushes or rock snags, and counting his paces, to stop approximately at the correct distance. He will have to get used to the pace-metre ratio.

 

(b)    The chain is straightened by "throwing up" each end, holding it lightly taut, and throwing a wave motion along the tape. Two hands should be used, one hand holding the end by balance or plumbob cord, the other stretched as far along the tape as possible to help in "throwing up" the tape, in the small wave motion mentioned. Do not jerk the chain sharply.

 

(c)     With chain straight and free, the front assistant puts on the 4.600 kgs (about 10lbs) tension to obtain an approximate position for placing the arrow. He eases off the tension, and with his heel kicks away the grass, etc., to make a clear spot for the plumbob mark.

 

(d)    He again applies the 4.600 kgs tension, holds his plumbob string right at the end of the chain, and lowers the plumbob to about 25 to 50 mm above the ground. The rear assistant holds his plumbob string at the rear end of the chain, with the plumbob point 12mm or less, above where the arrow enters the ground. Both assistants are holding the chain ends 450mm above the general supporting height of the tape.

 

(e)     When the tape is steady, it is kept thus for 3 or 4 seconds, and the front assistant drops his plumbob to make a light mark on the cleared surface. Then he eases off the tension. If either assistant is dissatisfied with the laying of the chain it must be done again.

 

The front assistant carefully inserts an arrow, slanting and at right angles to the line being traversed, in the centre of the plumbob mark. This completes the laying of one length of the chain, the procedure being repeated as many times as necessary. The above method of chaining gives a distance, for each length of chain laid, that is slightly short of the length of the chain; each 50 metre length will need to be corrected by the standard correction covering "sag", "tension", and "error in length" that was ascertained in the check against the standardised steel band. In addition each length laid will be subject to the temperature correction for the prevailing temperature.

 

 

1.19       Field Chaining – Odd Lengths

 

At the end of a traverse leg there is usually some odd length to be measured. The method is for the front assistant to hold his end of the chain at the peg, whereupon the rear assistant pulls the chain back until he, the rear assistant, is holding on a brass mark. The front assistant then reads the odd length, on the reader, at his end of the chain when tension is applied. On arrival at the peg, the rear assistant should be shown, and should check this intercept, and should report the value of the brass mark that he plumbed. (See Figure 1.10.2) Roller-grips for odd lengths are very desirable, and should always be used, if available. In all chaining, the body should be used to take the tension by resting the elbow just above the bent knees, or if the chain support is higher, by pressing the elbows or wrists hard against the body.

 

 

1.20       Corrections to chained distances

 

The following are brief notes on the corrections which affect third order traversing.

 

1.20.1    Standardisation

 

Normally, one tape has been standardised by an authority such as a State Lands Department for a small fee. A sample certificate can be seen here. Before commencing a task, field tapes have been checked against this tape as explained in 1.18.2.

 

1.20.2    Slope correction, and use of the Abney Level

 

This is the most frequent, and usually the largest correction applied in chaining; its purpose being to reduce measurements which have been taken on sloping ground, to horizontal measurements.

 

These slopes, or angles of elevation or depression, are generally read with an Abney Level; the rear assistant reading the same height (eye height) on the forward assistant. There is a probable error of 5 minutes with such a reading. This is not a cumulative error, but has a serious effect on corrections for slope over 4°. For these the theodolite should always be used.

 

In hilly country, where large slopes are common, consideration must also be given to chaining in catenary, so that accurate slopes may be determined.

 

Slope corrections are calculated by multiplying the versine of the slope angle, by the measured length. These corrections are always minus, whether slopes are elevation or depression.

 

A table of slope corrections for every 5¢ from 0° 25' to 5°, and covering the distances in use, is the quickest way to reduce slope distances, in normal country.

 

Natural versine values for every minute are listed in Chambers Mathematical Tables, and some slide-rules incorporate a versine scale.

 

1.20.3    Temperature correction

 

Since steel expands when heated, a chain standardized at 15°C (59°F) and used in the field at 32°(approx. 90°F) will be too long; requiring a plus correction, for temperature, for all measurements made with it.

 

A coefficient of expansion for steel chains may be taken 0.000 0113 per 1°C (0.000.0063 per 1°F). A table showing the correction for temperature and length can be seen here.

 

The formula for temperature correction is:-

Ct = 0.000 0113 L (T-To)

 

where    Ct                = Temperature correction.

0.000 0113   = co-efficient of expansion of steel per 1 C.

L                   = Measured length.

To                = Temperature of standardization of to

T                   = Temperature of tape in field, in °C

 

It is difficult to obtain accurate temperatures in the field; temperatures can be as much as 1° to 5°C in error, usually too high. If conditions are normal, it is not necessary to read a temperature at every length laid, and a reading every fourth tape laying should suffice.

 

Care should be taken to see that such temperatures are read at the height of the chain; that is, when chaining across foliage which supports the chain, at about 300 mm above the ground, the chaining thermometer should be laid horizontally, and at that height; not laid on the ground, which on a hot day with a light breeze, might give an error, of 5°C, or more, too high.

 

If the thermometer is placed at the correct height, then the chain laid, and the slope read and booked, enough time should have elapsed for the thermometer to have moved to the correct temperature.

 

Inver bands are sometimes used. This is an alloy of nickel and steel, with a very low coefficient of expansion, approximately 1/30th that of steel. If standardisation is made close to the prevailing field temperatures, then temperature corrections may be disregarded with these bands.

 

1.20.4    Tension correction

 

This is a correction which should seldom be necessary. If the tape is standardised at a correction suitable for field use, and used at the same tension, no correction is necessary. The formula for computing variation in tension is:-

 

Cp = { (P – Po)  L} / AE

 

                    where     Cp   = The correction per distance L, in metres.

P     = Applied tension in Kilograms.

Po   = Tension of tape at standardisation, in Kilograms

A     = Cross-sectional area, in square cm's.

E     = Young’s Modulus of elasticity of the steel in the tape

taken at 2,003,750 Kilograms per square cm.

 

 

1.20.5    Sag correction formula

 

Where           W    = Weight of tape in kilograms per metre.

L     = Length of unsupported tape, in metres.

P     = Tension in kilograms.

 

Sag correction Cs = { W2 *  L3 }  / {24 *   P2  }

 

When a tape is supported in equidistant spans, this formula becomes:-

 

Sag correction Cs = n  [ { W2 *  L3 }  / {24 *   P2  } ]

 

                    where            n     = Number of equal spans into which tape is divided.

L     = Length of each span in metres.

 

With slopes over 10°, a further factor is introduced due to the deformation of the catenary.

 

Formula for Sag correction on slope = sag correction on level x Cos2 slope angle.

 

To calculate sag using SI units this article is useful.

 

This will rarely be necessary. Since sag reduces the length, the measured distance is longer than the actual distance, so correction “negative”.

 

1.20.6    Sea level Correction

 

This will rarely be applied in the field. Generally mean height can be used for the traverse, the sea level factor is set on a computing machine, and all measured distances are multiplied, in turn, to give a sea level distance.

 

 

1.21       Summary of chaining Corrections and Errors

 

1.21.1    Standardisation

 

If incorrectly standardised, the one tape will give an accumulating error of the one sign. Tapes should be care­fully standardised, under good conditions.

 

1.21.2    Errors in slope reading

 

Where slopes are read with the theodolite, errors should be negligible. When the Abney Level is used, and is checked every few days, against the theodolite, errors of reading should cancel out, in lightly undulating country.

 

1.21.3    Temperature

 

The main source of error likely to occur, is from placing the thermometer at a different height from the tape; usually too near the ground which will make the readings too high.

 

A general mean of conditions, to which the tape is subjected, should also be chosen for the thermometer; that it is not protected from the wind, or put in the shade, unless the tape is under such conditions. The thermometer should be carried vertically so that the mercury column is not shaken apart, but laid horizontally, at the mean height of the tape, and given a chance to settle before reading. Much time can be lost, and little extra accuracy gained, through elaborate temperature reading, but reasonable care must be taken. Temperature errors are likely to be cumulative, on the one day, under similar weather conditions, and usually too high.

 

1.21.4    Tension

 

If the spring balance is reading incorrectly, this will give a cumulative error. It is advisable to check all balances, by lifting a known weight, or by pulling against the other balances.

 

1.21.5    Sag

 

In uneven country, sag must be watched carefully, and it will be decided whether to chain in catenary. Sag errors will rarely occur in easy, flattish, terrain. They are cumulative.

 

1.21.6    Alignment

 

Keep alignment within 150 to 300mm, and no appreciable error will result. Alignment is more easily maintained by the rear assistant, who should direct the front assistant on line before laying the chain.

 

 

1.22       Algebraic signs of errors using a single tape

 

When speaking of chaining errors:-

 

“+”  means an error which tends to make a distance measured longer than it actually is, on the ground; thus the correction to the measured distance is MINUS.

 

“-“  means an error which tends to make a distance measured longer than it actually is, on the ground; thus the correction to the measured distance is PLUS.

 

The following list of errors shows the accumulating effect.

 

 

Error

Accumulating effect

a

Standardization

All plus or all minus

b

Slope

Plus &  minus

c

Temperature

Plus usually

d

Tension

All plus or all minus

e

Sag

All plus

f

Alignment

All plus

g

Height of tape

Plus & minus

 

 

1.23       Errors of a full chain

 

Every distance laid must be entered, at once, in the field notes. Recourse should never be made to the counting of arrows, or to both assistants trying to remember the number of full lengths laid. The dropping of one full length is the most frequent source of gross error in chaining. Occasional wooden tally pegs, (about every ¾ kilometre) are useful, in case an arrow should be accidently knocked out, on a long traverse leg. This can prevent returning to the beginning of the leg.

 

 

1.24       Check measurements

 

These should be made if possible; more especially on large surrounds, to pick up gross errors. They may be made later, or by a second pair of assistants following the traverse party, and a lower order of accuracy is possible. Slopes and tensions are read, but not temperatures and other refinements.

 

 

1.25       Angular measurements

 

Angular measurements will normally be made with the Wild T2 theodolite, or similar instrument.

 

1.25.1    Horizontal Angles

 

The mean of 2 rounds is adopted as the observed angle at each station; each round consists of a face left and a face right pointing, on the distant stations. Settings are approximately:-

 

FL   000° 00’ 30" returning to the RO on 180° 00’ 30" approximately.

FR   270° 05’ 30" returning to the RO on 090° 05’ 30" approximately.

 

The RO should always be the backsight, and the difference between the pointings should not exceed 10 Seconds.

 

1.25.2    Vertical angles

 

Heights are carried through the traverse by vertical angles. Two pointings, a face right, and a face left, are read from each station, to both backsight and foresight, and always that order. The heights of the instrument, and of both targets are recorded in the field book, as each is measured.

 

 

1.26       The Surveyors Level

 

The function of the surveyors level, more commonly termed simply, the level, is to establish a horizontal line of sight, or nearly so. In its simplest form, it consists of a telescope with a defined line of sight and a spirit level tube to enable this line of sight to be set in a horizontal plane.

 

The modern levels which are likely to be met with, are:‑

 

The Tilting Level, and

 

The Automatic Level.

 

An almost obsolescent level is the Dumpy Level which had the telescope body fixed at 90° to the vertical spindle.

 

1.26.1    The Tilting Level

 

The main features of the telescopes incorporated in Surveyors Levels are that they have low magnification and a small field of view, suitable for accurate sighting over the short distances required. The diaphragm normally has a central horizontal and vertical wire; in addition two horizontal "stadia" wires are set equidistant, above and below the central horizontal wire. They are normally set so that the distance read on the staff between these two wires (known as the "intercept" or "S") is one hundredth of the distance between the level and the staff when the line of sight is horizontal. Ratios, other than one to one hundred can be ordered from the maker, if required.

 

The spirit level attached to the telescope is similar to those used on theodolites, and provision is also made for its adjust­ment in a similar manner.

 

To operate the instrument, the telescope with its attached level tube can be levelled by a finely pitched screw - called the tilting screw - independently of the vertical axis, and in consequence the line of collimation is not in general at right angles to the vertical axis. In using these instruments, the axis is set only approximately vertical with the three footscrews with reference to a circular bubble. Before reading the staff, the bubble in the main level tube which is attached to the, telescope, is centred exactly by means of the tilting screw.

 

In better instruments this is done by bringing the ends of a split bubble into coincidence. The bubble ends and the staff are viewed through the telescope at the same time, and co­incidence of the bubble ends is made at the instant of reading the staff. Mirrors to read the bubble are used instead of the split bubble on low priced instruments.

 

Figure 1.26.1(a)

 

Figure 1.26.1(b)

 

1.26.2    The Automatic Level

 

All leading surveying instrument manufacturers now have automatic levels available and at least one theodolite incorporates the system, instead of the alidade bubble, for use when observing vertical angles.

 

In appearance the automatic level is just like any conventional level; it has the usual three footscrews for levelling with the small circular bubble. However the orthodox bubble attached to the telescope has been abandoned. In its place are three prisms; one system has two of these prisms rigidly connected to the telescope tube with the third hung to swing freely; another system has one rigid prism with two swinging freely. A damper is incorporated to steady the line of sight and the whole unit of prisms and damper is called the "optical stabiliser".

 

The basic concept of the automatic level is that swinging freely, under the influence of gravity, the stabiliser automatically aligns the line of sight on the wires and in the horizontal plane, i.e., ninety degrees to the plumb line even though the telescope itself is slightly tilted. The range of the stabiliser of a good automatic level is plus or minus twenty minutes (±20¢) and this is well taken care of if the instrument is levelled with the small circular bubble, which however must be kept in adjustment.

 

It should be noted that most modern automatic levels give an upright image. The automatic level should be carried with the telescope in a vertical position, so that the stabiliser is at rest, when ravelling from job to job. The type of carrying case supplied by the maker usually takes care of this.

 

Figure 1.26.2. The Watts “Autoset” stabiliser and principle of operation.

In the “Autoset” level telescope there is the stabiliser consisting of two prisms on a suspended mount.

If the “Autoset” is tilted the stabiliser swings like a pendulum and keeps the horizontal ray on the cross-lines automatically

 

1.26.3    Level Tripod

 

The tripod is similar to that used for theodolites, the main difference being the absence of a moveable centring device. The same care should be given to the level tripods as is given to the theodolite tripod or the quality of the observations will suffer; check for loose bolts, screws or ferrules and keep the tripod well varnished.

 

1.26.4    Staff

 

Many types of staves are available, however the one most likely to be encountered at present is the "Sopwith" two piece hinged type, or the "Sopwith" three piece telescopic type, both of which are graduated in feet and hundredths.

 

Figure 1.26.4(b) shows this system of graduating the staff and indicates the method of reading these graduations.

 

The telescopic staff is easier to carry, however the more rigid two piece hinged type is more accurate since it maintains its length better over a period of time. It also usually has a, circular staff bubble attached, while the telescopic type requires a hand held staff bubble. Needless to say, all staff bubbles must be kept in adjustment.

 

Foot-metric staves are also available. With these, all readings are taken both in feet and metres, thus providing constant checks and greater accuracy.

 

All staves should be carefully looked after, kept clean and dry and always returned to their carrying cases when not in use. When carried in the vehicles they should preferably be strapped high up inside the vehicle to prevent damage from digging tools or other heavy sharp equipment, as will occur if the staff is laid on the floor.

 

Figure 1.26.4(a)

 

A steel footplate, upon which to stand the staff at change points, is necessary to ensure a firm base at such points. A suitable type is shown in Figure 1.26.4(a).

 

Figure 1.26.4(b) Levelling Staff “Sopwith” type.

 

 

 

1.26.5    Testing and adjusting the Surveyors Level

 

The "Two Peg Test" is used to ascertain any error in either a Tilting or an Automatic level. The test will be described first and the adjustment to each typo of level will be described in general terms. However it is advisable to consult the handbook of the particular brand of instrument in use before adjusting any instrument with which the user is not familiar.

 

Two Peg Test

 

(i)      Two points A and B are selected 200 feet apart and pegs driven in firmly.

 

(ii)     The level is set up at C, midway between the marks (plus or minus a couple of feet). Carefully take readings to a staff held on A and B in turn. The difference between those is the accurate difference in height regardless of the adjustment of the instrument. This is because the horizontal distances AC and BC are the same; therefore if the line of sight is not horizontal, both staff readings will be an equivalent amount too high or too low. See Figure 1.26.5 (a).

 

(iii)    Move the level to the vicinity of Peg A; set up on an extension of the line AB at minimum focus distance from the peg (about 6 feet). Again carefully take readings on the staff, hold on A and B in turn. If the difference between these two staff readings does not agree with the, difference in height as found when the staff readings were taken from the mid-point, the level needs adjusting. See Figure 1.26.5(b).

 

Unless the instrument has a large error, it can be considered that the line of sight and the horizontal line as shown at rA in Figure 1.26.5(b) are so close that no different reading on the staff at that point could be made after the bubble was adjusted.

 

Therefore the reading A of 4.68 - the accurate difference in height of 1.93 would give the point where the horizontal line would cut the staff at B, i.e. 2.75. See Figure 1.26.5(c).

 

 

Procedure where the instrumental error is large

 

If the error is known or thought to be very large, instead of making the second set-up of the instrument at minimum focus from the staff, it should be set up at a known distance on the extension of the line AB. This known distance should be some convenient fraction of the distance AB, for example AB = 200 ft, setup at 20 ft from A, ratio 1:10. Proceed with the test, noting that by similar triangles, a correction to the line of sight will need to be made at both peg A and peg B and that it will be in the ratio 1:10. See figure 1.26.5(d).

 

 

Figure 1.26.5(d).  Triangles IHB and IHC are similar;

therefore the error in the line of sight at BH is 1/5 the error at CH.

 

Adjusting the tilting level after the Two Peg Test

 

The staff is taken to peg B, and the central crosswire is laid on the staff with the tilting screw at the calculated correct reading, in the case of the example from Figures 1.26.5 (a,b & c) it is 2.75. Naturally this moves the ends of the split bubble apart but the line of sight is now horizontal.

 

With the bubble adjusting screw, the ends are then brought into co­incidence thus the line of sight remains horizontal and the bubble is now in agreement with the horizontal line as defined by the line of sight through the central crosswire of the telescope.

 

To check the instrument, take a couple of careful readings on the staff which is still at A, bringing the bubble ends into co-incidence with the tilting screw in the normal manner, move the staff to B and repeat. The difference in the readings rA - rB should now agree with the difference height.

 

Third order levelling specifications state that the vertical collimation error must not exceed ten seconds of arc, which is just on 0.01ft at 200 feet, therefore if agreement is within 0.01ft no further adjustment is necessary. If the difference is greater than 0.01ft repeat the adjustment until this accuracy is achieved.

 

Adjusting the Automatic Level after the Two Peg Test

 

The staff is taken to peg B, and the central crosswire is brought onto the staff at the calculated correct reading, in this case 2.75, by means of graticule adjusting screws.

 

Thus the central crosswire has now been brought into coincidence with the horizontal line of sight as defined by the stabiliser unit and this line will be correct unless the stabiliser has been damaged. To check that the adjustment has been performed correctly proceed exactly as for the check of the adjustment to the tilting level.

 

 

1.27        Level Traversing – Hints

 

1.27.1    The Instrument and type of levelling

 

The instrument to be used would most likely be the Watts "Autoset", or a similar type of automatic level.

 

The tasks likely to be encountered will most likely be level traverses with few, if any, intermediate points. In mapping surveys "grids" of levels are rarely required.

 

1.27.2      Extracts from "Specifications for contract Third Order Levelling

 

(i)      Vertical collimation error of instruments shall not exceed ten seconds of arc (0.01ft at 200 feet). Field tests to be made before work commences each day. Tests to be booked on 1 complete page of the fieldbook immediately preceding that day's level observations. Results are to indicate the error before, and residual error after adjustment, together with distances over which the test were conducted.

 

(ii)     Periodic tests to be made to ensure proper adjustment of the staff bubbles.

 

(iii)    With Automatic Levels:

 

(a)     The circular bubble must be in precise adjustment at all times.

 

(b)    Each time the level is set up to take readings, the dislevelment shall not exceed the tolerance laid down in the manufacturers hand book.

 

(c)     To mitigate systematic error due to dislevelment of the horizontal plane, the following routine is to be followed:-

 

At consecutive bays, level the instrument with the telescope pointing in opposite directions, i.e. at first and third setups the telescope should point towards the backsight, and at second and fourth setups the telescope should point towards the foresight.

 

When two staves are employed and the staffmen are "leap frogging" this is resolved by always pointing the telescope at the same staff when levelling the instrument.

 

(d)    To ensure the stabiliser is free to oscillate, prior to every reading the telescope is to be turned slightly in one direction then the other.

 

(iv)   Placement of the Staff

 

(a)     Bases to be inspected and cleaned if necessary at every change point. The staff shall always be placed on a steel footplate at each change point, unless change point is a Bench or other station mark, temporary BM, concrete culvert, firmly driven survey peg, etc.

 

(b)    When two staves are being used, there must always an even number of instrument stations between consecutive BM's so that the same staff is placed on the starting mark as a backsight and on the next as a foresight. This eliminates any zero error i.e. the graduations of the two staves.

 

(v)     Length of sights

 

(a)     The length of any sight shall be such as to allow the positive resolution of the staff graduations, and no sight shall exceed three hundred feet, even under conditions of very good visibility. (As a general rule, it is advisable to keep sights to about 200 ft. Also see that the centre of the graticule is kept higher than one foot from the base of the staff to prevent refraction causing errors in rays which are too close to ground level).

 

(b)    As shown in the notes for adjusting the level, back and fore sights should be balanced at the same length to help mitigate any instrumental errors: this is probably best controlled by dragging a standard long rope; when only a short sight can be obtained because of a steep slope, the next sight must be a correspondingly short sight, even though a normal length sight could have been made. Upper and lower stadia readings are always recorded to prove that the sights have been balanced and to measure the overall length of the traverse.

 

(vi)   Accuracy

 

In general, the forward and back levelings of a section (or, in the case of a loop, the closure on the commencing station) shall not differ by more than ± 0.05 ÖM feet, where M is the distance in miles between the BM's (or the length of the traverse in the case of a loop).

 

For details of checks for accuracy of all cases that may be met with in third order levelling consult the appropriate specifications, section 5.1.

 

1.27.3           The Level Field Book : Rise & Fall Method

   

Figure 1.27.3(a)

 

Figure 1.27.3 shows the procedure when levelling:-

 

Step 1: The staff is set up on the BM, termed point A in the diagram, height 100 ft.

 

Step 2: The level is set up about 200 feet from A along the line of advance.

 

Step 3: The second staff is setup on the steel footplate at change point B, a further 200 feet along the line of advance.

 

Step 4: A reading is taken on the staff held at A; this is booked as a backsight, and in this example is 3.245 ft. Note that sights of 200 feet or under should be read to the nearest 0.005 ft. Stadia readings to the nearest 0.01ft are also taken.

 

Step 5: A reading is taken on the staff held at B, this is booked as a foresight, and in this example is, 7.630. If only one staff is available the observer must wait for the staffman to move from A to B before this reading can be taken.

 

Step 6: As the foresight is larger than the backsight B is lower than A, therefore the difference between the backsight and the foresight is booked as a “fall” in the appropriate column, i.e. 7.630 - 3.245 = a "fall" of 4.385, therefore the height of B is 100 - 4.385 = 95.615 feet.

 

A suitable field book layout is shown in Figure 1.27.3(b). This is eminently suitable for a level traverse, without intermediate sights and using either a foot or metric staff. In the case where the foot/metric type staff is to be used, the extra columns for metric readings are provided on the right hand side of the field book page. The appropriate lines are "blanked out" to ensure that the first foresight is written one line below the first backsight.

 

Checking the Reductions

 

Backsights and Foresights are totalled at the foot of each page, as are the Rise and Fall columns. The difference between the Backsights and Foresights is noted and this should be the same as the difference between the Rise and Fall columns. It should be noted that to apply this method of checking, the first sight on the page of levels must be a backsight and the last sight on the page must be a Foresight, with this entry repeated as a Backsight as the first entry of the next page.

 

Where a Reduced Level value is available for the commencing BM, Reduced Levels are carried forward in the appropriate column, this gives a further check on the reductions as the difference between the first and last Reduced Levels should be the same as that of the difference between the total Backsights and total Foresights, and the difference between the total Rise and the total Fall.

 

This book is hardly suitable for use when booking a "grid" of levels with many intermediate sights. In that case it probably would be better to especially rule up a plain fieldbook to suit the task in hand. Where only a few intermediate sights are required the fieldbook described could be used by entering these sights in one of the columns designed for metric readings, providing of course that the foot/metric staff is not being used.

 

1.27.4    The Level Field Book : Collimation Method

 

This method which is suitable for certain types of engineering surveys - the booking for a stadia traverse with a theodolite is a variant of the Collimation Method - is unlikely to be met with in mapping surveys; however the following explanation and example is provided.

 

The method consists of finding the Reduced Level of the line of sight at each station (referred to as the Reduced Level of height of Instrument, or just height of Instrument) and subtracting from this value the reading on the staff at each point to obtain the reduced level at that point:-

 

Figure 1.27.3(b)

 

Step1. This R.L. Line of sight is always found by adding the backsight reading to the R.L. of that station.

 

Step 2: From this Line of sight, the RL, of the forward station is always found by subtracting the foresight reading on the staff.  See Figure 1.27.4(a).

 

Figure 1.27.4(a)

 

In the above Figure, RL of A = 956.650 + backsight reading on staff 6.160 = 962.810 which is RL, Line of sight (or height of instrument). Then 962.810 - reading on staff at B, 3.940 = RL of B is 958.870, and so on.

 

One check only is available, i.e. that on any page the difference between the total backsights and the total foresight should equal the difference between the R.L. of the commencing and final stations on that page, providing of course that the first entry on the page is a backsight and the closing entry a foresight.

   

 

Levelling Field Book page.

 

 

 

 

 

2          Theodolite – General Description

 

2.1.0      General Description

 

The theodolite is an instrument for measuring horizontal and vertical angles. There are numerous types, but they all have the following essentials.

 

2.1.1      A "lower plate" revolving about a hollow vertical axis, and fitted with a graduated circle. It is also provided with a circle setting screw, so that the circle can be set at any selected point in its rotation.

 

2.1.2      An "upper plate" which rotates about a vertical axis, fitted into, and concentric with, the axis of the lower plate. To this upper plate are rigidly attached a pair of standards and a levelling bubble. It also carries the horizontal clamp and tangent screw, and the reading device, normally a micrometer.

 

2.1.3      An "Alidade" which is the name given to the combination which consists of the horizontal axis, telescope and vertical circle together with a levelling bubble. The vertical circle is fitted with a clamp and tangent screw, for use in measuring vertical angles. The "alidade" bubble is fitted with an adjusting screw, either of the ordinary tangent type, or fitted with a lock-nut, to set the zero in its correct position.

 

2.1.4      Other parts are, levelling screws by which the axes of the plates can be set truly vertical, a traversing head with which the instrument can be moved for a short distance, in any direction, without disturbing the tripod; and a plumbob suspended from the centre of the vertical axes, with which the instrument can be set up, vertically, above a point on the ground.

 

2.1.5      For a theodolite to be in perfect adjustment, the following requirements must be fulfilled:-

 

(a)    The horizontal axis must be truly perpendicular to the vertical axis.

 

(b)    The line of sight, as defined by the cross hairs in the telescope, must be truly perpendicular to the horizontal axis.

 

(c)     The centre of rotation, of the upper plate, must coincide, with great precision, with the centre of the graduations of the circle, on the lower plate.

 

(d)    At least one levelling bubble must have its axis truly perpendicular to the vertical axis.

 

(e)    The alidade must be so adjusted that, when the vertical axis is vertical, the reading on the vertical circle correctly indicates the inclination of the line of sight.

 

2.1.6      When these conditions are fulfilled, if the instrument is "Levelled" (i.e., if the, levelling screws are adjusted until the bubble remains central, for a complete revolution, about the vertical axis) it will be possible correctly to read horizontal and vertical angles.

 

Figure 2.1.7.

 

2.1.7      It must be realized that when the instrument is in adjustment, the line of sight traces out a vertical plane, at right angles, to the horizontal axis, as the telescope is elevated, or depressed.

 

If the theodolite is set up at "T" (Figure 2.1.7.) and the telescope directed, in turn, first to "A" and then to "B", the angle read is the angle between the vertical planes passing through TA and TB. That is to say, if perpendiculars are dropped from A and B to the horizontal plane containing T, the angle read is that subtended by the feet of these perpendiculars, and not by the points A and B, themselves, unless those points happen to be on that horizontal plane.

 

 

 

 

 

 

3          Theodolite – WILD T2 - its use in all types of observation

 

 

3.1.       General preparation.

 

             While not the official Wild T2 manual this version provides very similar information.

 

3.1.1      Care and adjustment of the instrument and tripod

 

At the end of each field season, the theodolite will normally be completely overhauled by the maker, or agent, and should be issued in tip top condition for the season’s work. Only minor adjustments are to be made by the party leader or observer, in the field.

 

Before leaving for the field the instrument should be checked to see that no fault has been overlooked in the laboratory by the maker or agent. Mainly, these will be:-

 

(a)     All lenses not cleaned.

 

(b)    Telescope lighting inadequate.

 

(c)     All scales focus properly.

 

(d)    Horizontal collimation is within a few seconds.

 

Any of the above faults should be rectified immediately they cannot be done under field conditions.

 

3.1.2      The minor adjustments which can be done are :

 

(a)     Adjustment of tension of slow motion and footscrews with the capstan bar provided.

 

(b)    Centralising the plate bubble, if badly off centre. This is done by levelling the instrument inside a screen (or in the shade), then bringing the plate bubble close to the central position, with a capstan bar. This is not a precise adjustment as the bubble will almost certainly move off a little, during the season.

 

(c)     Adjustment of vertical collimation : This is done by reading a FL and FR vertical angle to a prominent point. If these 2 angles agree within a few seconds, no adjustment is necessary. If not, mean the FL and FR angles to get the true vertical angle to the prominent point. Then proceed as follows :

 

(i)      Lay on prominent point, clamping lightly both horizontal and vertical circles.

 

(ii)     With alidade bubble setting screw, set the vertical circle to read the true vertical angle. While doing so, notice that the bubble ends, as viewed through the prism, will move apart.

 

(iii)    Using the screw provided for adjusting the Alidade bubble, the ends of this bubble are brought into co-incidence, as viewed through the prism, and the adjusting screw is locked.

 

The vertical circle has now had the collimation error eliminated. It is advisable to again read the FL and FR vertical angles to check that the adjustment has been successful.

 

(d)    The lighting set should be checked, by the observer prior to the commencement of the season. See all connections are clean and firmly soldered, and the rheostat free from rust. If it is not allowed to get wet, the lighting set should give no trouble during the season. Power supply is three, 1.5 volt dry cells coupled in series, and packed in a plywood box. The rheostat should be turned well down while the dry cells are new.

 

(e)     Maintenance. Keep the theodolite clean, and all parts free from dust, at all times. Use a camel hairbrush and lens tissues, also cover the instrument with a plastic bag, when set up and not in use.

 

3.1.3      Tripod

 

This should be re-varnished at the end of each field season, and left stored with all bolts slackened, in case humidity expands the timber. Before again using the tripod, check that all bolts are tight, and that there is no movement at any point where the timber fits into any metal socket, either at the head or foot, of the tripod. This should be done each day the instrument is used, particularly if the weather is getting drier and hotter. The tripod should be wrapped in hessian or canvas for vehicle transport.

 

 

3.2.1      Setting up the instrument

 

The tripod should be set over the station or eccentric mark so that the height is just right for the observer; no straining because it is too high, and no excessive stooping because it is too low. However; it is better a little low, than too high.   

 

When the instrument is too high, there is a tendency to drag it off level; or to fail to get rid of parallax, owing to the eye not being directly behind the telescope. If azimuths are to be observed as well, the tripod must be oriented so that the inst­rument can be set up with two footscrews along a north south line.

 

Once the tripod has been positioned, pegs should be driven if at all possible. 450mm x 75mm square wooden pegs on firm soil, 1 metre x 75mm square for sandhills, or 300mm to 450mm steel pegs on rocky hills. If unable to drive in all pegs, put in as many as possible. Set feet in plaster of paris (use plenty) where pegs cannot be driven. See that when driving pegs, the tripod has not become displaced from its original position, tilting the head badly from the horizontal, and displacing the centre of the tripod from a position vertically over the mark, thus making it impossible to plumb the instrument accurately over the mark, without overhanging the tripod head.

 

Spend some time in clearing the observing platform of rocks, either loose or partly buried; stamp near each leg, and check for any slight movement of the instrument or tripod. Remember that a partly buried rock, well clear of the tripod, may touch other buried rocks, which in turn, do touch the tripod feet.

 

3.2.2      Observing screens

 

This is set up to give plenty of room to move around the instrument; see that the screen poles are not on line to the distant stations; and star, if azimuth is to be observed.

 

3.2.3      Levelling the Wild T2 theodolite for second order observations

 

This is done in two stages:-

 

(a)     Fairly accurately, with the plate bubble.

(b)    Final accurate levelling with the alidade (split) bubble.

 

Stage (a):-

 

Firstly, bring the plate bubble along the line of two foot-screws, and note the position of one end of the bubble, say the vertical circle end. See Figure 3.2.3(a) Turn through 180°, note the position of the same end of the bubble. (Figure 3.2.3(b)) Correct by half the difference of these positions, turn through 180°, until the bubble is level over the two foot-screws. Then turn through 90°, where the bubble will be in line with the remaining footscrew; Figure 3.2.3(c) shows this position. Use the same method to level the instrument along this line, with the single footscrew, this time.

 

Stage (b):-

 

Now bring the alidade bubble along the line of two footscrews, bring the bubble ends, as seen through the prism, into coincidence, and turn the theodolite through 180°. Note the amount of error. Take half out with footscrews, and half with the alidade screw. Turn instrument through 180°, and repeat until level along the line of these two footscrews. Now turn through 90°, so bubble is aligned over the remaining footscrew, bring bubble into coincidence, turn through 180°, note amount of error, take half out with remaining footscrew and half with alidade screw. Turn through 180°, and repeat until level along the line of this footscrew. The instrument is now completely level. When shielded properly from the sun, and strong winds, the Wild T2 will hold the level for long periods. It should be remembered to position the footscrews approximately centrally, before commencing levelling.

 

 

3.3.1      Horizontal and Vertical scales

 

While it is not difficult to focus the telescope and scales, great care must be taken, or the observations will be below standard. Remember, as all observers eyes are different, no one else can help by checking your focus.

 

 

 

The telescope:‑

 

(a)     Elevate the telescope to the sky, and bring the crosshairs to the clearest and sharpest focus obtainable, by turning the ocular focusing lens.

 

(b)    Sight distant station through the telescope, and focus until the distant station is also clear and sharp.

 

Move the eye around, when both crosshairs and the distant station are in focus, there will be no relative movement (parallax) between them. Once it is dark, and the light is turned on, in the telescope, invariably, both the distant station, and cross-hairs will need re-focusing.

 

The scales:-

 

Always use the lighting set to illuminate the scales (except for reference mark work, around the station.) Carefully focus the scales until the figures are sharp and clear. There may be a slight difference in focus between the horizontal and vertical scales but this rarely matters.

 

3.3.2      Types of horizontal and vertical scales

 

The following is an explanation of the Wild T2 theodolite scales these being the instrument mostly in use. However, the observer need only to master the technique of reading the Wild system, to easily change to whichever Wild theodolite is at hand.

 

3.3.3      Horizontal Circle

 

This is graduated to 20 minutes, and the 10 minute is found by interpolation. The micrometer drum is graduated to 1 second, with a run of 10 minutes. Looking into the scale telescope, two windows are seen. In the top window, by means of prisms, two diametrically opposite sections of the horizontal circle are seen, one the correct way up, and the other upside down. An index line is shown in the centre of the scale. In the bottom window, a section of the minute and second scale, with index line, is seen.

 

3.3.4      Reading the horizontal circle

 

When the micrometer drum is turned, the minutes and seconds will move past their index line, and the opposite sections of the horizontal circle, will move so that the graduations appear to approach one another movement of the micrometer drum is continued until the equivalent graduations of the horizontal circle are brought into coincidence. Now the index line, in the upper window, will either coincide with a graduation mark, or will come half-way between two. In the former case, the degrees and minutes are read direct, using the 20 minute mark which coincides with the index mark; in the latter case, interpolate to the ten minute lying between the two 20 minute marks. The reading on the micrometer scale gives the number of minutes and seconds to be added to the degrees, and tens of minutes, read on the main scale. Figure 3.3.4 shows an example, and mentions an alternative method of ascertaining the value of the divisions.

 

Figure 3.3.4. Horizontal circle

 

Figure 3.3.5. Vertical circle reading on one face only.

 

Figure 3.3.4. shows the image in the reading microscope eyepiece after coincidence. In the upper window, the index line shows the approximate value will be close to 256° and the first upright figure left of the index line, shows a reading of 255°. Now count the intervals from 255° to the diametrically opposite 75° mark. There are 4 intervals, that is, four tens of minutes, or 40'. A reading of 255° 40' is thus obtained from the upper image. In the lower image of the seconds drum scale, we read 7 minutes and 51.8 seconds. Thus shown on the drum, the complete reading is 255° 47' 52", the nearest second always being recorded.

 

3.3.5      Vertical circle

 

The vertical circle on the Wild T2 is graduated similarly to the horizontal circle. However, it should be noted that on FL it reads ZENITH DISTANCE, and on FR, 180° plus the zenith distance.

 

As the altitude is normally the vertical angle required (however the Sun azimuth proforma uses the zenith distance) it will be necessary to make the following calculations:-

 

Face left :

 

If the observed angle is less than 90°, take it from 90°, and the answer is a FL angle of Elevation.

 

If the observed angle is more than 90°, take 90° from it, and the answer is a FL angle of Depression.

 

Face right :

 

If the observed angle is more than 270°, take 270° from it, and the answer is a FR angle of Elevation.

 

If the observed angle is less than 270°, take it from 270°, and the answer is a FR angle of Depression.

 

The mean of the FL and FR angles gives the altitude free from collimation.

 

3.3.6      Reading the Vertical Circle

 

The graduations are read in exactly the same manner as with the horizontal circle, with the exception that immediately before the graduations are brought into co-incidence, the two ends of the alidade bubble, as viewed through the prism, must be brought into coincidence. The horizontal cross-hair has been set exactly on the aiming point, and the alidade bubble ends brought into coincidence with the tangent screw. Then the diametrically opposite graduations of the vertical circle are brought into coincidence, by turning the micrometer drum.

 

The reading from the upper window is                   :     94°       10¢

and from the lower window                                   :            03¢ 43.8²

Thus the full reading (always to nearest second)    :     94°       13¢ 44"

 

 

3.4.1      Observing

 

The following method of observing horizontal angles (most of which also applies to observing azimuths) has been designed so that all movement becomes automatic, and the hands always go to the right control on the instrument, whether in daylight or darkness. Also, to eliminate errors, which could result from friction, or any slight wear of the instrument. Once the technique is mastered, the observer should work quickly, and smoothly, acquire a very light touch on the instrument, move quickly, but carefully, around the instrument. It should be turned with two hands, one lightly holding each standard, not by the end of the telescope.

 

Targets normally will be either opaque beacons, helio's, lights either in daylight or immediately after dark.

 

Observations will be made in the last couple of hours of daylight or immediately after dark. In theodolite and tellurometer traversing generally only two distant stations will be observed.

 

3.4.2      Double pointing system

 

Most time is consumed in locating each distant station, and the greatest source of error in observing, is pointing at these targets, therefore, once the target is located, much greater accuracy is obtained if two distinctly different pointings are made, the micrometer drum being read at each pointing. This method is known as double pointing.

 

Before commencing observing, see that both horizontal and vertical slow motion screws are centrally positioned, to ensure an equal amount of movement, in both directions.

 

The rear station of the direction of advance of the traverse will normally be the reference object (R.O.), so that any traverse angle shown in the field book; will be the clockwise angle from the rear to forward station. On face left, bring this target between the double wires, set about 30" on the micrometer drum, and with the circle setting knob, set the circle to 00° 00'.

 

The instrument is now ready to commence observations, proceed as follows:-

 

(a)     Face left, swing left through 360° until the R.O. is close to the cross wires in the telescope, clamp the instrument, and bring the target centrally within the double wires, (fairly close to the horizontal wire) using the horizontal slow motion screw and making the last movement of this screw, a "screwing in” motion against the spring. Bring the scales into coincidence with the micrometer drum, the last movement of which should also be "screwing in". Read the angle, move the cross wires clear of the target with the slow motion screw, and again centralize the target within the double wires, once again making the last movement of the screw, as previously. (This movement of "screwing in" the slow motion screw is most importnat to keep tension against the spring. Remember also that when the instrument is on face right, the screw is on the opposite side of the theodolite to the observer, therefore, great care must be taken by the observer to ensure he still uses the "screwing in" motion on this face). Bring the scales into coincidence and read the angle. If the pointings are over 3" apart, discard both, and take two more. If still wide apart, the focus is probably incorrect, on either telescope or scale, or both. If the focus of the instrument is satisfactory, conditions must still be unsatisfactory for observing.

 

(b)    Unclamp the theodolite, swing left until the distant station is close to the vertical cross wires (and about a similar distance from the horizontal cross wire, as was the R.O.). Repeat exactly as in (a). If the instrument is swung too far past the station to lay on the target with the slow motion screw, continue the swing, in the same direction, through 360°.

 

(c)     Unclamp the theodolite, change to face right, swing right until the same station is close to the cross wires, clamp, and repeat as in (a).

 

(d)    Unclamp the theodolite, swing right, until the R.O. is close to the cross wires, and repeat as in (a). That completes the observations on this scale setting.

 

(e)     Set micrometer drum to 03¢ 50", set scale to required setting with circle setting knob (in this case 240° 00'). Swing right through 360° and bring target centrally between the double wires, as previously explained. Continue observing in this manner, until 6 arcs, which comprise one set, are completed.

 

3.4.3      Scale settings

 

 

1st Set

 

3rd Set

 

5th Set

FL

000°

00'

30"

 

15°

001

 

 

  20°

00'

30"

FR

180°

00'

30"

 

195°

00'

30"

 

200°

00'

30"

FR

240°

03'

50"

 

255°

03'

50"

 

260°

03'

50"

FL

  60°

03'

50"

 

  75°

03'

50"

 

  80°

03'

50"

FL

120°

07'

10"

 

135°

07'

10"

 

140°

07'

10"

FR

300°

07'

10"

 

315°

07'

10"

 

320°

07'

10"

 

 

2nd  Set

 

4th Set

 

6th Set

FR

210°

02'

10"

 

225°

02'

10"

 

230°

02'

10"

FL

  30°

02

10"

 

  45°

02'

10"

 

  50°

02

10"

FL

  90°

05'

30"

 

105°

05'

30"

 

110°

05'

30"

FR

270°

05¢

30"

 

285°

0.5'

30"

 

290°

05¢

30"

FR

330°

08¢

50"

 

347°

09'

55"

random

350°

08¢

50"

FL

150°

08'

50"

 

167°

09'

55"

arcs

170°

08'

50"

 

Settings are slightly approximate.

Naturally, on return to the R.O., collimation will give some variation to the original settings.

 

Each of the above sets is meaned, and normally, at least 4 to 6 sets are observed.

 

Usually, the range in each set is about 5", with an odd arc to 7" or 8"; however, if conditions are difficult, this range may not be achieved. Once the observer is experienced, and carefully and conscientiously observes the targets, and scales, as he sees them, the spread in the arcs is really a measure of the observing conditions. Thus results below standard, by an experienced observer, would indicate the need to re-observe that station under better observing conditions.

 

3.4.4      Check or random arcs

 

From a random, initial setting on the R.O. in any one of the sets, two arcs are read just as carefully, in the normal manner, to the distant station. This is to ensure that the degrees and minutes, have not been read consistently wrong. The usual care in reading those arcs, is required so that they can be used in the set. There is such a short period of good visibility each evening that full advantage must be taken of it.

 

3.4.5      Booking horizontal angles

 

The booker will record the name and/or number of each station observed, also the type of target observed. The observer will call out the degrees and minutes, a slight pause during which the booker calls back the degrees and minutes. The observer, who has read the micrometer drum, for the first pointing, during the pause, calls out the "seconds" reading; points again, and calls out the "seconds" reading, once again. The booker calls back these readings, as he records them.

 

All calling out should be sharp and business-like.

 

The booker should mean the two seconds readings, and subtract the mean reading on the R.O. from the mean reading on the distant station, as the observations are being taken, meaning these answers at the bottom of the page, when the set is completed. See example Figure 3.4.5(a).

 

At the conclusion of the night's observations, the observer will check all reductions and the means of the sets. Both booker and observer will sign each page. The observer should cover the previous answer with scribbling paper, while he completes his checking, to get a completely independent answer.

 

3.4.6      Vertical Angles

 

These will be truly simultaneous, and should be read between 1400 hours and 1600 hours LMT (Local Mean Time), when the air is most evenly heated. However, if lines are less than 16 Km (10 miles) in length, they may be observed between 1000 & 1700 hours, but still must be observed simultaneously. Lines less than 3km (2 miles) in length may be read non-simultaneously.

 

 

Figure 3.4.5(a) – Booking Horizontal Angles and Figure 3.4.10(a) - Booking Vertical Angles.

 

3.4.7      Probably the best type of target over the average length of line is a hello, and for shorter lines, the daylight (Flamethrower) lamp. The top of the vanes makes a fair target on lines up to 32km (20 miles) in length, if the lines have a good drop away at each end. Heights of targets above a station mark (or below, in rare cases) must always be recorded.

 

3.4.8      Screens should always be used for vertical angles; normally at the time of observation the sun will be beating strongly on both the instrument and tripod, unless they are shielded. If conditions are not too windy, and the time is short, a makeshift shelter which completely shades the instrument and tripod will suffice; i.e. the vehicle and part of the observing screen, or swag cover, etc.

 

3.4.9      Observing technique

 

A similar system of double pointing to that used for observing horizontal angles, is used for observing vertical angles. To keep in line with this system, it is essential that the alidade bubble ends are brought into coincidence just prior to each reading of the micrometer drum, even though the ends appear to still be in coincidence from the previous reading. This helps to even out erroneous readings arising from "flat" spots in the grinding of the level vial.

 

Observing procedure:-

 

(a)     Face left, intersect the target with the horizontal cross wire close to the central vertical wire, making the last movement of the slow motion screw against the spring, i.e. "screwing in".

 

(b)    Bring the alidade bubble ends into coincidence, in the same manner, read the graduations on the scale, Move the alidade bubble slightly off, move horizontal cross wire slightly off, then intersect the target once again exactly as before, again bring the bubble ends into coincidence, and again read the graduations on the scale.

 

(c)     Change to Face right, and repeat as above. The difference between the readings obtained on these faces, is the vertical angle, and 3 such angles make up a set. To be sure of best results, the observer must change face after each pair of double pointings.

 

3.4.10    Booking vertical angles

 

On face left, after pointing on distant station, and levelling alidade bubble, the observer will call out the degrees and minutes, a slight pause during which the booker calls back the degrees and minutes. The observer, who has read the micrometer drum for the first pointing, during the pause, calls the "seconds" reading, points, and levels the alidade bubble again, then calls out the “second” once more. The booker calls back the readings as he records them, and should mean the seconds readings, bringing the Face Left angle forward, into the next column to the right, in the field book. The observer changes to Face Right, and both observer and booker, repeat the above. The booker means the FL and FR vertical angles, and brings the resultant answer forward to the last column on the right, in the field book. When three such angles have been obtained, the set is complete, and the mean is brought down to the bottom of the page. Measure and record, heights of instrument and targets above station mark. See Figure 3.4.10(a) for an example.

 

The observer will check the reductions, and both will sign each page. The booker should check that there is no gross error, in the degrees and minutes, while the observation is in progress, by noting the approximate total of the readings on both faces. This should be about 360°, unless the instrument is badly out of adjustment.

 

 

3.5         Measuring and Recording Reference Marks, Eccentric Stations, and Recovery Marks

(This section is to be read in conjunction with 1. Chaining and 7. Station Marking)

 

The normal method adopted for measuring reference marks, has been to set a theodolite over the station mark (if accessible) or if not, an eccentric mark, and measure all distances by vertical angle and slope distances. Horizontal angles related to a distant station, and the station mark where applicable) are also observed. As marks are usually within 4 to 10 metres, the tops of hills rough with large boulders, and generally windy conditions prevail, the above method has been found to be more accurate than horizontal measuring with tape and plumbobs. If time permits, set up over a second mark, so that all distances can be checked by calculation.

 

If time is short, measure tie distances, horizontally with tape and plumbobs, and check slope distances by direct horizontal measurement. There should always be three reference marks.

 

It is impossible to cover all problems which will be encountered at the various types of set ups, however the following three will cover most cases.

 

3.5.1      Where the station mark is accessible

 

Set the theodolite over the station mark. Lay on a distant station as RO, and set 00°00'05" approximately on the horizontal scale. Read horizontal and vertical angles to each mark on FL. Change to FR and do the same, but this time, measure slope distances, while laid on each RM. Measure height of instrument above station mark.

 

If plenty of time, set theodolite over one of the RMs and with 00°00' 05" on the scale, lay on the station mark, read horizontal and vertical angles to the station mark and RMs on FL; change face, read angles and measure slope distances and height of instrument. See figure 3.5.1(a).

 

If time is short, measure tie distances horizontally with tape and plumbobs. See figure 3.5.1(b).

 

 

 

 

 

3.5.2      Where the station mark is inaccessible

 

This will normally be where a large cairn with pole and vanes, covers the station mark. If this is a new station, the distance, eccentric mark to station mark, will have been measured by the beaconing party, as will also the horizontal angles to the two RMs. This data must be with the observer who will lay on the centre pin on top of the beacon with 00°00'05" set on the horizontal scale. Read horizontal and vertical angles to the station and reference marks. Also measure height of instrument, slope distances, cut in at least one of the distant stations. The observer will check against the data supplied, for gross error in the original work of the beaconing party wherever possible, also set up over an RM, and read horizontal and vertical angles to the station mark, eccentric mark and the other RM, on both faces of course. Measure the remaining distance horizontally. See figure 3.5.2(a).

 

3.5.3      Where there is a distant recovery mark

(This section should be read in conjunction with 7.2.3)

 

This type of mark will only be placed where the station mark is likely to be lost, either permanently or temporarily i.e. on a sandridge which may erode, swampy & ground or tidal flats. When the above conditions occur, a substantial recovery mark (or marks) will be placed on the nearest firm ground.

 

Set up the theodolite over the station mark, lay on a distant RO, and set 00°00'05" approximately on the horizontal scale. Read horizontal and vertical angles to the recovery mark, and the two base terminals.

 

Set over the recovery marks and the two base terminals, in turn, reading all horizontal and vertical angles, thus closing both triangles. Be sure to measure all the heights of instruments, and heights of targets. These observations must be done in good visibility. Targets must be carefully plumbed, and very small; i.e. tripods with plumbobs (laying on plumbob string near hook). If care is taken, the triangles will close within about 10" to 20". Each, almost exact, 100 metre base line is to be measured twice (with an invar tape, if possible) the tape being laid on the ground, temperature taken and a pull of 6.800 kg (about 15lb) applied. This must be done in the very early morning, when the temperature is cool. If a 50 metre band is used, pull will need only to be about 4.600kg (10lb).

 

Figure 3.5.3 shows a typical Recovery Mark and base line. In 7.2.3 the preparation of the base line, and the Recovery Mark, are described.

 

All angles are read, so that distance, Station Mark to Recovery Mark, can be calculated from each triangle.

 

 

3.5.4      Reference Mark measuring

 

Figure 3.5.4(a) gives an example of measuring from 2 different set ups. The station mark is covered by a large cairn. Pages, appropriately ruled, are provided in the Traverse, Trig., and Azimuth field books for this purpose.

 

 

 

3.5.5      Computation of Reference Marks      

 

Where the theodolite has been set over two reference marks, all distances can be checked by simple calculation using the formula:-

 

       a/Sin A   =    b/Sin B   =    c/Sin C

 

See Figures 3.5.5(c) and 3.5.5(d) for examples.

 

Where only two sides, and the included angle are known, the remaining sides and angles can be calculated, as shown on the proforma Figure 3.5.5(e). Where Measurements have been made twice, they should normally agree within 3 to 4mm. If over 6mm measure again. Calculated checks should also have about the same agreement, if the triangles formed, are reasonably well shaped.

 

 

 

 

3.6         Eccentric Corrections

 

3.6.1      Formula

 

Eccentric corrections, which many find difficult to understand, are really quite simple, once the principle is grasped.

 

The Sine formula is used:—

 

a/Sin A   =    b/Sin B   =    c/Sin C

 

The distance, Eccentric Station to Station Mark, is required, also the angle (at the eccentric) between the Station Mark and the Distant Station(s).

 

The distance to each distant station is required. This does not have to be exact; thus distance, eccentric to eccentric as measured by the tellurometer is quite accurate enough.

 

3.6.2      Computation

 

In Figure 3.6.2(a), the bearing, or direction, we have is from the eccentric to the distant station, and we need the correction to apply to it, to get the bearing from the station mark to the distant station. The broken line, from the station mark has been drawn parallel with the line, eccentric to distant station therefore, it is on the same bearing.

 

 

 

 

The eccentric correction is the angle B1, and, as the bearing is greater, the sign is +.    

 

B1 is the same value as B, therefore the calculation is:-

 

       a            22 452   =    b            4.349

       Sin A      42º 28’         Sin B

 

Or

 

Sin B =   Sin 42º 28’ x 4.349 / 22 452

 

 

 

Log        4.349            0.638 39

       Log Sin   42º 28’         9.829 41

       Sum                           0.467 80

       Log        22 452   -     4.351 26

Log Sin Ecce C'n          6.116 54 (between 26 & 27 seconds) 

+    5.314 43 (Log Cosec 1")(*)

Log Ecce C’n                1.430 97 (in seconds)

Ecce C'n                      + 26.98"

 

(*) This is applied so that the angle can be looked up as a direct logarithm (rule for small angles; Chambers Tables).

 

The above formula is used in the proforma in the field book. However, to avoid subtractions, in the calculation, the Co-log of the distance, Station Mark to Distant Station, is used; and the Cosec 1" is added to the distance between Eccentric and the Station Mark, to give Log "K", and save 1 line in the main addition.

 

It should be noted, where the angle at the eccentric station, between the Station Mark and the Distant Station is under 180°, the correction is plus, and where the angle is more than 180°, the correction is minus. If in doubt, draw a thumb-nail sketch. See Figure 3.6.2(b) for an example of an eccentric correction, worked out on a proforma.

 

3.6.3      Small corrections to observations where target at the Distant Station is slightly off line.

 

The following plotted method is normally used where targets are eccentric by small amounts only, up to 1 metre. If care is taken it is quite accurate. It is also a valuable check for gross error in ordinary eccentric corrections:-

 

(a)     Plot station "A" (Station where target is eccentric) with ray to station "B" (Station where observations are being made to "A"). Use magnetic bearing for plotting this ray which is not to any scale. Note distance to nearest Kilometre against this ray.

 

(b)    At a suitable scale, plot eccentric target by magnetic bearing and distance, which should be in mm.

 

(c)     It is necessary to find the distance that the target is off line, at right angles to the ray, "A" to "B".

 

(d)    The eccentric correction will be the amount this distance subtends at the distance between stations. Use the close approximation that 1 second of arc = 5mm per Kilometre.

 

(e)     The 2 examples below show the two types of plot required to cover all situations.

 

(f)      It is easy to decide, by inspection of the plot, whether the direction observed is too great or too small, and thus give the corrections its appropriate sign.

 

 

Refer Figure 3.6.3(a) : Target is eccentric by 67mm on a Mag. Bearing of 340°. This gives a distance off line of 46mm from plot.

 

Calculation:- 5mm x 21km gives 105mm per sec at 21km. Correction is 46mm, which means correction in seconds will be about 0.5"  or 105/46 = 0.44".

 

Looking in from B it is seen that the bearing observed is too small, therefore correction is plus.

 

 

 

Refer Figure 3.6.3(b) : Same target is sighted from C. This gives a distance off line of 62mm from plot. Note that ray A to C has to be extended to measure right angle distance which target is off line.

 

Calculation:- 5mm x 44Km gives 220mm per sec at 44 Km. Correction is 62mm, which means the correction in seconds will be about 0.3² or 220/62 = 0.28"

 

Looking in from C, it is seen that the bearing observed, is too large, therefore the correction is minus.

  

3.6.4          To ascertain amount of lean on a pole, the base of which is a cairn

 

(a)     Mark a line around the pole, 1 metre, or some other suitable distance, from the top.

 

(b)    Stand about 7 metres from the cairn, and at right angles to a face of the pole, point "A" in the diagram 3.6.4(a).

 

(c)     With plumbob, sight edge of pole at "X", and mark x vertically above, on the top edge of the pole. If greater accuracy is required, use the theodolite, instead of the plumbob. Measure distance from corner of pole C to x. This is the amount of lean over 1 metre. If this was 20mm, the lean over the full length of the normal 3.380 metre pole would be:- 20 x (3.38 /1) = 66mm.

 

(d)    Mark this distance along the top edge of the pole, from corner C and call it point “a”.

 

(e)     From “a” draw a line across the top of the pole, parallel with the edge.

 

(f)      Move around 90° to point B and repeat all in (b), except that the last point to be marked will be "b".

 

(g)    The point where lines "a" and "b" cross, at "c", is the point where the corner of the pole C would be, if the pole had no lean. Measure distance "c" to C, and take Mag. Bearing from "c" to C.

 

Record that pole leans on a bearing of ...° for a distance of ...mm.

 

(h)    From the centre of the leaning pole at D, mark true centre of pole at "d", using above bearing and distance. Take all measurements angles to RM's, and distant stations from point "d".

 

 

 

 

3.7.        Plumbing Towers, Tripods and Beacons.

      

3.7.1.     Towers.

 

These can be plumbed quickly and accurately over the station mark, with two theodolites. When engaged on tower work, it has been found necessary to carry an extra theodolite with the party erecting the towers.

      

The following method was adopted:-

 

See that the adjusting slot on each tower leg is approximately central on the bolts, so that adequate adjustment is available.

 

Set up the two theodolites about 120° apart, so that they can sight the station mark centrally between two tower feet. They should be about 30 metres from the tower.

 

Clear bushes, grass etc., so that the station mark can be seen - set match in the centre of the mark.

 

Level the theodolites, lay on station mark with both instruments and elevate them until they are laid on the tower head.

 

Look through theodolite No 1 first; loosen retaining bolts on tower foot opposite No 2 theodolite; move tower until the theodolite retaining bolt in the tower head, is cut centrally by the vertical graticule, in the theodolite telescope; tighten retaining bolts on foot opposite No 2 theodolite.

 

Look through theodolite No 2; repeat operation as above this time adjusting with foot opposite No 1 theodolite; as this is opposite theodolite No 1, this adjustment will not greatly move the tower off line, from that instrument.

 

If necessary, readjust for instrument No 1, tighten retaining bolts and lock. Do likewise for instrument No 2.

 

Remember all adjustments are done at the foot opposite the instrument to the one through which the tower head is being viewed.

 

 

3.7.2.     Plumbing tripods or beacons.

 

Tripod, or quadrupod beacons, where the station mark is accessible would need to be plumbed as in 3.7.1., if observations are to be done to the vanes.

 

If observations have already been taken, the reverse method will have to be used; i.e., lay on centre of vanes from two positions, depress telescope, and mark plumb point on the ground, near station mark. Measure distance vanes off line, and take magnetic bearing. Draw plot to scale, showing the above details; calculate the eccentric correction as in 3.6.3.

 

Where lights are used and are plumbed over the station mark, naturally, the above does not apply.

 

3.8         Sigma Octantis Azimuth determination

 

3.8.1      Single-ended azimuth determinations, consisting of one set of 6 rounds, shall be observed on the terminal leg of every spur traverse, in a control survey. Additional azimuth determinations may be observed at any stage, to check the "carried through” geodetic azimuth.

 

3.8.2      Simultaneous reciprocal azimuth observations, consisting of two sets, shall be observed on specified lines, as required. They do not demand exact simultaneity of pointings by each observer. However, it is important that the two observers, at each end of the line, commence observing at almost the same time, and finish the two sets, within 10 minutes or so, of each other.

Figure 3.8.8

 

3.8.3      Main equipment necessary

 

Theodolite and lighting set

Radio, capable of receiving WWV or VNG.

Split hand stop watch

Pocket-watch with second sweep hand.

Observing screen or tent.

Booking lamp.

Torch (for reading plate bubble and stop watch.)

Lucas lamp and battery.

Traeger Transceiver for inter-communication with distant station.

 

3.8.4      Time of observation

 

Observations should commence immediately after sunset, or as soon as Sigma Octantis is visible. This is the most accurate period in which to observe, the RO light being at its steadiest at this time.

 

3.8.5      Light from RO

 

A Lucas Lamp, or other suitable light will be used. It is important, particularly in flat terrain, to keep the lamp as high above the ground as possible. The lamp should be plumbed over the station mark, if possible. If observations are also in progress at the station, the light should be placed exactly on line to the distant station with the theodolite.

 

3.8.6      Preparations for Azimuth observing

 

The zenith distance and azimuth of the star, to the nearest 2 minutes of arc, is calculated for the approximate start time of the observation. This is done on the graph, Figure 3.8.

 

Before consulting the graph, it is necessary to calculate the Local Sidereal Time at which it is desired to commence observations.

 

To compute Local Sidereal Time :

 

At NM/E/110 Latitude 26° 08', Longitude 132° 30'

Time, 1950 hours, Central Australian Time, on 1 March 1970

 

-west )

L.S.T. = R + U.T.  +east )   Longitude

 

h     m

Central Australian Time             19   50 (Time to nearest minute.)

09   30  East of Greenwich – 09h 30m

Universal time                          10   20

R for 10h 20m U.T                           10    35 (Pg 6 Star Almanac)

Longitude (East)                       08    50 (132.5° Long in time /15)

29    45

       -24 00

Therefore L.S.T is                      05  45

 

3.8.8      To find zenith distance and azimuth of Simga Octantis

 

Using the computed L.S.T., the graph is used to find DH, and the azimuth of the star. DH is applied to the co-latitude, either positively or negatively, to give Zenith Distance, depending on whether the star is in upper or lower transit. In the example the correction is positive. Figure 3.8.8.

 

3.8.9      Setting the watches

 

The pocket watch should be set about 10 seconds fast, on Standard Time. The stop watch should be started at a suitable time, i.e. if a 30 minute dial, at 00 or 30 minutes, if a 15 minute dial, at 00, 15, 30 or 45 minutes. It should be started, within 1 or 2 seconds, of the same reading as the pocket watch. This means that both watches are about 10 seconds fast on Standard Time, and therefore any errors are more easily detected. The stop watch should be compared with the WWVH, WWV, or VNG time signal, noting the error to the nearest 0.10 second, just prior to the commencement of the azimuth observations, and also after half the observation has been completed, and at the conclusion of the observation.

 

3.8.10    Sequential Description of the Observing Method

 

After checking that the theodolite has been carefully levelled, parallax eliminated, focus adjusted, and the lighting in the telescope and circles suitable, then:—

 

(a)     With the theodolite FL, take 2 pointings, and 2 micrometer readings on the RO light, in the same manner as for horizontal angles.

 

(b)    Set-the zenith distance, and horizontal angle of the star, as called out by the booker.

 

(c)     Adjust the vertical pointing of the telescope, so that the star appears just clear of the horizontal wire, and bring the star centrally between the 2 parallel vertical wires, calling "up" and pressing the stop watch button at that instant. On the call "up", the booker records the time indicated by the pocket watch.

 

(d)    The observer calls out the stop watch reading, and the plate bubble readings, East and West, in that order.

 

(e)     The observer calls out the horizontal circle reading.

 

(f)      Take another pointing and micrometer reading, again reading the stop watch and plate bubble.

 

(g)    Call out the horizontal circle reading; on this occasion read the vertical circle to the nearest minute, and call it out.

 

(h)    Change face on the star. The booker will call out the vertical and horizontal circle settings, if desired by the observer.

 

(i)      Take 2 more pointings and bubble readings, etc., on the star as before.

 

(j)      Take a vertical circle reading, to the nearest minute of arc, on the star, after the second pointing.

 

(k)     Swing back on the RO light and take 2 pointings and micrometer readings. This completes 1 round.

 

(l)      The instrument should be relevelled after each 3 rounds. However, if at any stage it is noticed that the instrument is badly off level, it should be relevelled before commencing the next round from the RO.

 

(m)   When observations are complete, compare the stop watch readings with the coarse readings of the pocket watch, looking for 30 second discrepancies. Reduce the field book as shown in Figures 3.8.10(a) & (b).

 

 

 

3.9         Hints on Ex-Meridian Sun Observation for Azimuth: Method and Booking.

 

(a)    Time to observe

 

The best time to observe, i.e. when any error in Declination, Altitude, or Latitude will have least effect on the computed result, is when the sun is on or near the Prime Vertical, either East or West, and at an altitude of 20° to 30°.

 

However owing to the sun's path through the changing seasons, it will frequently be impossible to fulfill the above conditions. For example, in mid-winter, in Latitude 400 (just south of Victoria), observations between 0930 - 1000 hours, and 1500 - 1530 hours EST will only give altitudes of from 17° to 21°, and bearings of approximately 40° or 320° which are well away from the Prime Vertical.

 

Obviously a compromise is necessary, and the observer must decide on a time to suit the time of year and the locality. Luckily, as the observer moves north in Australia and the Latitude becomes smaller, the conditions for the shape of the astronomical triangle improve for ex-meridian sun observations.

 

(b)    Observing technique

 

As the tabulated values of Declination and "R" for the sun are referred to its centre, the observations are arranged in such a way that the mean of the Face Left and Face Right pointings will give an observation to the sun's centre. Observations are on the limb of the sun. Remember, in the morning the sun will appear to be descending, and in the afternoon it will appear to be ascending. Figures 3,9,(a) and (b) show the technique.

 

Initial location of the sun in the telescope.

 

The sun can blind if the observer forgets to fit the sun filter to the eyepiece end of the telescope.

 

To avoid danger from this, the following method of locating the sun, is recommended:-

 

(i)      Standing beside the instrument, bring the shadow of the foresight onto the rear sight; lock the horizontal clamp.

 

(ii)     Hold the palm of the hand behind the eyepiece, move telescope vertically until the image of the sun shows on the palm; lock the vertical clamp.

 

(iii)    Immediately, slip the sun filter onto the eyepiece end of the telescope.

 

 

 

 

Laying on the sun

 

Experience has shown that the best method or laying on the sun is to use only one tangent screw to keep one limb of the sun on the appropriate crosshair, letting the sun's own movement bring the other limb onto its appropriate crosshair. When viewed through the sun filter the crosshair is only clearly visible against the bright disc of the sun, therefore the crosshair is initially laid close to the edge of the sun as shown in the first position in figures 3.9.(a) and (b).

 

It is then easy to concentrate on the diminishing-gap between the crosshair and the limb while still keeping the other limb on its crosshair with the tangent screw. The method can be clearly seen in the following

 

(c)     Sequence of observation

 

FL on RO             00° 00’ 30” approx   )

Attach Sun Filter         FL on Sun                                              )

Change face                FR on Sun                                              ) 1 round

Remove Sun Filter       FR on RO       1800 0030” approx          )

 

The second round commences with FR on the RC; leave scale setting as set, but re-lay on the RO, once again following the above sequence.

 

At least 4 rounds, possibly 6, are taken. Figure 3.9.(c) page of F.B.

 

 

(d)    Additional data required

 

Time : Should be booked to the nearest second. Watch should be checked against a radio time signal; correct the booked time, if necessary.

 

Temperature & Pressure : Readings should be taken for use with the Refraction Tables. Those in the Chambers are based on a standard temperature of 10°C, and a standard pressure of 754mm (1005.25mbs). Where observations are taken under conditions differing considerably from standard a noticeable error is introduced if actual readings or both temperature and pressure are not used in the computation.

 

Refraction taken from Chambers is multiplied by:

 

(Actual Pressure (millibar)   ) *   (                   283 )                 

(1005.25                                 )     (273 + Actual T°C       )

 

Refraction increases as pressure increases BUT decreases as temperature increases.

 

The back page of the Sun Observation reduction proforma has refraction and parallax tables for the sun based on zenith distance.

 

The Refraction Table is based on 57”*tanZD

The Parallax Table is based on 8.8”*sinZD.

 

Plate bubble : Usually,with a sun observation for azimuth, it is not considered necessary to record, and correct for, any dislevelment shown by the plate bubble. However, it must be emphasised that if great accuracy is the aim, any dislevelment of the horizontal axis must be taken into account.

 

 

 

 

3.9         Sun observation for Azimuth – Hour Angle and Accurate Time

 

Traditionally, the method used for observing the sun for azimuth has been as previously described, i.e., reading simultaneously the altitude and the horizontal angle to a reference point using time within one minute. As this method requires no sophisticated equipment and only an accurate Latitude, it is not surprising that it became the method almost exclusively used.

 

The main drawback to this observation is the limited time each day that the sun is in a suitable position, and the time necessary for the observer to become proficient in the technique of simultaneously pointing to both the horizontal and vertical limbs of the sun.

 

It is pointed out by Dr. G. Bennett of the University of NSW in an article in "The Australian Surveyor", March 1974, that the Hour Angle method using accurate time is now well worth considering because:-

 

(i)      Time signals from VNG should be audible over most parts of Australia during daylight hours.

 

(ii)     Small transistor short wave radios for receiving these time signals are readily available.

 

(iii)    Split hand stopwatches are also readily available.

 

(iv)   Current map coverage is such that Longitude can now be scaled as accurately as Latitude.

 

(v)    The method permits the surveyor to take observations over a greater time range, (even observations at noon, in the winter months should be quite satisfactory.)

 

(vi)   The observer has only to concentrate on laying on the vertical limb of the sun and reading the horizontal angle.

 

(vii)  In an observation where speed is essential, considerable time is saved in not having to adjust the alidade bubble and read the vertical angle.

 

Setting the watches and Time Signals

 

The procedure laid down in 3.8.9 should be followed, however it should be emphasised once again that accurate time is critical in this observation therefore care must be taken to rhythmically "beat" the stopwatch in unison with the "beep" of the radio signal. Beat the finger on the stopwatch button a number of times until this slight sound is synchronized with the "beep" of the radio time signal. Once this is achieved press the button on one of the "beeps". Do not "snatch" at the button on this "beep" or good synchronisation will be lost; this is a common fault while learning.

 

The mean of at least five synchronizations should be taken. Unless cloud causes delay, the sun observation is finalized quickly; where this is the case a time signal check immediately prior to and immediately following the observation is sufficient. Where delay occurs take farther time checks during the waiting period.

 

Observing and booking

 

Reading the stopwatch and recording the observed data is similar to that of the Sigma Octantis observation for azimuth except that the plate bubble is not read and no vertical angle is required. As the altitude of the sun is not observed, temperature and pressure readings are not required.

 

The example in Figure 3.9(d) shows the booking method using the same field book page as for the Sigma Octantis observation. It is advisable for the observer to call out each vertical limb of the sun as he lays on it; the booker can record this in the Vertical Circle column as shown. This procedure should ensure that the observer does not forget to change to the opposite limb of the sun as he changes face. The observation in the example was done using single pointings, however any observer, once he has attained sufficient speed, would be advised to use the double pointing method for greater accuracy and less chance of gross error.

 

The computation of this observation is shown in Figure 12.7(3), Volume 2 of these notes.

 

 

 

3.10       Meridian Transit Observations for Latitude & Longitude – Rimington’s Method

 

A method of astronomical observations for Latitude & Longitude was needed mainly to provide control for minor traverses in the N.T. and also the 4 mile map series owing to the fact that little triangulation control was available at that time (1940-1955).

 

To make the observation an economical proposition the requirements were:-

 

(a)     Observations for both Latitude & Longitude needed to be done on the one night and take no more than a couple of hours.

 

(b)    Field computations to prove that the result was acceptable had to take no more than about the same length of time, so that they could be done on the same night or first thing next morning, to enable the observer to move on (unless, of course, the computations indicated further observations were necessary).

 

After considerable research, the following method was evolved by Mr. G.R.L. Rimington. His paper in the Australian Surveyor, combines a description of the method and the calculations necessary, with the historical background of the first trial observations.

 

The following is a brief description; this is then amplified in a "step by step" procedure.

 

(i)      A programme of stars is prepared.

 

(ii)     Theodolite is laid out on a N-S line, stars are paired alternatively N & S, or vice versa.

 

(iii)    The accurate time and "rate” of the chronometer is found; it is advisable, but not necessary, for the chronometer to be slightly fast, and it is probably best set on the standard time of whichever Australian Time Zone the observer is in. However, it can be set on GMT (UT), if preferred.

 

(iv)   Longitude observation. Using the "early stadia" wire, the star is timed on FR by stopwatch and chronometer prior to its reaching the centre wire (the meridian), and timed again, this time on FL as it reaches the same "offset" wire, now termed "late stadia". From this it can be seen that the star is not timed as it crosses the meridian, the time that this actually took place being the mean of the "early" and "late" stadia times.

 

(v)     Latitude observation. As the star crosses the meridian (centre wire) on FL, the vertical angle is read. This is the Z.D. with the Wild T2.

 

(vi)   The above procedure is repeated with a star in the opposite direction to give a "pair". Computation of this pair will give both a Latitude and Longitude of the position.

 

The observation needs no elaborate equipment; the main requirements are :

 

(i)      Theodolite, Wild T2, or similar, with Talcott Bubble if possible. Also lighting set, prismatic eyepieces and tripod. The instrument to read to one second, the telescope to elevate to about 70°, and to have two, "offset" vertical hairs. The instrument selected was the Wild T2, and the two "offset" vertical hairs were placed at the same distance L & R of the centre vertical wire as the normal stadia wires are above and below the horizontal wire, i.e., about 17 minutes of arc. Thus the names "early Stadia" and "late Stadia" have been adopted for these two hairs. See Figure 3.10(a).

 

 

(ii)     Surveyor’s or ship's chronometer, half second beat. Good stopwatch reading to one-tenth of a second, with wide enough graduations to estimate to one-hundredth of a second, pocket-watch.

 

(iii)    Apparent Places of Fundamental Stars (FK4), star programmes, Sigma Octantis graph, field books, maps, etc.

 

(iv)   Table and light for booker, thermometer.

 

(v)     Observing pegs for theodolite tripod.

 

For this observation there are four main steps :

 

(i)      Office preparation of a star programme and the Sigma Octantis graph.

 

(ii)     Field preparations before dark

 

(iii)    The actual observation after dark.

 

(iv)   The field computation before leaving the station.

 

Step 1    Office preparations

 

(a)     Programme of stars

 

Once the general area for the field work is known a programme of stars is prepared for the Mid-Latitude of that area. A long list of suitable stars is extracted from the FK4. They are listed as North or South, Name, Magnification, RA & Dec, and columns are left in which to enter (360°-ZD) and ZD, on arrival at the place where the observation is to take place.

 

The RA is not listed as such but as "Early Stadia", and a time allowance of approximately two minutes to the RA is made to allow for the difference in time between the stars arrival on the "Early Stadia" and its arrival on the centre wire (the meridian).

 

As the North stars move a lot faster than the South stars, it is worth calculating this time allowance for both North & South stars of a suitable ZD for observing. This can be done thus:‑

 

The value of the space between the stadia Wires is 1:100 which is 34' of arc (2.26 minutes of time). Thus from a stadia wire to the centre wire as 17' of arc (1.13 minutes of time).

 

This time interval x Secant Declination of the star gives the time the star will take to travel from the stadia to the centre wire, (or stadia to stadia, if required).

 

A North star with a Sec. Dec. of 1.0610 x 1.13min = 1.20min. Therefore "Early Stadia" for this star is RA -1.20min, allow 2min.

A South star with a Sec. Dec. of 2.0050 x 1.13min = 2.26min. Therefore "Early Stadia" for this star is RA-2.26min, allow 3min.

 

The above figures are approximate only; as no correction has been made for Latitude, they apply to a point on the Equator.

 

This can be used also to check doubtful observations, and is an indication of the time available for changing face and reading the ZD as the star crosses the centre wire. When checking doubtful observations always allow for the Latitude.

 

Diagrams for 30° South Latitude

 

 

(i)       Star with Nth Dec. of 12° would have a ZD of 30° + 12° = 42°. It would be to the observers north and would be O.K.

 

Stars in the shaded area are unsuitable, thus stars with North Dec. of 0° to 20° & South Dec. of 0° to 10° are suitable North stars. Stars with a South Dec. between 50° & 80°, are suitable South stars

(ii)    Star with a Sth Dec. of 55° would have a ZD of 55° - 30° = 25°. It would be to the observers south and would be O.K.

 

In selecting stars for the programme, list those between about 1.0 and 6.0 magnitude. Use in the observation, wherever possible, those between 2.5 and 5.5. As the Wild T2 will only elevate to about 70 (20° ZD) and because of greater unreliability of refraction in lower altitudes, stars with a ZD over 50° should not be selected, another limitation is placed on the stars which can be entered in the programme. Draw rough diagrams as in Figures 3.10(b) & 3.10(c) to give a clear picture of the stars which can be selected.

 

The selected stars for a six to seven months observing season cover about three foolscap pages and will be useable for some years. Sufficient copies to permit the using of one programme per station should be made available to each observer.

 

A computer programme is now available to select stars for such a season’s work.

 

(b)    Graph for the location of Sigma Octantis

 

A graph giving the ZD and Azimuth of Sigma Octantis at any LST at the Equator should be made.

 

For the accuracy required there is no need to solve the astronomical triangle; just use a series of plane triangles with the hour angle each half hour between 0hr and 06hrs and the hypotenuse the CO - ZD (Polar Distance). Thus the Polar Distance x sine hour angle gives the Azimuth correction, and the Polar Distance x cosine hour angle gives the ZD. See Figure 3.10(d).

 

 

As the RA of the star is the LST when the star is on the meridian, this is the start point for the graph, points are plotted to obtain both ZD and Azimuth curves for each half hour from this start point. Thus in 1971, with the RA and Dec. of Sigma Octantis 20h 40m 04.36s and S89° 04' 05.48² respectively, 10 right angled triangles with the hour angle each half hour (in arc 7.5°) increasing from 7.5° to 82.5°, and with the hypotenuse (Co-dec.) a constant, can be quickly solved on a calculating machine. Signs for these corrections are indicated in Figure 3.10(e).

 

 

There is a slight variation in the movement of Sigma Octantis from year to year; while this is not sufficient to cause trouble in locating the star, if it is required to use the graph to lay out on a reasonably accurate azimuth, the graph should be recalculated each couple of years. Figure 3.10(f) shows one form of this graph while another type is shown in the chapter "Sigma Octantis azimuth determinations", Figure 3.8.

 

Step 2    Field Preparations

 

Setting up

 

The following requirements must be satisfied:-

 

(i)      The instrument must be oriented with two footscrews along a N-S line so that the instrument can be levelled in the plane of the meridian and across the plane of the meridian. Keeping the instrument perfectly level across the meridian is vital to the accuracy of the longitude part of the observation.

 

(ii)     The vehicle should be positioned so that it protects both the theodolite and the booker from the wind, and is close enough to satisfy the next step.

 

(iii)    The booker's table, on which the chronometer will be placed, must be positioned within 3 paces of the theodolite and beside the vehicle. The chronometer must be placed so that the observer can get to it without stepping over a tripod leg.

 

(iv)   All usual precautions in setting up the theodolite for accurate work must be taken.

 

(v)     Booker prepares his set up.

 

 

Figure 3.10(g) shows a good lay-out.

 

(b)    Preparations before dark

 

(i)      Scale from the map, the Latitude & Longitude to the nearest minute. Decide on the time when Sigma Octanis should become visible and calculate the LST at this time:‑

 

LST for 1900hrs WST on 1/3/71. Latitude 29°08'. Longitude 127° 16¢.

 

WST                                                      19       00   00

minus zone                                     08   00       00

GMT (UT)                                       11   00       00

+ Sidereal Correction                             01       49

+ Longitude in Time. (127° 16' /15) 08   29       04

+ Sid. time at 0hrs UT, 1/3/71.        10   32       35

                                                             30       03   28

-24h gives LST            24   00 00         

06   03  28

 

From the Sigma Octantis graph calculate the ZD & Azimuth of the star at the above LST. At 1900 hours the booker should start the pocket watch at this LST (nearest minute.). The fact that the watch is running at mean time rate does not matter over the short period between the time the watch is started and the conclusion of the observation.

 

(ii)     On the observing programme, fill in the ZD & (360°—ZD) of each star which it is intended to use and bracket them in "pairs" North and South; make sure a surplus of stars are ready in case of delays. From Figure 3.10(h) the procedure is evident.

 

The selection of pairs is a matter of compromise, but the difference in the ZD's should not generally exceed 10°. The stars magnitude should generally range between 2.5 and 5.5 for easy intersection.

 

The observer may at times have to observe outside these limits. However, it is generally found that stars brighter than 2.5 are too large to intersect easily & accurately, while those smaller than 5.5 are not easy to see. The clarity of the night will also effect this; on a very clear but moonless night, stars in the vicinity of 6 magnitude may by intersected quite easily, while on quite a few cloudless nights there is sufficient "murk” in the air to make stars which would normally be quite bright, appear very faint. Therefore these stars become the only ones suitable for observations on this type of night.

 

With the ZD's of the stars, remember that the higher they are in the sky, the less they will be influenced by refraction, thus the aim is to use N & S stars of almost similar ZD's and as near the highest altitude the instrument is capable of as is possible.

 

Obviously a N star with a ZD of 20° and a S star with a ZD of 60° do not make a good pair as they rely too much on something which is impossible to calculate accurately, i.e., refraction.

 

 

(iii)    As darkness closes in, the telescope and graticule focus are adjusted by sighting on a bright star and "taped" with Durex to prevent movement during the observation. The same thing applies to the micrometer telescope. The reasons for this are fully explained later in the "Method of Observation". The theodolite should now be levelled using the "Talcott" bubble and then laid out on an approximate N-S line with a prismatic compass, taking into account the Mag. Declination.

 

(c)     Preparations after dark

 

(i)      Time signal check

 

Obtain a time comparison on VNG, the Australian P.O. time signal station at Lyndhurst, Victoria. (See Annexure C of "Specifications for Ground Control Survey" for details of this and other time signals.) Check the minute and second for gross error on WWVH (or WWV).

 

If unable to receive VNG, use WWVH (or WWV) and check minute and second with the hourly ABC time signals.

 

Obtaining accurate time is entirely a matter of constant practise in achieving a rhythmic one second beat of the finger on the stopwatch button. Hold the stopwatch with the index finger lightly pressing on the stopwatch button; beat with an up and down motion of the hand until the beating of the hand and finger is in unison with the beat of the time signal. Once this synchronization has been obtained, press the button on the stopwatch. Do not "snatch" the button on this beat thus taking a decimal which can be widely in error. This tendency to "snatch" and thus press the button too early is very noticeable in the learner. A good quality stopwatch, the second divisions of which are wide enough apart to estimate the "hundredths" is necessary.

 

Step by step procedure for taking time signals.

 

1.   Switch on the radio, beat watch until in unison with the second beat on the radio.

 

2.   Switch off radio and go through the same procedure with the chronometer. As the chronometer beats half-seconds make sure that synchronization is made on a full second beat. About 10 of these comparisons must be made; the mean of all these is recorded as the decimal of the second. Record two places of decimals.

 

3.   About 5 seconds before any 5 minute time signal start to beat the  watch and on the exact five minute signal press the button to start the watch.

 

4.   Switch of the radio, beat until in synchronization with the chronometer, then stop the watch on a ten second division on the chronometer. It must be remembered that with VNG, WWVH & WWV, the 59th second of every minute is not sounded therefore care must be taken to start beating the watch at about the 54th or 55th second so that coincidence with the time signal is obtained by the 58th second and kept over the missing 59th second to ensure there is good synchronization when the button is pressed on the 60th second.

 

5.   Write down the second and decimal reading on the stopwatch and the chronometer. In the stopwatch reading replace the decimal with the decimal obtained in step 2, i.e.; if the single reading on the 5 minute is 17.8s, and the mean of the 10 readings was 0.93s the booked stopwatch reading is to be 17.93s not 17.8. Thus if the chronometer read 19h 20m 50s and stopwatch read 17.93s at 19h 20m 00s, the chronometer is fast:-

 

Chronometer reads                                       19h 20m 50s

Stopwatch reads                                                              17.93s

Chronometer time (when time signal taken)       19   20   32.07s

WST (when time signal taken)                        19    20   00

Chronometer fast                                                       32.07s

 

Always take a second time check to ensure there is no mean error of one or more seconds. If using VNG check with WWVH or WWV, or if using either of the latter stations, check with the ABC on the hour.

 

(ii)     Locating Sigma Octantis using the graph

 

Just prior to 1900hrs, set the calculated ZD of the star on the theodolite and commence searching East and West of the approximate meridian until the star is identified. The ZD is the main factor in locating the star as the Latitude is normally known fairly accurately therefore the ZD interpolated from the graph should bring the star fairly close to the horizontal cross wire.

 

(iii)    Final check of level

 

Having located the star and before laying the theodolite accurately on the meridian, it is best to finally level the instrument as it probably may have been moved off level while searching for the star. Level first with the two footscrews along the meridian, then with the single footscrew across the meridian. In future relevelling, as the level along the meridian is not so critical it need only to be done carefully at the present juncture, unless the theodolite is accidently knocked when complete relevelling would be necessary. If the star was located quickly and easily, leaving the observer confident he has not moved the level of the instrument, he may prefer to lay on the meridian, then just touch up the level before commencing the observation.

 

(iv)   Laying the theodolite on the meridian

 

Now calculate the ZD and Azimuth of Sigma Octantis for a convenient LST a few minutes ahead, and intersect the star between the double wires, at that instant. Once the star has been intersected, set the calculated Azimuth on the horizontal circle. Turn the theodolite to 00° 00' 00" (if a North star is to observed first) or 180° 00' 00" (if the first star is to be a South.) Make sure the micrometer drum has been turned to 00' 00". The theodolite is then assumed to be in the plane of the meridian and all preparations for the observations have been completed.

 

The actual observation


Notes :

 

(a)     The calculated values (360°- ZD) & ZD on the programme refer to the vertical circle setting of the Wild T2 theodolite FR & FL respectively. If another type of instrument, graduated differently, is used these values will have to be adjusted to suit.

 

(b)    As the prismatic eyepieces are only screwed in by normal thread, a drill for reversing them must be adhered to during the observation. Otherwise they may be screwed either right out (and fall on the ground), or right in (and cause the focus to be altered). Therefore prior to plunging the telescope, turn the eyepieces one half turn out when changing from FL to FR, and one half turn in when changing from FR to FL.

 

(c)     Except when actually reading the ZD of a star, the micrometer drum must always be set at, and remain at 00' 00". If this procedure is followed the possibility of error in setting on the meridian will be eliminated, as the theodolite has to be laid on the meridian a minimum of 10 times during the observation, and speed is essential, any safeguard is important. Remember, at all times, that the horizontal circle itself is the R.O. for orienting the instrument.

 

Step by step procedure

 

1.       As the theodolite is laid out on the meridian the first star of a pair is selected. If the star is to the North, the instrument will be laid out at 00° 00' 00", and if the star is to the South, it will laid out at 180° 00' 00" on FR, in both cases.

 

2.       Set the programmed 360°- ZD on the vertical circle, always estimating the minutes. A few minutes before the programmed Early Stadia time, watch for the star to appear. Check the identity by the star's magnitude and time of appearance. With the vertical tangent screw bring the star to a position where it moves across the diaphragm, just slightly above or below, the horizontal wire. See figure 3.10(a).

 

3.       At the instant the star cuts the Early Stadia wire press the stopwatch button.

 

4.       Move to the chronometer, beat the watch until in rhythm with the beat of the chronometer and stop the watch on a 10 second division of the chronometer.

 

5.       Call to the booker this chronometer time in the order, seconds, then minutes, then the hour, and lastly the stopwatch reading. The assistant should repeat these readings as he books them; also read and book the thermometer value.

 

6.       Return to the theodolite, reverse the eyepieces, plunge the telescope, change to FL and lay on the meridian at 180 00' 00" (North star) or 00° 00' 00" (South star).

 

7.       Set the programmed ZD on the vertical circle, again estimating the minutes. Identify the star, and when it is near the centre wire intersect it on the horizontal wire.

 

8.       Bring the ends of the alidade bubble into coincidence, bring the vertical circle graduations into coincidence with the micrometer drum, call out the ZD reading, the assistant repeating it back as he books it. Reset the micrometer drum to 00' 00".

 

9.       Move the star slightly off the horizontal wire and at the instant it intersects the Late Stadia, press the stopwatch button.

 

10.    Again move to the chronometer, beat the watch until in rhythm with the beat of the chronometer, then stop the watch on a 10 second division of the chronometer.

 

11.    Again call the readings to the assistant as in step 5, this time there is no need to read the thermometer.

 

The above steps complete one star; proceed similarly with the other star of the pair. Five good pairs are necessary, but if in doubt of the quality of any observations, take an extra pair or two.

 

Relevelling between pairs of stars

 

Relevel, across the meridian with the single footscrew, between each pair of North and South stars which form a complete observation. Remember that the quality of this observation depends entirely on keeping the vertical axis of the instrument truly vertical, particularly across the meridian and bearing in mind that during a period of 20 or more minutes, it is exceedingly unlikely that the instrument will remain truly level.

 

Time check in the middle of the programme.

 

Always obtain a time check somewhere near the mid-point of the observation, say, after the third pair. This is necessary to see if the observer is consistent in his time-keeping, or whether the chronometer has an uneven "rate".

 

Time check after completion of the observing program - Drawing time graph

 

The final time check should be made immediately after the last star has been observed. Plot a graph showing the times fast or slow against the chronometer times at which each time signal was taken. Draw a “line of best fit" between the three plotted points to obtain a graph from which can be read the varying amounts that the chronometer is fast or slow at the times which each star was observed. The station number and date is noted against this graph.

 

The observation with a split-hand stopwatch.

 

To avoid having to carry a chronometer this observation could be done with a good quality split-hand stopwatch and using a pocket or wristwatch for rough times.

 

This system would be ideal for any field party which is only required to observe an occasional astrofix among its normal duties. Naturally, if the party's full time task was the astrofix, a chronometer would be more satisfactory. Full details for using the split-hand watch for Azimuth observations are given in 3.8.10. When observing for Latitude and Longitude these lines would be followed except that the time check procedure must be adapted to ensure very accurate times.

 

As well as the full time checks prior to and after the observation, a time check for the second and decimal (to hundredths) would need to be taken immediately before and immediately after, each pair of stars. This is for the decimal and second only, the other checks taking care of the minute and hour. This check can be done quite quickly, however the delay may cause the observer to miss some stars he would normally use; even so the full time of the observation should not be beyond that which is acceptable.

 

Computation

 

The calculation of the Latitude and Longitude from this observation is dealt with in 12.10.

 

 

3.11       Tacheometry or Stadia Surveying

 

Stadia provides a method of measuring distances and differences of elevation by merely sighting a staff. This can be done with a level or an orthodox theodolite providing the instrument has two horizontal crosswires, called "Stadia Wires", at equal distances above and below the central horizontal crosswire. These stadia wires are so arranged that the "intercept" (the distance between the two staff readings, as read against each stadia wire and usually called "S") is 1/100th of the distance, instrument to staff, when the line of sight is horizontal and the staff is truly vertical. See figure 3.11.

 

The level is mentioned only in passing, these notes henceforth will deal with tacheometry where the line of sight may be inclined and where horizon angles or true bearings will be required.

 

When the line of sight is inclined, the intercept is multiplied by appropriate factors, depending on the angle of inclination; the results give the horizontal and vertical distances from the point on the staff cut by the central crosswire, to the axis of the theodolite.

 

It will thus be seen that the bearing, distance and level of a point can be obtained in one observation.

 

3.11.1    Theory

 

As shown in figure 3.11.1, the vertical angle, a, and stadia intercept DE (or S) have been read; required are AB (the horizontal distance) and BC the vertical distance between the axis of the theodolite and the central reading on the staff.

 

 

 

 

 

Step 1

 

The intercept on the staff DE, has to be turned into a distance GF, which is a line perpendicular to the line of sight AC. The vertical angle “a”, is equivalent to “a'”, therefore DE x cos a' = GF. In the example DE (or S) = 4.21 and “a” = 10°, therefore 4.21 x .984 =4.146.

 

Step 2

 

With stadia 1 to 100, AC = 100 x 4.146 = 414.6.

 

Step 3

 

Solving the triangle ABC for the horizontal distance AB, 414.6 x .9648 = 408.30.

 

Step 4

 

Solving the triangle ABC for the vertical distance BC, multiply AC by sine 10°, that is 414.6 x  .17365 = 71.995.

 

The above is normally shortened to:

 

AB (the horizontal component, known as H)    = 100S cos2 a, and,

 

BC (vertical component, known as V)              = 100S sin a x cos a or

= 100S  ½sin 2a.

 

Thus to obtain the H & V components of the sighting, the intercept S, must be multiplied by the factors shown above. Tables are available for these and many slide rules have special graduations so that when the intercept on one scale is placed opposite the zero angular graduation the horizontal component appears against the observed vertical angle in the portion of the scale marked "H", and the vertical component appears against the observed vertical angle in the portion of the scale marked "V".

 

3.1.2      Reduction of Stadia Observations

 

Case 1:

 

Angle of Elevation with base of staff above Bench or Station Mark. As shown in Figure 3.11.2(a) the vertical angle is an angle of Elevation, and the base of the staff is above the BM. BM value + Height of Instrument = Reduced Level, height of Instrument.

 

The vertical component (AB in diagram) is now computed and is positive.

 

Add to R.L., height of Instrument to obtain R.L. of Middle Reading on staff (A in diagram).

 

To obtain R.L. of point C (Ground level at base of staff), subtract the Middle Reading on the staff from the RL of point A.

 

Case 2:

 

Angle of elevation with base of staff below Bench Mark or Station Mark. This can occur on slightly sloping ground where it has been necessary to elevate the line of sight to clear bushes, long grass, etc. The V.C. is computed and is positive. Add this to. R.L. height of instrument to obtain RL of Middle Reading on staff (A).

 

As in Case 1, just subtract the Middle Reading on the staff from the RL of point A to get RL of point C. Note that in this case the R.L. so obtained will be seen to be lower than that of the BM even though a vertical angle of Elevation was read. See Figure 3.11.2(b).

 

Case 3:

 

Angle of Depression. The V.C. is computed and is negative. Subtract from R.L. height of Instrument to obtain R.L. of Middle Reading (A).

 

To obtain the RL of point C, subtract the Middle Reading on the staff from the RL of point A. See Figure 3.11.2(c).

 

Formula:-

 

In all cases it is R.L. Stn B = R.L. Stn A.+ Height Instrument ± VC – MR.

 

In practise it is most convenient to evaluate  ± VC – MR for each point, the result being called the "difference in elevation", then add or subtract this from the R.L.  Height of instrument.

 

Equipment

 

Special theodolites and staves are available for Tacheometry work also levels which incorporate, a horizontal circle. However mostly an orthodox theodolite and staff will be used; these notes, therefore will be confined to such equipment. If one understands the theory and practise using this equipment, it is but a small step to change to more sophisticated equipment should the occasion arise.

 

3.11.3    A Detail traverse using Tacheometric Methods – Wild T2 or similar theodolite

 

The traverse would be through a line of main stations, picking up detail by means of subsidiary points along the traverse route.

 

Angular Work

 

The instrument should be checked to see that it is in good adjustment as it is customary when laying on subsidiary points to read both horizontal and vertical angles to the nearest minute on one face only, usually face left. Unless a higher degree of accuracy is required, the main traverse angles, both horizontal and vertical will be read to the nearest 10 seconds.

 

When the arc on Face Left has been completed, change to Face Right on the RO and read the main traverse horizontal and vertical angle only on this face. This helps increase the accuracy of the main traverse angles and is a check that the circle was not disturbed during the single face readings to the subsidiary points.

 

Reading the Staff

 

The staff must be equipped with a bubble to ensure verticality, and a check made to see that the bubble is in adjustment before the traverse commences.

 

The most simple method is to lay the bottom stadia wire on an even foot graduation on the staff, with the centre wire somewhere in the vicinity of 5 to 6 feet; i.e., approximately the same height as that of the theodolite.

 

Staff readings along the main traverse line are read twice, i.e. forward and backward, the distances and heights must be calculated in the field to check for gross error. Distances should agree within 1 foot and difference heights within 0.10 ft.

 

3.11.4    Field Book

 

There are various forms of field notes, That shown in Figure 3.11 is recommended for completeness and for clarity.

 

Column 1.     The number (or name) of the station, RL station mark, height of Instrument.

Column 2.     Sketch of the traverse legs and details of subsidiary points oriented on magnetic bearing.

Column 3.     The station observed.

Column 4.     The Horizontal angle observed.

Column 5.     The Vertical angle observed; indicated positive or negative.

Column 6.     The three readings on the staff.

Column 7.     The "intercept", S.

Column 8.     The calculated horizontal distance.

Column 9.     The calculated vertical component, indicated positive or negative.

Column 10.   The difference in elevation, indicated positive or negative (obtained from the algebraic sum of Mean Reading on staff & V.C.).

Column 11.   The Reduced Level of the height of instrument; data from Col 1.

Column 12.   The Reduced Level of the distant traverse station or subsidiary point; obtained from the algebraic sum of columns 10 and 11.

Column 13.   Space for any necessary notes.

 

3.11.5    Errors caused by changing focus of the theodolite telescope

 

For internal focusing telescopes, which are the only type likely to be encountered, the factor D = 100 S, changes slightly with changing focus and varies slightly from instrument to instrument.

 

These variations are negligible except for very accurate measurements. For such determinations, it will be necessary to plot a correction curve for the instrument being used. The corrections are obtained by measuring exact stadia intercepts at various accurately measured distances; the following are recommended: 25, 50, 100, 200, 400, 800 and 1600 feet.

 

3.11.6    Accuracy

 

Horizontal Distances

 

An accuracy of about 1 in 1,000 would be about the best expected. The serious sources of error are in the measurement of the intercept and the verticality of the staff.

 

Errors arising from the measurement of the vertical angle and, the multiplying constants are negligible.

 

Heights

 

On a sight of 1,000ft, with a vertical angle of 6°, and allowing for a horizontal distance accuracy of 1 in 1,000, the error in the difference height could be about plus or minus 0.10ft; however with a sight of 500ft and a vertical angle of 1°, the error could be only about plus or minus 0.01ft. Therefore unless size of vertical angle and length of sight are taken into account, no figure for accuracy can be given. The following can be used as a guide :

 

For average length lines, (up to about 700ft) and with average vertical angles (up to about 5°) the best accuracy of difference heights between points would be about plus or minus 0.05ft.

 

3.11.7    Curvature & Refraction

 

The influence of curvature and refraction on heighting by Tacheometric means commences to show once sights reach 700 feet in length, where it is still only about +0.01ft. However, as it increases with the square of the distance, it becomes about +0.57ft at one mile (5280ft).

 

From these figures it can be seen that not a great number of sights will be affected. If the vertical angles on sights above 700ft are observed reciprocally, and the mean of such angles used curvature and refraction will be eliminated. This is the best method to adopt.

 

For further notes on curvature and refraction, including the calculations necessary to obtain the curvature and refraction for any line where angles have been observed from one end, only, see Section 12.4.

 


Figure 3.11

 

 

 

 


 

3.12       Almucantar observation for Longitude with Wild T3 Theodolite and stopwatch

 

For this observation, the instrument must be fitted with a graticule having 5 horizontal intersections on the vertical wire, each 5 minutes of arc apart (i.e. two above and two below the central horizontal cross-hair).

 

Also the alidade bubble must be graduated at approximately 2 mm intervals.

 

Graticule                    Alidade bubble graduations, Wild T3 on F.L.

Figure 3.12 (a)

 

Stopwatch

 

This must be of the split-hand type and be of good quality with a large dial, clear figures and graduated to 1/10 second; estimate to 1/100 sec.

 

Pocketwatches

 

An accurate Pocket or sweephand wrist watch is necessary. This watch must have the capability of the second hand "marking time" when the winding button is held out so that second and minute hands can be synchronised.

 

In addition another watch, or even an alarm or travelling clock is necessary as a "Prediction" watch.

 

Prediction Sheets

 

See Technical Report 4 for details of the preparation of Data Sheets for the electronic computation of Prediction Sheets for this observation with the Wild T3 theodolite.

 

The predictions are prepared for the approximate date that observations are to take place; in the Longitude programme each star is listed by Number, Magnitude, True bearing (nearest minute) and Time. The time is the standard time for the relevant time zone, i.e. in Australia EST, CST or WST as the case may be. If observations are not done on the exact date programmed, an allowance of 3.94 minutes (3 min 56 secs) per day must be made. That is, stars will be at the sane elevation 3.94 minutes earlier each day. This can be allowed for by pencilling in the correct time for the observing date or by setting a separate "prediction" watch to agree with the programme. If observations are later than the programmed date, the stars will be early therefore the watch must be set fast. See Figure 3.12 (b) for a prediction sheet, Wild T3.

 

 

Radio

 

A good quality transistor radio with a short wave band capable of receiving WWVH or VNG (Lyndhurst, Victoria) is required. It should be noted that with the recent introduction of "atomic" time there will now be a correction, varying with the date, to be applied.

 

Number of Pairs

 

As distinct from the Latitude observation there is nothing to gain by selecting pairs in advance. Any East star can be paired with any West star, providing they are observed within twenty minutes of time. The aim should be 16 pairs, 8 on each of 2 nights; the minimum is 12 pairs with not less than 6 pairs on each of 2 nights.

 

Time Signals : setting the main watch and stopwatch

 

About 30 minutes before observations are to commence, but not on an exact hour or half hour, the main watch should be set by radio time signal, about 10 seconds fast. Take care to synchronise the minute hand and second hand or in other words don't have the second hand 10 seconds fast and the minute hand in a position which indicates about 30 seconds fast (or slow).

 

On the next even hour or half hour on this watch, the starting button on the stopwatch is pressed so that the stopwatch is started in syncronisation with the main watch. Lock the starting button of the stopwatch with a clip made from a "glider" clip. This will prevent the whole observation being wasted if the wrong button is pressed during the observation.

 

Beating the watch

 

The accuracy of the Longitude observation using a stopwatch is completely bound up in the observer's ability to rhythmically beat the stopwatch in unison with the "beep" of the radio time signal obtaining such consistency that the mean of his beatings will be close to 0.05 seconds plus or minus personal error. (See personal equation).

 

Much practice is needed and care must be taken to avoid making whole second or whole minute errors while concentrating on obtaining the accurate decimal of a second.

 

Beat the finger on the stopwatch button a number of times until this slight sound is synchronised with the beat of the radio time signal. Once this is achieved press the button on one of the beats. Do not "snatch" on this beat; learners tend to do just this after having got into a good rhythm. Thus having lost this rhythm on the final beat their result could be 0.1 second or more in error. The mean of 5 series of signals is taken, see Figure 3.12 (c) for an example of the time signal page of the field book.

 

 

 

When to take time signals

 

In the longitude observation using a stopwatch, a fresh time signal is required just before every star; now and again it is permissible to omit one of these signals when stars follow in close succession, however never book more than two stars without taking time signals. If there is a long interval of about 10 or more minutes between stars, a time signal should be taken immediately after the star has been booked and a fresh time signal just prior to the next star.

 

The "rate" of the stopwatch

 

This is most likely to be even if the tension on the main spring is kept about the same; therefore make a drill of keeping the watch fully wound – wind it just before taking each time signal. At the conclusion of the observation, graph the time signals at a scale which can easily be read to 0.01 second. Join each point with a straight line. If the correct procedure has been maintained the graph will be reasonably smooth; a "jagged" graph can indicate any of the following and gives warning that some action is required :

 

                                 i.            More practice, or care in beating the stopwatch.

                                ii.            Watch not being kept fully wound, thus tension on the main spring is inconsistent and "rate" suffers.

                              iii.            Watch in poor condition, needs overhaul.

 

The graph will also show at a glance if too few time signals have been taken, or if they have been inconsistently taken, i.e., a few at close intervals but long gaps between others. Too few time signals combined with a jagged graph would mean the observation must be considered unreliable. See Figure 3.12 (d) for a time signal graph.

 

It is a good plan, for safety, to have the stopwatch on a loop of string around the neck. Do not let it swing free when not in use but keep in a coat or shirt pocket. Although a stopwatch is robust it must be treated as a delicate instrument where an even "rate" suitable for accurate Longitude observations is required.

 

Theodolite setup

 

An observing screen should be used. The tripod should be set on three firmly driven pegs, wooden for preference. Pegs to be driven on an angle in conformity with the slope of the tripod leg.

 

The tripod should be set so that the theodolite will have two footscrews along the line of the meridian; this can be done accurately enough with a prismatic compass. An essential of this observation is that the alidade bubble must be altered slightly after each timing of the star, by moving the ex-meridian footscrew.

 

Level the instrument carefully, firstly with the plate bubble then finally with the alidade bubble. The instrument will be used on Face Left to agree with the prediction programme. Set the horizontal circle on the meridian by laying on Sigma Octantis at its calculated true bearing or by turning a true bearing from a distant survey control point, if available.

 

The Almucantar prediction will be for either 30° or 35° altitude, with 30° being best for the T3. This altitude plus refraction must be set on the vertical circle. With the older model Wild T3 theodolites which have vertical circles that read half the angle, the setting will approximately be 105° 00' 25" or 107° 30' 20" depending whether 30° or 35° predictions are to be used. Clamp the vertical circle firmly, throughout the observations.

 

The following three points should be kept in mind during this observation.

 

(i)      The essence of the observation is timing a star across a series of 5 hairs, and each time reading the alidade bubble.

 

(ii)     Not one angle is read while laid on each star.

 

(iii)    The only control screws moved are the ex-meridian footscrew to vary the bubble and the horizontal slow motion screw to keep the star close to the vertical wire as it cuts the five horizontal wires.

 

The observation

 

Look for a trial star of a fair magnitude to test the predictions, the time set on the prediction watch, the azimuth and altitude setting.

 

The eyepiece prisms will be required on the theodolite. Stars come into view about two minutes before the predicted time assuming the correct data has been supplied for the electronic computing of the programme. If the star is not sighted fairly close to the predicted time make the following checks in the order listed :

 

(i)      Check that the prediction watch has been set correctly, i.e., 3.94 minutes (3m 56s) per day adjustment may have been applied the wrong way or not applied at all.

 

(ii)     Check that the theodolite has been laid accurately in azimuth.

 

(iii)    Check that the theodolite has been laid on the same Altitude as shown on top of the Almucantar prediction sheet.

 

If all the above are correct it would appear that an error has been made in the data supplied for the prediction. If this is a gross error it may possibly be rectified if an FK4 star catalogue is available, i.e. locate a well known star which is predicted, observe to the nearest minute its azimuth at the moment it cuts the almucantar circle and record the time to the nearest minute. There is every possibility that if the predicted stars are all corrected by the same difference in bearing and time as indicated by the observation on the known star, the prediction sheet will then be accurate and the observation can go ahead.

 

If this does not solve the problem it will be necessary to request new prediction sheets.

 

Assuming that the trial star appeared as predicted, get ready to proceed with the observation :

 

1)       Check and adjust level if necessary.

 

2)       Check that the vertical circle has been set correctly, get booker to record setting on top of field book page.

 

3)       Decide on first star, lay on predicted bearing.

 

4)       Take time signal, record results.

 

5)       Watch for star to come into view; verify its identity by estimating the magnitude, set alidade bubble with the ex-meridian footscrew so that the ends are just a little apart (say between 0.1 & 0.4 of a graduation).

 

6)       With the horizontal slow motion screw the star is positioned so that it will cut the first horizontal wire close to the vertical wire, call to the booker "Star coming in", so that he can concentrate on reading the main watch to the nearest second.

 

In Australian latitudes the interval between the hairs is about 22 seconds of time; during this interval the observer has to complete the following 4 steps :

 

1.       Call "Up", simultaneously pressing the stop watch button.

 

2.       Read the stopwatch, and when the booker has called back the reading, re-start the second hand.

 

3.       Read the alidade, alter it by touching the ex-meridian footscrew, balancing the error in so doing.

 

4.       Adjust the horizontal slow motion screw to bring the star close to the vertical wire ready for timing it across the next hair.

 

Proceed with the second, third, fourth and fifth hairs in the same manner. Swing to the azimuth of the next star, making sure that the horizontal slow motion screw is about central in its run.

 

Take a time signal, return to the theodolite and observe again as outlined for the previous star.

 

Two points which need further emphasis are :

 

1.       Alidade bubble readings.

 

The bubble is graduated as shown in Figure 3.12 (a) each division is about 5" to 6" of arc. No attempt is made to bring the ends into exact co-incidence, the readings are estimated to the nearest tenth of a division, and if the reading on the first hair is +0.3, the bubble is altered with the ex-meridian footscrew to read -0.3 for the second hair and so on. If the plus and minus readings over the five hairs are deliberately set so as to almost balance out, any error in the calibrating of the bubble automatically cancels out.

 

In becoming familiar with his instrument the observer should do two things, i.e. :

 

1)       Move the bubble with the alidade screw and assure himself that the vertical angle is indeed plus or minus of the actual reading when in the positions shown in Figure 3.12 (a).

 

2)       Calibrate the alidade bubble to ascertain the value of the graduations; proceed as follows :

 

(i)                  On Face Left lay on some target that can be finely bisected. This is only necessary to prove that the vertical axis is not moved during the course of the calibration.

 

(ii)                 To calibrate, move the bubble with the alidade adjusting screw to one end of its run; let it settle.

 

(iii)                Check that the telescope has not been moved off target, read vertical circle and bubble.

 

(iv)               Move bubble about one sixth of its run, let it settle and again take vertical circle and bubble readings.

 

(v)                 Repeat until bubble is at the other end of its run. Readings can more advantageously be made more frequently towards the ends of the bubble’s run and less frequently in the middle.

 

(vi)               Check again that the telescope is still on target, and take another series of readings back up the bubble’s run, to the starting point.

 

(vii)              Make a final check that the telescope is still on target.

 

(viii)             Calculation of the value of a division is best done graphically. Firstly convert the T3 readings to seconds of arc remembering that the older model reads only half the angle on the vertical circle and that both models also have the micrometer drum graduated at 60" for a two minute run. Plot a graph of seconds of altitude against bubble divisions. Draw a straight line through the points using a transparent ruler to judge the mean position. Avoid simply joining the two end points, which in effect discards all the other readings. Determine the slope of the line in seconds per division. With some instruments it may be found that separate parallel lines are obtained on the graph, one when the altitude is increasing and the other when it is decreasing - this is due to backlash. When this defect is found, the cure is always to make the last adjustment to the alidade bubble in a clockwise direction, regardless of whether one needs to move the bubble up or down. Few observers do this, and with a new instrument it is not essential, however it is clearly a good habit to get into.

 

2.       Missed Stopwatch readings on any hair

 

One missed hair does not invalidate that star. If a hair is missed :

 

(i)      In finalizing the field book, the observations for the symmetrical hair must be cancelled. If the first or last hair is missed, use the centre three, if the second or fourth, use hairs one, three and five, if the centre is missed use the other four.

 

(ii)     Observations for the same hairs must be struck out for the other star in the pair.

 

(iii)    Count a pair of stars with missing hairs as half a pair only: if the programme requires eight pairs, they could consist of seven perfect pairs, plus two pairs with missing hairs.

 

Check the Vertical Setting

 

After every four pairs, and at the end of the observations, check the vertical circle setting and record it on the top of the page of the field book, thus :

 

"Vertical circle checked and found to read………………..”

 

If the setting has changed more than 2", record this and reset the circle to the original value before continuing with the observation. If the error is found while a pair is incomplete, complete that pair before re-setting the circle. Remember that if during the observation of a pair, the vertical circle slow motion screw or the alidade adjusting screw are moved the observation on that pair is ruined.

 

Booking

 

As in most astronomical observations, apart from "position lines", the observer relies heavily on his booker. The booker should have a table and chair if possible. If this cannot be managed he must have a large booking board and a rolled up swag to sit on, also a good light which can be shielded so as not to hinder the observer. Paper clips or rubber bands to prevent the field book pages and prediction sheets from becoming unmanageable, are a necessity.

 

If the booker is experienced, in many ways he will run the observation by selecting the stars, advising the observer when and on which bearing to look for the next star, also advising the time available in which to take a time signal.

 

The observer will advise "Star sighted" and give estimated magnitude. The, booker will check this with the magnitude of the predicted star and call "Seems OK" or "Large difference in magnitude" as the case may be. Observations on many wrong stars have been prevented by this simple check.

 

If the magnitude indicated that the correct star was in view the booker carries out the following sequence as the observation on that star progresses :

 

(i)      Writes the page, star number and aspect in the field book.

 

(ii)     Concentrates on the main watch and records in the appropriate "box" the time to the nearest second at the observers call of "Up".

 

(iii)    Enters stopwatch time and bubble reading in the appropriate "box" beneath the main watch time calls these back to the observer.

 

The above sequence is completed for each of the five hairs; if a hair is missed write that word in the appropriate "box".

 

On completion of that star the booker calls the next bearing and time available, and so on through the observation, also advises the observer to check the vertical circle after each 4 pairs have been completed. During this observation the booker has no reductions to do; however he should keep alert for gross errors in the stopwatch readings, and mean the 5 bubble readings to ensure they are indeed being "balanced" as mentioned previously and should advise the observer if care is not being taken along these lines.

 

"Pairs" are numbered as they are completed, not in advance, too often some type of delay prevents a planned observation taking place. With a very experienced booker the best plan is to have all the East stars on the Left hand page and the corresponding West stars on the Right hand page, thus the pairs are on the same line across the double page. However it has been found that a less experienced booker soon enters an East star among the West or vice versa. For this reason it is probably better to enter all stars in chronological order down the page. Always save the prediction sheets and return them with their respective field books. See Figure 3.12 (e), for a field book page.

 

Observers Personal Equation

 

This is determined by observing stopwatch longitudes at a station whose longitude has already been determined impersonally. The minimum of observations to give a single reliable calibration would be eight pairs on each of three, or preferably four nights.

 

As time is not always available for such a programme a good practical solution is to make the normal observation of eight pairs on two nights at the calibration station before the first and after the last of a group of up to 5 new stopwatch longitude stations.

 

Compilation of Longitude data sheets

 

The preparation of these for the T3 observation is described in Technical Report No.4. Also there are now available, from the Division's Canberra Office, field books in the form of data sheets for many types of field observation. They incorporate carbon-impregnated paper for the original page, thus the data sheet is available without rewriting and a duplicate copy is left in the field book as a record of the original observations.

 

 

 

 

3.13       Latitude observations with the Wild T3 Theodolite – Meridian or Circum-Meridian Altitudes

 

General

 

This is the companion observation to the Almucantar Longitude observation. Data sheets for predictions are prepared at the same time as those for Longitude - See Technical Report No. 4 for notes appertaining to the Wild T3.

 

With that instrument stars within the altitude band 30° to 60° are suitable, and all readings are taken on Face Left.

      

Much of the data in the notes on the Almucantar observation of Longitude, with the Wild T3 and stopwatchl apply to this observation and will not be repeated, but the main differences in emphasis will be pointed out. These are :

 

(a)     In the Longitude observation, very accurate time and alidade bubble readings are the main factors and no angles are read. In the Latitude observation, almost the reverse applies, very accurate vertical angles combined with alidade bubble readings are the basis of the observation. Time signals are taken in the same manner as described for the Longitude observation but only at the commencement, mid-way and the conclusion of the observation. If cloud causes long delays time signals should then be taken each half hour during this delay. Time signals are graphed at the conclusion of the observation.

 

(b)    Alidade bubble movements in the Longitude observation are made with the ex-meridian footscrew. In the Latitude Observation normal usage of the instrument applies therefore the alidade bubble is moved with the alidade adjusting screw.

 

Selecting "Pairs"

 

In contrast to the Longitude observation it is advisable to select pairs in advance of the observation. They are paired North and South within 4° of altitude and 20 minutes of time, trying to find a partner among the many North stars for each of the rarer South stars.

 

Observations on a single night are acceptable but 8 pairs on each of two nights should be the aim, 12 pairs being the minimum.

 

Number of Shots per Star

 

With the wild T3 which has a maximum altitude of about 60°, six shots are required. The maximum time allowed in which to complete these is six minutes, i.e. three minutes each side of upper transit. Note that it is better to obtain a few shots to many stars, than many shots to few stars.

 

The observation

 

The setup, laying out of the theodolite on the meridian, time signals etc are as for the Longitude observation except for the slight differences mentioned previously.

 

If the setting of the horizontal circle and the prediction watch have not already been tested on the Longitude programme, follow the same procedure by checking the transit time and altitude of the first reasonably bright star.

 

Assuming all is correct proceed as follows :

 

(i)      Set the predicted reading on the vertical circle and swing on to the meridian, North or South as the case may be.

 

(ii)     Find the star, call "Star seen" and verify the magnitude with the booker.

 

(iii)    Estimate how long it will take to get 3 shots before upper transit, move the theodolite horizontally so that the first cut can be taken on the horizontal wire but close to the vertical wire. Set alidade bubble with the alidade bubble adjusting screw just slightly off level, and call "star coming in" to warn booker.

 

(iv)   Call "Up", simultaneously pressing the stopwatch button.

 

(v)     Read stopwatch, bubble and vertical circle. The booker will read these back as they are given. Re-start stopwatch second hand once this has been read back.

 

(vi)   Move alidade bubble fractionally with alidade adjusting screw.

 

(vii)  Again move theodolite horizontally so that the second shot will also be taken close to the vertical wire. Repeat the above sequence until the six shots are taken, a shot every 30 seconds being the aim.

 

As in the Longitude observation the plus and minus bubble readings should purposely be made to balance out; they should range somewhere between +0.5 and -0.5 over the 6 shots on each star. This system helps to nullify any error in the graduation of the bubble, and also a "sticking" bubble, by keeping the mean altitude almost independent of bubble readings.

 

The degrees and minutes of altitude need only be read on the first and last shots. After the last shot immediately re-set the horizontal and vertical slow motion screws to the centre of their runs, then set the instrument on the meridian and at the predicted altitude of the next star.

 

Booking

 

Most of the general notes regarding booking of the Longitude observation will again apply and the same field book is used.

 

It is best to book the North stars on the Left hand page and the South stars on the Righthand page, however once again if an inexperienced booker is likely to get them mixed it is better to book them in chronological order down the page. The sequence of operations for the booker is :

 

(i)      Advise the observer the time available, the altitude and aspect of the star.

 

(ii)     Observer will give estimated magnitude; booker will check this with the actual magnitude listed and advise observer if there appears doubt.

 

(iii)    On the observers call "Star coming in", concentrate on the main watch and record time to the nearest second on the call, "Up".

 

(iv)   Read back in turn, stopwatch, bubble and vertical circle readings.

 

Proceed with steps (iii) and (iv) again until the six shots on that star are completed; enter page, star number, pair number and aspect in the field book. See Figure 3.13 (a) for an example of a field book page.

 

During gaps in the programme the booker should advise the observer when to look for the next star, when to take time signals etc. He is also responsible for recording temperatures and pressures for Refraction. The thermometer must be hung where it indicates the true external air temperature, the thermometer being read to the nearest degree Celsius and once per pair of stars, unless it is falling rapidly when it should be read once per star.

 

The pressure should be taken every half hour. If a battery of altimeters is used, readings will later have to be converted to millibars.

 

Compilation of Latitude data sheets

 

See notes in Longitude observation.

 

 

 

 

 

 

4          Tellurometer MRA-2

 

4.0.1      Setting up

 

Set the tripod firmly in the ground using foot pressure on the metal shoes. Level the tripod head by adjusting the tripod legs. In very windy conditions it is wise to take precautions to prevent the instrument from being blown over. The tripod should be securely anchored to the ground by retaining stays tied to the top of the tripod legs. Alternatively rocks can be stacked around the tripod shoes.

 

Procedure :

 

(a)     Remove from the haversack and place the instrument on the tripod head. Steady it with one hand and secure it loosely with the tripod securing screw. Move the instrument on the ball joint on the head until the point of the plumbob is exactly over the station mark. Tighten the screw until the instrument can just be rotated on the tripod.

 

(b)    Remove the operating-panel cover by unscrewing the wing-headed screw. Also remove the cover of the antenna boss on the side of the instrument by operating the lever and pulling of the cover off.

 

(c)     In order to remove the reflecting dish and the dipole which are securely held inside the operating panel-cover turn the knurled head of the retaining device anticlockwise until the spring-loaded and plunger arm coincides with the long slot. Turn the knurled head up to the limit of the slot then anticlockwise as far as it will go. Disengage the dipole from its spring clip and withdraw the reflecting dish. Protect the dipole while the reflecting dish is being fixed into its position.

 

(d)    Secure the reflecting dish into its operating position on the instrument by inserting the pegs (on rear of the reflector) into the holes provided in the antenna hub releasing the spring-loaded locking lever.

 

(e)     Plug the dipole securely into the sockets.

 

(f)      Using the cable provider connect the instrument to the battery watch carefully that the polarity is correct. The cycle lamp should light up immediately.

 

(g)    Allow 10 minutes for the oven to warm up. The oven should cycle four times before measurements are commenced.

 

(h)    The instrument is now ready to use.

 

4.1         Description of Tellurometer MRA-2

 

4.1.1      General

 

The following is a description of the various assemblies, and controls, switches, meters etc on the operating panel. It also furnishes the operator with sufficient information for the proper operation of the instrument.

 

The major component assemblies of the instrument are :

 

(a)     the antenna assembly comprising the reflecting dish and dipole.

 

(b)    the instrument case and covers.

 

(c)     the operating panel.

 

(d)    the transistorised power supply.

 

4.1.3      Controls, switches, meters

 

Brilliance

 

This control is used to adjust the brilliance of the trace on the cathode ray tube (CRT). The FOCUS control should be used in conjunction with the brilliance control.

 

Focus

 

This control is used to adjust the sharpness of the trace on the CRT.

 

X Shift

 

This control moves the spot in a horizontal direction across the face of the CRT.  It should be adjusted until the spot is a centred within the graticule.

 

Y Shift

 

This control moves the spot in a vertical direction across the face of the CRT. It should be adjusted until the spot is centred within the graticule.

 

Shape

 

This control is used when the instrument is operating as a MASTER; it adjusts the shape of the display on the face of the CRT. The control should be adjusted until the major axis of the ellipse corresponds with the X axis.

 

Y Amplitude

 

This control is used when instrument is operated as a MASTER, in order to adjust the amplitude of the ellipse in the vertical direction until it becomes a circle. After the axes of the ellipse have been bought into coincidence with the X and Y axes of the CRT and the Circle Amplitude control has been used to just the major diameter of the ellipse to be equal to the diameter of the graticule circle, the Y Amplitude control is used to adjust the miner diameter to be the same as the diameter of the graticule circle.

 

Circle Amplitude

 

This control is used when instrument is operated as a MASTER, to adjust the circular presentation on the CRT by increasing or decreasing its diameter, until a satisfactory circular trace is obtained.

 

Check pulse

 

This switch is used in the Master position to convert the circular presentation on the CRT to a display on the master from the remote station thus the master operator can ensure sufficient pulse is being received from the remote station and if not instruct the remote operator to increase the pulse amplitude.

 

Graticule lamp

 

This is used to set the level of illumination necessary on the graticule.

 

Cavity Tune

 

This is situated at the top left of the panel and comprises a knob with an integral turns counting dial.

 

The control is used to adjust the resonance frequency of the cavity by altering the position of double plunger inside the cavity. As the knob is turned clockwise the plunger is moved further into the cavity thus increasing the resonance frequency. When the tuning adjustment is made it is usually necessary to retune the klystron reflector using the reflector tuning control. Tuning of klystron cavity should be undertaken only when the instrument is in the SPEAK position otherwise it is possible to tune into a side band. There are many cavities spaced about 10mc/s apart. The cavity should always be tuned for maximum AVC reading. The Master instrument should always tune to the Remote and should always be 33mc/s lower in frequency. The knob is graduated from 0 to 10 and has a fine scale on which 100 divisions corresponding to one division on the coarse scale.

 

Speak/Measure switch

 

This key switch is used to select the “Speak” or “Measure” functions of the instrument. It is also used as a means of signalling when the Master operated wishes the Remote operator to change patterns. When this switch is momentarily flicked from “Measure” to “Speak” the 1kc/s monitoring signals in the remote earphones and on the remote cathode ray disappear, and this is customarily used as an indication to the Remote operator to change to the next pattern.

 

The Pattern Selector switch

 

This is located below the Speak/Measure switch. It is used to select first the function MASTER or REMOTE, then the pattern (A, B, C or D), and at the Remote station that type of 1kc/s signal (Forward or Reverse) on the A+ and A- patterns. It has twelve positions as follows :

      

Master          Remote

A                  A+R, A-R, A-F or A+F

B                  B

C                  C

D                  D

 

If the selector switches are not synchronised the monitoring signal in earphones and a presentation on the screens of both the Master and Remote stations will disappear.

 

Pulse amplitude

 

This is used when instrument is operated as a REMOTE. Adjusting as required by the Master operator in order to increase or decrease the pulse level until the optimum size of the break is obtained on the circular trace.

 

Reflector tune

 

This is situated at the bottom left of the panel and is adjusted for peak crystal current which is in effect a measure of the output power from the klystron.

 

Input supply socket

 

This is located at the bottom centre of the panel and it should be connected with the cable supplied to the battery.

 

Power switches

 

The LT (low tension) On/Off switch is used for switching power to the tube heaters, the klystron heater, and the transistorised power supply. The HT (high tension) On/Off switch, which must be operated not less than half a minute after the LT switch, is used to switching to be +250V and -230V outputs from the power supply.

 

Fuses

 

Two fuses are incorporated in the units :

 

The LT fuse is rated at 10A;

the HT fuse is in the HT line and is rated at 100mA.

 

Crystal current meter

 

This is situated to the left of the LT fuse and indicates the current flowing through the crystal mixer in the dipole assembly. The current is adjusted by the Reflector Tune control.

 

Switched meter

 

This is situated to the right of the HT fuse, and used in conjunction with the METER selector switch, to monitor the instrument. When the switch is set to REG the meter indications should be between 20 and 80μA. A reading below 20μA indicates a flat battery or faulty power supply. When the switch is in the MOD position the meter should indicate 40μA for the A, B and C patterns and 36μA for the D pattern. When the switch is in the AVC position the meter reading for the short range operations should be about 60μA and for long-range operations about 20μA.

 

Meter selection switch

 

This is situated below the HT fuse and is used in conjunction with the Switched Meter above. It has three working positions :

 

REG : where current through the regulator tubes is measured;

 

MOD : where the level of the output from the oscillator i.e. the level of modulation is measured;

 

AVC : where the strength of receiving signals are indicated on the meter.

 

Panel lamp control

 

This is situated on the left of the Cavity Tune and it sets the level of the internal illumination of the panel.

 

Oven cycle lamp

 

This is situated top centre of the panel. It indicates whether power is being supplied to the crystal oven and lights up when instrument is connected to a battery.

 

Headset socket

 

This socket marked PHONE is situated the bottom right of the panel. The headset is plugged into the socket for speech communication.

 

4.1.4      Pre-operational checking

 

(a)     Switch on the LT switch. After 30 seconds switch on the HT switch.

 

(b)    Set the Meter Selector switch to read REG. A reading of at least 20μA on the Switched Meter indicates a flat battery or faulty power supply.

 

(c)     Set the Speak/Measure switch to Measure and the Meter Selector switch to MOD. Switch the Pattern Selector in turn to A, B, C and D, Master and Remote. In positions A, B and C the reading on the Switched Meter should be 40μA; in position D it should be 36μA.

 

(d)    Rotate the Reflector Tune control for maximum reading on the Crystal Current Meter. A reading of reasonable amplitude signifies that the Klystron is oscillating and the crystal mixer is functioning.

 

(e)     Set the Speak/Measure switch to Speak and check the thermal noise in earphones.

 

(f)      Observe whether there is a spot on the cathode ray tube and check the operation of the X Shift, Y Shift, Focus and Brilliance controls.

 

(g)    Check whether the graticule lamp control varies the level of illumination on the graticule and also whether the panel-lighting control operates satisfactorily.

 

4.2         Operation under usual conditions

 

The following general pattern should be followed for all measurements :

 

(a)     Setup the instruments at 2 stations and tune them in.

 

(b)    With the Remote unit, on its initial CAVITY TUNE setting (say ONE) and the Master tuned below it take a complete set of "coarse” readings (A+, A-, B, C, and D). Repeat on cavities THREE and TEN.

 

(c)     Take initial readings of atmospheric pressure and wet and dry bulb temperatures

 

(d)    On CAVITY TUNE setting TEN, take a set of “fine" readings (A+F, A-F, A-R, A+R). Repeat in half cavity settings down to cavity THREE.

 

(e)     Take a final set of atmospherics. This is also the first set for Remote.

 

(f)      The Remote now becomes the Master, "fine" readings are repeated exactly as in (d).

 

(g)    The final set of atmospherics is taken, followed by three sets of "coarse" readings to complete the measurement. The atmospheric readings are exchanged by the two operators.

 

4.2.2      Sequential method of measuring with the MRA-2 Tellurometer

 

 

Master

Remote

(a)

Rotate the Cavity Tune knob for about half a rotation on each side of the previously decided starting point. If the Remote is not yet switched on to SPEAK only a small deflection of the needle will be seen. In this case, keep on turning the control through the above tuning range until the meter deflection becomes large; then carefully tune for maximum deflection, adjusting the CAVITY TUNE and REFLECTOR TUNE controls.

 

Set the CAVITY TUNE knob to the previously decided starting point (say 5.0). A large increase in the reading on the SWITCHED METER indicates that the Master instrument is in contact with the Remote.

 

(b)

Adjust the direction of the instrument for maximum AVC reading.

Adjust the direction of the instrument for maximum AVC reading. Listen for any instructions from the Master.

 

(c)

Record the REG reading.

 

Record the REG reading.

 

(d)

Instruct the Remote operator to switch to MEASURE. Switch to MEASURE and MASTER A positions. Using the CIRCLE AMP control, set the circle to a reasonable diameter.

 

When instructed, switch to MEASURE and Remote A+F positions.

 

(e)

Adjust the brightness, focusing, position and shape of the circle. Re-adjust the diameter of the circle. Make a final adjustment of the REFLECTOR TUNE for a suit­able break in the circle. (Failure to obtain any break or a break of suitable width must be treated as an instr­umental fault.)

 

Check the presentation, adjust­ment. (BRILLIANCE, FOCUS, X SHIFT, and Y SHIFT.

 

(f)

Switch to SPEAK and instruct the Remote operator that "coarse" readings will now be taken. Set the Speak/Measure switch to MEASURE. Read the angular position (between 0 and 100) of the leading edge of the break in the circular trace. (If the circle is traversed in a clockwise direction the first edge of the break that is encountered is the leading edge). Record this reading and the A+ reading. Momentarily flick the Speak/Measure switch to indicate to the Remote that he must change patterns. Take another reading of the position of the leading edge of the break. Record this as the A- reading.

 

When instructed that "coarse" readings are to be taken switch to MEASURE and either listen to the tone signal, in the earphones or watch the pulse display on the cathode ray tube. When they disappear momentarily switch to the A-F position.

 

(g)

Switch the pattern selector to MASTER B. When the circular trace reappears, take a reading and record it as the B reading.

 

When the display and tone disappear, switch the pattern selector to REMOTE B.

 

(h)

Repeat (g) for the       MASTER C and D positions.

 

Repeat (g) for the REMOTE C and D positions.

 

(i)

Switch to CAVITY TUNE 3. Tune to the Remote as motioned in (a). Take a set of coarse readings as described in (f) to (h).

 

Switch to CAVITY TUNE 3. When contact is made with the Master, switch to MEASURE and proceed with coarse readings as described in (f) to (h).

 

(j)

Switch to CAVITY TUNE 10. Tune to the Remote as motioned in (a). Take a set of coarse readings as described in (f) to (h).

 

Switch to CAVITY TUNE 10. When contact is made with the Master, switch to MEASURE and proceed with coarse readings as described in (f) to (h).

 

(k)

Switch to SPEAK and instruct the Remote operator to take a set of atmospheric readings. Calculate the vapour pressure, and compare with the Remote to see they come within the allowable limits.

 

When instructed take a set of atmospheric readings. Calculate the vapour pressure, and compare with the Remote to see they come within the allowable limits.

 

(l)

Inform the Remote operator that

Fine readings will now be taken.
Allow the Remote operator sufficient time to return to his instrument; then with the REFLECTOR TUNE control adjust for maximum AVC reading. Switch to MEASURE. Take a reading on the CRT graticule and record it as the A+F reading. Flick the Speak/Measure switch and record the next reading as the A-F. Repeat for A-R and A+R.

 

When instructed by the Master operator that Fine readings will now be taken adjust the REFLECTOR TUNE control for peak crystal current. When instructed switch to MEASURE. When the tone or the display disappear momentarily switch to the A-F position. Repeat for A-R and A+R. Note this order must be adhered to unless changed prior to measuring by the Master operator.

 

(m)

Switch to SPEAK get Remote AVC reading. Instruct Remote operator to change frequency.

Retune the instrument to its new setting below that of the Remote.

Take a further set of 4 "fine" readings.

 

Switch to SPEAK report Remote AVC reading, change to the frequency instructed by the Master operator, switch to A+F and repeat step (l).

(n)

Repeat step (m) through the tuning range.

 

Repeat step (m) through the tuning range.

 

(o)

Take a set of atmospheric readings, compare vapour pressure as before.

 

Take a set of atmospheric readings, compare vapour pressure as before.

 

(p)

This completes one half of the measurement. The Remote operator now becomes the Master operator and the measurement proceeds.

 

The Remote operator now changes to Master operator, and the measurement proceeds.

 

 

      

The sequence for this second half of the measurement is in reverse of the first half, the order being :

 

(i)      Fine readings.

(ii)     Atmospherics.

(iii)    Coarse readings.

 

Atmospherics are now exchanged, also any data about eccentric or station marks. The instrument can now be packed away. First switch off the HT, then the LT, disconnect the battery, headset, dipole and reflecting dish.

 

4.2.3      Operation over land

 

Although in principle, any line over which it is possible to transmit and receive signals, can be measured by the Tellurometer system, circumstances may be such that a choice of sites for the instrument can be made. This applies particularly to surveying in country where beacons either do not exist, or need not be used. As operation of the instrument at sites with suitable properties may improve the accuracy ­and ease of measurement, some attention should be paid to site selection.

 

Two factors influence the choice of a line for good working reception of signals and ground reflection.

 

In the first place, the line should be free from obstruction, and the plane of the radio beam (22° wide), should not be obstructed for the first 30 metres. This latter point can be ensured by raising the instrument about 2 metres, if the ground is level; or by selecting a site where the ground falls gradually away from the station for at least 30 metres. The terrain should be free from obstructions such as trees or buildings in a cone of about 10° on each side of the line. If it is impossible to select a site with this last requirement it is essential that the trees do not move during the measuring period. In other words wait for still weather conditions.

 

In the second place a line should be selected so that the ground reflection effects are negligible. Since this is not usually possible, the next best course is to select sites that result in at least one full cycle of swing.

 

If the ground is well wooded or otherwise broken up, the indirect ray can be scattered, and not reflected. Even in this event the power of the indirect ray which reaches the receiver may not be negligibly small. To prevent the resulting errors it is best to adopt the second procedure above, i.e., to select a line that has good ground reflection properties and results in at least one cycle of swing.

 

Such a line has a ground clearance of about 70 metres over a distance of 32km, 45 metres over a distance of 16km, and so on. Since more than one cycle of swing is desirable, sites with clearances at the middle point of over 70 metres for 32km lines, over 45m for 16km lines and over 30m for 8km lines and so on, should be selected.

 

4.2.4      Operation over water

 

Certain conditions of a water surface, such as a very choppy sea, can cause scattering of the indirect ray, in a similar manner to rough ground; but, in general, the conditions are similar to those of flat, bare ground.

 

An additional effect from an over water path, is a regular or irregular change in the length of the indirect ray due to a vertical rise and fall of the surface caused by "swell". This rise and fall results in a changing of the relative phase of the direct and indirect rays, in the same way as a change of carrier frequency does. Thus, if the carrier frequency were kept constant, the readings would nevertheless swing about a mean value; in principle, it would be sufficient to average this swing, instead of obtaining a swing by frequency diversity. In practise, however, an operator cannot be certain that a full swing has been developed, and the method of frequency variation must be carried out.

 

Since "swell" can introduce errors even though frequency is employed, sites should be selected where possible so that the ground obscures the water surface from the instrument thus there will be no reflection from the water. Sometimes this can be made possible by lowering the instrument.

 

4.2.5      Atmospheric effects

      

The final limiting factor in obtaining maximum accuracy, at medium and long ranges, is the effect of atmospheric conditions. The procedure set out for taking atmospheric readings, can be regarded as being adequate under most conditions. This procedure assumes that the atmospheric conditions along the line are constant or vary uniformly. If either condition does not exist, an error in measurement can result.

 

Since there is no way of determining the atmospheric conditions along the line, the best procedure is to carry out measurements during periods of certain weather conditions.

 

Fine, dry, sunny weather, which induces vertical air currents are ideal. A fair breeze, blowing along the line, is to be preferred to any other type of wind. Night measurements tend to be less accurate than day measurements.

 

In damp climates measurements on cooler days will be more accurate than those on warmer days when the vapour pressure may be higher. In coastal areas anomalies may be experienced due to variations in vapour pressure along the line; however, in general the vapour pressure is constant over large areas and changes only slowly with time.

 

4.3         Field computation of Tellurometer measurements

 

For the reduction of vapour pressure, dry and wet bulb temperatures are required, also the barometric pressure. Tables have been made up so that these can be calculated using Centigrade readings for temperature, and millibar readings for pressure. See (h) below. NOTE : The tables in these notes have been constructed with Excel and final values differ from the original tables above 30 degrees by up to 0.04 due to evaluation of power term.

 

Taking the readings :

 

(a)     The dry and wet bulb reading of the psychrometer should be taken with the instrument in the shade and at the height of the instrument. The psychrometer should be held well away from the observer’s body and in a position where the air-vent is pointing into the wind. The observer should watch the mercury throughout the observation. The mercury sometimes tends to oscillate, but readings should not be made until the thermometers have reached their minimum values. It will take 3 or more minutes for this to happen.

 

(b)    The thermometers are calibrated and the chart showing the index corrections for the temperature ranges should be kept in the box containing the psychrometer.

 

(c)     The time of observation is recorded to the nearest minute and the Master operator enters his wet and dry bulb readings, in their appropriate column in the field book. The index corrections are then applied, and the final values entered.

 

(d)    The results are checked with the Remote operator to see that the vapour pressure, at each end of the line, agrees within the required limits before "fine" readings are proceeded with.

 

(e)     The wick on the wet bulb should be kept clean, and replaced when dirty. Only clean water should be used. Be sure no water gets on the dry bulb.

In the Bendix model, care should be taken to ensure that the batteries are in good condition.

 

(f)      The barometer should be read immediately after the dry and wet bulb temperatures have been read. The readings should be recorded in the appropriate places in the field book, index corrections applied, and the final adopted values shown.

 

(g)    Barometer comparisons should be carried out at regular intervals throughout the course of the survey. The mechanism barometers are compared against a standard mercury barometer at a Department of Civil Aviation Meteorological Office or other Meteorological Station.

 

(h)    Figures 4.3.1(a) & (b) show Tables "A" & "B". These are' necessary to calculate the Vapour Pressure from the atmospheric readings. A set of these tables must be carries with each instrument to enable the calculated vapour pressure at each end of the line to be compared before and after each measurement. This is to ensure that they agree within the limits specified for the particular task in hand. Figure 4.3.2 shows these calculations on the appropriate field book page.

 

 

TABLE A

 

Δe = 0.00066*(1+(0.00115*t'))p

 

 

 

 

 

 

WET

 

 

 

 

 

 

 

 

 

 

 

 

BULB

Millibars

Celcius

820

830

840

850

860

870

880

890

900

910

920

930

0

0.541

0.548

0.554

0.561

0.568

0.574

0.581

0.587

0.594

0.601

0.607

0.614

5

0.544

0.551

0.558

0.564

0.571

0.578

0.584

0.591

0.597

0.604

0.611

0.617

10

0.547

0.554

0.561

0.567

0.574

0.581

0.587

0.594

0.601

0.608

0.614

0.621

15

0.551

0.557

0.564

0.571

0.577

0.584

0.591

0.598

0.604

0.611

0.618

0.624

20

0.554

0.560

0.567

0.574

0.581

0.587

0.594

0.601

0.608

0.614

0.621

0.628

 

 

 

 

 

 

 

 

 

 

 

 

 

25

0.557

0.564

0.570

0.577

0.584

0.591

0.597

0.604

0.611

0.618

0.625

0.631

30

0.560

0.567

0.574

0.580

0.587

0.594

0.601

0.608

0.614

0.621

0.628

0.635

35

0.563

0.570

0.577

0.584

0.590

0.597

0.604

0.611

0.618

0.625

0.632

0.639

40

0.566

0.573

0.580

0.587

0.594

0.601

0.608

0.614

0.621

0.628

0.635

0.642

45

0.569

0.576

0.583

0.590

0.597

0.604

0.611

0.618

0.625

0.632

0.639

0.646

 

Millibars

 

940

950

960

970

980

990

1000

1010

1020

1030

1040

1050

0

0.620

0.627

0.634

0.640

0.647

0.653

0.660

0.667

0.673

0.680

0.686

0.693

5

0.624

0.631

0.637

0.644

0.651

0.657

0.664

0.670

0.677

0.684

0.690

0.697

10

0.628

0.634

0.641

0.648

0.654

0.661

0.668

0.674

0.681

0.688

0.694

0.701

15

0.631

0.638

0.645

0.651

0.658

0.665

0.671

0.678

0.685

0.692

0.698

0.705

20

0.635

0.641

0.648

0.655

0.662

0.668

0.675

0.682

0.689

0.695

0.702

0.709

 

 

 

 

 

 

 

 

 

 

 

 

 

25

0.638

0.645

0.652

0.659

0.665

0.672

0.679

0.686

0.693

0.699

0.706

0.713

30

0.642

0.649

0.655

0.662

0.669

0.676

0.683

0.690

0.696

0.703

0.710

0.717

35

0.645

0.652

0.659

0.666

0.673

0.680

0.687

0.693

0.700

0.707

0.714

0.721

40

0.649

0.656

0.663

0.670

0.677

0.683

0.690

0.697

0.704

0.711

0.718

0.725

45

0.653

0.659

0.666

0.673

0.680

0.687

0.694

0.701

0.708

0.715

0.722

0.729

FORMULAE

:

e = e' - (t - t') Δe

and

 

Δe = 0.00066 *(1+(0.00115* t')) p

 

 

 

and

e' = 6.107* (10^ ((7.5* t') / (237.3+ t')))

 

 

 

where

:

T

is the

dry bulb temperature °C

 

 

t'

is the

wet bulb temperature °C

 

 

e

is the

Vapour pressure (millibars)

 

 

e’

is the

Vapour pressure at saturation (millibars) (Table B)

 

 

p

is the

barometric pressure millibars

 

 

Δe

from

Table A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To find Vapour Pressure e :

 

Example :

 

 

 

 

 

 

 

 

Pressure

1010

Millibars

 

 

 

Dry bulb

26.1

°C

 

 

 

Wet bulb

24.4

°C

 

 

 

Depression

1.7

(Dry - Wet)

 

(a)

Extract value from Table B

 

 

 

 

 

 

 

 

 

for wet bulb temperature

From Table B - wet bulb value extract :

30.56

 

 

 

 

(b)

Extract constant from

 

From Table A - wet bulb & pressure values extract :

0.686

 

 

Table A and multiply by

multiply by wet bulb depression

1.7

 

 

wet bulb depression.

 

subtract from Table B value

1.166

 

 

Subtract from Table B value

e

millibars

=

29.39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.3.1(a) : Table "A"

 

 

 

TABLE B

 

 

 

Vapour pressure at saturation - e'

 

 

WET

 

BULB

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

6.107

6.152

6.196

6.242

6.287

6.333

6.379

6.425

6.472

6.519

1

6.566

6.614

6.661

6.710

6.758

6.807

6.856

6.905

6.955

7.005

2

7.055

7.106

7.157

7.208

7.260

7.312

7.364

7.417

7.469

7.523

3

7.576

7.630

7.685

7.739

7.794

7.849

7.905

7.961

8.017

8.074

4

8.131

8.189

8.246

8.304

8.363

8.422

8.481

8.541

8.601

8.661

5

8.722

8.783

8.844

8.906

8.968

9.031

9.094

9.157

9.221

9.285

6

9.349

9.414

9.480

9.545

9.612

9.678

9.745

9.812

9.880

9.948

7

10.017

10.086

10.155

10.225

10.295

10.366

10.437

10.509

10.580

10.653

8

10.726

10.799

10.873

10.947

11.021

11.096

11.172

11.248

11.324

11.401

9

11.478

11.556

11.634

11.713

11.792

11.872

11.952

12.033

12.114

12.195

10

12.277

12.360

12.443

12.526

12.610

12.695

12.780

12.865

12.951

13.038

 

 

 

 

 

 

 

 

 

 

 

11

13.125

13.212

13.300

13.389

13.478

13.567

13.657

13.748

13.839

13.931

12

14.023

14.116

14.209

14.303

14.397

14.492

14.587

14.683

14.780

14.877

13

14.975

15.073

15.172

15.271

15.371

15.472

15.573

15.674

15.777

15.879

14

15.983

16.087

16.192

16.297

16.403

16.509

16.616

16.724

16.832

16.941

15

17.050

17.160

17.271

17.382

17.494

17.607

17.720

17.834

17.948

18.063

16

18.179

18.296

18.413

18.530

18.649

18.768

18.888

19.008

19.129

19.251

17

19.373

19.496

19.620

19.745

19.870

19.996

20.122

20.250

20.378

20.506

18

20.636

20.766

20.897

21.028

21.160

21.293

21.427

21.562

21.697

21.833

19

21.969

22.107

22.245

22.384

22.524

22.664

22.805

22.947

23.090

23.234

20

23.378

23.523

23.669

23.816

23.963

24.111

24.260

24.410

24.561

24.712

 

 

 

 

 

 

 

 

 

 

 

21

24.865

25.018

25.172

25.327

25.482

25.639

25.796

25.954

26.113

26.273

22

26.434

26.595

26.758

26.921

27.085

27.250

27.416

27.583

27.750

27.919

23

28.088

28.259

28.430

28.602

28.775

28.949

29.124

29.300

29.476

29.654

24

29.833

30.012

30.193

30.374

30.556

30.740

30.924

31.109

31.295

31.483

25

31.671

31.860

32.050

32.241

32.433

32.626

32.820

33.015

33.212

33.409

26

33.607

33.806

34.006

34.207

34.410

34.613

34.817

35.023

35.229

35.437

27

35.645

35.855

36.066

36.278

36.490

36.704

36.919

37.136

37.353

37.571

28

37.791

38.011

38.233

38.456

38.680

38.905

39.131

39.358

39.587

39.817

29

40.048

40.280

40.513

40.747

40.983

41.219

41.457

41.696

41.937

42.178

30

42.421

42.665

42.910

43.156

43.404

43.653

43.903

44.154

44.407

44.660

 

 

 

 

 

 

 

 

 

 

 

31

44.915

45.172

45.429

45.688

45.948

46.210

46.473

46.737

47.002

47.269

32

47.537

47.806

48.076

48.348

48.622

48.896

49.172

49.449

49.728

50.008

33

50.289

50.572

50.856

51.142

51.429

51.717

52.007

52.298

52.590

52.884

34

53.180

53.477

53.775

54.075

54.376

54.678

54.982

55.288

55.595

55.903

35

56.213

56.525

56.838

57.152

57.468

57.785

58.104

58.425

58.747

59.070

36

59.395

59.722

60.050

60.380

60.711

61.044

61.379

61.715

62.053

62.392

37

62.733

63.075

63.419

63.765

64.112

64.461

64.812

65.164

65.518

65.874

38

66.231

66.590

66.951

67.313

67.677

68.043

68.410

68.779

69.150

69.523

39

69.897

70.273

70.651

71.031

71.412

71.795

72.180

72.567

72.955

73.345

40

73.738

74.131

74.527

74.925

75.324

75.725

76.128

76.533

76.940

77.349

 

This table was constructed with Excel and differs from the original,

 

 

 

 

above 30 degrees by 0.04, due to evaluation of power term

 

 

 

 

Figure 4.3.1(b) : Table "B"

 

 

The formulae form which these tables are calculated are :

 

e  = e’ – (t-t’)*Δe        and Δe = 0.000 66(1+0.00115*t’)p

                                       

                                               e’ = 6.107 *10a  where a = (7.5t’)/(237.3+t’)

where :

                           e     =    Vapour pressure (millibars)

                           t      =    dry bulb temperature °C

t’     =    wet bulb temperature °C

                           p     =    barometric pressure millibars

                           e’    =    Vapour pressure at saturation (millibars) (Table B)

                           Δe   =    Table A

 

             Example :

             Wet bulb 24.4°C, Dry 26.1°C, Pressure 1010.0mbar

 

             Δe   = 0.000 66(1+0.00115*24.4)*1010.0     =    0.6853

0.686 from Table A

 

                           a     = (7.5*24.4)/(237.3+24.4)       = 0.6993

 

             e’    = 6.107x100.6993                                     =    30.556

30.556 from Table B

 

             e     =    30.553 – (26.1-24.4)*0.686            =    29.391

29.390 using Tables

 

4.3.2      Atmospheric readings required for the computation

 

These have been taken simultaneously, at each end of the line :

 

(a)     Immediately before the first "fine" readings were commenced.

(b)    At the Conclusion of these "fine" readings.

(c)     Immediately after the next series of "fine" readings.

 

Dry bulb, Barometric Pressure and Vapour Pressure for (a) and (b) at both stations, are meaned and used in calculating the first measurement.

 

Dry bulb, Barometric Pressure and Vapour Pressure for (b) and (c) at both stations, are meaned and used in calculating the second measurement.

 

See 4.3.2 for an example of atmospheric readings and calculation.

 

4.3.3      Explanation of the “coarse” figure

 

Coarse patterns are :

 

A-B          10        kc/s pattern   50,000 ft.        (15,240         metres)

A-C        100       kc/s pattern     5,000 ft.      (  1,524            metres)

A-D        1000      kc/s pattern        500 ft.     (     152.4     metres)

A alone      10       mc/s pattern         50 ft.     (       15.24     metres)

 

For lines longer than 50,000ft (15,240 metres) the first figure must be provided by a rough knowledge of the length of the line :

 

KILOMETRES

 

MILES

0  to  15

first figure

0

 

0   to 10

first figure

0

15 to 30

 

1

 

10 to 20

 

1

30 to 45

2

 

20 to 30

2

45 to 60

3

 

30 to 40

3

60 to 75

4

 

40 to 50

4

75 to 90

5

 

50 to 60

5

 

Example of a set of coarse readings, rough distance between 15 & 30km

 

A+ 16   A+ 16   A+ 16   A+ 16   (add 100, if necessary)

B     09   C     42   D     75   A-   84

                     07          74          41      2) 32

                                                             16   (should be close to A+)

"Coarse” figure : 1 0 7 4 16       (first figure is 1 as distance 15-30km)

 

Example of a set of coarse readings, rough distance between 30 & 45km

 

A+ 06   A+ 06   A+ 06   A+ 06   (add 100, if necessary.)

B     75   C     80   D     36   A-   92

                     31          26          70      2) 14

                                                             07   (should be close to A+)

"Coarse” figure : 2 3 2 7 07       (first figure is 2 as distance 30-45km)

 

Ambiguous discrepancies in the difference readings

 

Assume that the following readings are obtained :

 

A+  16   A+  16   A+  16   A+         16

B     09   C     42   D     78   A-          80

07          74          38                2)    36

A=  18

 

Considering the A-D figure, it is seen that the 8 of the 33 does not readily check with the 1 of the 18. On the other hand, considering the A-C figure, the 4 of the 74 checks with the 3 of the 38; thus it may leave some doubt whether the coarse figures are 07318 or 07418. However, since only 3 needs to be added to 38 to give 41, a value of which the 1 checks with the 1 of the 13, it can be seen the 33 should be 41, the discrepancy being due possibly to a alight error in the instrument, or in the reading of the trace. Then the 4 of the 74 checks with the 4 of the 41, and the 1 of the 41 with the 1 of the 18. Thus the coarse figure is 07418.

 

“Bracketing” method to resolve ambiguities

 

In the measurement under discussion the difference readings are :

      

A-B 07, A-C 74, A-D 38 and A 18. Proceed as follows;

 

(i)      Write down the A-D and A figures on the one line with a bracket in the space between the, thus :     38       [     18

 

(ii)     Enter in the centre of the bracket a figure which consists of the tenths digit of the A-D value, and the tenths digit of the A value :

 

38      [31      18

 

(iii)    Bracket the figure so obtained with values 10 above and 10 below, thus :

 

41

38      [31      18

                                                                                                                                                                                      21

 

The value in the bracket that is closest to the observed value is the true difference reading, i.e., of the three, 41 is closest to 38. Therefore the A-D coarse digit is 4.

 

Where it is necessary to carry out this method on the A-C, and A-B values as well, always treat the A-D reading first, then repeat the others, thus :

 

A+  16          A+  16          A+  16          A+         16

B     09          C     38          D     18          A-          80

07                78                98                2)    36

                                                                                       A=  18

 

                                                                                01√

                                                                   98          [91        18

                                                                                81

                                                     80√                                  Step 1

                                              78   [70        01

                                                     60

                                 18                              Step 2

                           07   [08√      80

                                 98

                                                      Step 3

 

Step 1 :  The correct A-D value is 01, therefore use the "0" (tenths digit) in Step 2.

 

Step 2 :  The correct A-C value is 80, therefore use the "8" (tenths digit) in Step 3.

 

Step 3 :  The correct A-B value is 08.

 

The coarse figure therefore is 08018, which is not readily apparent from the difference readings.

 

Unresolvable difference readings

 

Consider the following set of readings :

 

A+  16          A+  16          A+  16          A+         16

B     11          C     37          D     74          A-          76

05                79                42                2)    40

                                                                                 A=  20

 

The 2 of the 42 (A-D value) checks with the 2 of the 20 (a value). Using the method of “bracketing” on the A-C value the following is obtained :

 

                                        84

                           79          [74        18

                                        64

                   

However, as 79 is midway between 74 and 84, the A-C value can either be 74 or 84, and the coarse reading 07420 or 08420.

 

Provided that there is not too large a difference between the A+ and A values, the A value can be substituted for the A+ value, in evaluating the, difference readings, thus:-

 

A+  20          A+  20          A+  20          A+         16

B     11          C     37          D     74          A-          76

09                83                46                2)    40

                                                                                 A=  20

 

This gives a coarse figure of 08420 which should be correct. However to accept these figures would not be good surveying practise, therefore the coarse figures should be taken again, preferably with a different instrument.

 

The cause of ambiguities in the Coarse readings

 

Assuming the trace has been properly