Locating points, objects, and/or details on the surface of the earth requires an established system of control stations. An engineering tech can easily determine the relative positions of detail points if these points are tied into a local control station, or if the control station is tied into a geodetic control, those positions can be located relative to a worldwide control system. The main control system is formed by a triangulation network supplemented by a line surveyed across a plot of ground (a traverse). A traverse that has been established and is used to locate detail points and objects is often called a control traverse. Any line from which points and objects are located is a control line. A survey is controlled horizontally by measuring horizontal distances and horizontal angles. This type of survey is often referred to as a horizontal control. Additionally, horizontal control surveys establish supplementary control stations for use in construction surveys. Supplementary control stations usually consist of one or more short traverses running close to or across a construction area to afford easy tieins for various projects. These stations are established to the degree of accuracy needed for the purpose of the survey. In this lesson, we will identify common procedures used in converting angular measurements taken from a compass or transit survey, recognize the methods used in establishing horizontal control, and identify various field procedures used in running a traverse survey.
When you have completed this lesson, you will be able to:
1.0.0 Directions and Distances
2.0.0 TransitTape Survey 3.0.0 Organizing the Party 
There are various ways of describing the horizontal locations of a point. In the final analysis, these ways are all reducible to the basic method of description of stating the length (distance) and direction of a straight line between the point whose location is being described and a reference point. Direction, like horizontal location itself, is also relative to the direction of a line and can only be stated relative to a reference line of known (or sometimes of assumed) direction. In true geographical direction, the reference line is the meridian passing through the point where the observer is located, and the direction of a line passing through that point is described in terms of the horizontal angle between that line and the meridian. In magnetic geographical direction, the reference line is the magnetic meridian instead of the true meridian.
Most typically, the bearing gives the direction of a traverse line. In field traversing, however, turning deflection angles with a transit is more convenient than orienting each traverse line to a meridian.
Converting bearings to deflection angles is based on a wellknown geometrical proposition (Figure 141). When two meridians (or parallel lines) are intersected by another line (a traverse), angles (vertically opposite angles) are equal. It is also the case that , and (corresponding angles). 1 21 23 3 ,,, BandBAandABandBAandA = AA 2 = BB 2 Therefore:
• === AAAA 321
• === BBBB 321 The sum of the angles that form a straight line is 180°; the sum of angles around the point is 360°. When a traverse contains traverse lines AB, BC, and CD (Figure 142) the meridians through the traverse stations are indicated by the lines NS, N’S’, and N’’S’’. Although meridians are not, in fact, exactly parallel, assume they are for conversion purposes. Consequently, we have here three parallel lines intersected by traverses, and the angles created will therefore be equal (Figure 14 2). The bearing of AB is N20°E, which means that angle NAB measures 20°. To determine the deflection angle between AB and BC:
• If angle NAB measures 20°, then angle N’BB’ must also measure 20° because the two corresponding angles are equal. Figure 141 – The relationship of corresponding angles. 144
• The bearing of BC is given as S50°E, which means angle S’BC measures 50°E. The sum of the angle N’BB’ plus S’BC plus the deflection angle between AB and BC (angle B’BC) is 180°. Therefore, the size of the deflection angle is: o 180°  (N’BB’ + S’BC) or o 180°  (50° + 20°) = 110° The figure indicates that the angle should be turned to the right; therefore, the complete deflection angle description is 110°R. The bearing of CD is N70°E; therefore, angle N’’CD measures 70°. Angle S’’CC’ is equal to angle S’BC and therefore measures 50°. The deflection angle between BC and CD equals:
• 180°  (S’’CC + N’’CD) or
• 180°  (50° + 70°) = 60° Therefore, the angle should be turned to the left.
Converting deflection angles to bearings applies the process for converting bearings into deflection angles. Suppose that you know the deflection angles (Figure 142) and want to determine the corresponding bearings. To do this, you must know at least one traverse line bearing. Assume that the bearing of AB is known, and you need the bearing of BC. The size of the deflection angle B’BC is 110°, and the size of angle N’BB’ is the same as the size of NAB, which is 20°. BC’s angle of bearing size is:
• 180°  (B’BC +NAB) or
• 180°  (110 + 20°) = 50° BC lies in the second or SE quadrant (Figure 142); therefore, the full description of the bearing is S50°E.
Converting a bearing to an interior angle or exterior angle also applies the procedure used to convert deflection angles into bearings. Suppose that (Figure 142), angle ABC is an interior angle and you want to determine the size. You know that angle ABS´ equals angle NAB, and therefore measures 20°. You know from the bearing of BC that, angle S’BC measures 50°. The interior angle ABC is: Figure 142 – Converting bearings to deflection angles from given traverse data. 145 ABS’ + S’BC or 20° + 50° = 70° The sum of the interior and exterior angles at any traverse station or point equals the sum of all the angles around that point, or 360°. Therefore, the exterior angle at station B equals 360° minus the interior angle or 360°  70° = 290° The process of measuring angles around a point to obtain a check on their sum, which should equal 360°00’, is sometimes referred to as closing the horizon.
Suppose you want to convert an azimuth of 135° to the corresponding bearing. This azimuth is greater than 90° but less than 180°; therefore, the line lies in the southeast quadrant (Figure 143). Always measure the bearing angles from the north and south ends of the reference meridian. (When solving any bearing problem, draw a sketch to get a clear picture.) For the azimuth, initiate the horizontal direction clockwise from the meridian plane. Measure it between either the north or the south end of the reference meridian and the line in question. When we talk about azimuth in this training manual, however, you must understand that the azimuth is referenced clockwise from the north point of the meridian. The numerical value of this 135° azimuth angle is measured from the north. Therefore, in this figure, the value of the bearing is 180°  135° = 45° The complete description of the bearing then is S45°E. For example, in converting a bearing of N30°W into an azimuth angle, the angle location must be in the northwest quadrant. Draw an angle of 30° from the north end of the reference meridian because azimuth angles are measured clockwise from the north end of the reference meridian. To compute this azimuth angle, subtract 30° from 360°; the result is 330°. Therefore, the bearing of N30°W is equal to 330° azimuth angle. Figure 143 – Converting azimuths to bearings and vice versa. 146
The basic method of establishing direction of a survey line or point is with a surveyor’s compass. (Notice that on most surveyor’s compasses, the east and west indicators are in the opposite positions from those of the east and west indicators on a map or chart.) Determine the magnetic bearing of the dotted line labeled Line of Sight (LOS) (Figure 144). First, mount the compass on asteady support, level it, and wait for the needle to stop oscillating. Then, carefully rotate the compass until the northsouth line on the card lies exactly along the line whose bearing is being taken. The bearing is now indicated by the needlepoint. The needlepoint indicates a numerical value of 40°. The card indicates the northeast quadrant. The magnetic bearing is, therefore, N40°E.
The compass needle lying along the magnetic meridian (Figure 144) means either that the compass is in an area free of local magnetic attraction or that the effect of local attraction has been eliminated by adjustment of the compass card. Local magnetic attraction refers to the deflection of the compass needle caused by a local magnetic force, such as that created by nearby electrical equipment or by a mass of metal, such as a bulldozer. When local attraction exists and is not compensated for, the resultant bearing is a compass bearing. A compass bearing does not become a magnetic bearing until it has been corrected for local attraction. Suppose, for example, you read a compass bearing of N37°E. Suppose the effect of the magnetic attraction of a nearby pole transformer is enough to deflect the compass needle 4° to the west of the magnetic meridian. In the absence of this local attraction, the compass would read N33°E, not N37°E. Therefore, the correct magnetic bearing is N33°E. To correct a compass bearing for local attraction, determine the amount and direction (east or west) of the local attraction. First, set up the compass where you propose to take the bearing. Then, select a distant object that you may presume to be outside the range of any local attraction. Take the bearing of this object. If you read a bearing of S60°W, shift the compass to the immediate vicinity of the object on which you sighted; and take, from there, the bearing of the original setup point. In the absence of any local attraction at the original setup point, read the back bearing of the original bearing or N60°E. Suppose instead you read N48°E. The back bearing of this is S48°W. Therefore, the bearing as indicated by the compass under local attraction is S60°W, but Figure 144 – A magnetic compass reading corrected for local attraction. 147 as indicated by the compass not under local attraction, it is S48°W. The amount and direction of local attraction is, therefore, 12°W. Whether you add the local attraction to, or subtract it from, the compass bearing to get the magnetic bearing depends on the direction of the local attraction and the quadrant the bearing is in. As a rule, for a bearing in the northeast quadrant, add an easterly attraction to the compass bearing to get the magnetic bearing and subtract a westerly attraction from the compass bearing to get the magnetic bearing. A compass (Figure 145) indicates a bearing of S40°W. Suppose the local attraction is 12°W. The needle, then, is 12°W of where it would be without local attraction. In the southwest quadrant, subtract westerly attraction and add easterly attraction. From a study of the paragraphs above, it becomes obvious that the procedure is the opposite for bearings in the northwest or southeast quadrants. In these quadrants, add westerly attraction and subtract easterly attraction to the compass bearing to get the magnetic bearing.
The angle between the true meridian and the magnetic meridian is magnetic declination. If the north end of the compass needle is pointing to the east of the true meridian, the declination is east. If the north end of the compass needle is pointing west of the true meridian, the declination is west (Figure 146). The magnetic needle aligns itself with the earth’s magnetic field and points toward the earth’s magnetic pole. In horizontal projections, these lines incline downward toward the north in the Northern Hemisphere and downward toward the south in the Southern Hemisphere. Since the bar takes the position parallel with the lines of force, it inclines with the horizontal. This phenomenon is known as the magnetic dip. Figure 145 – Compass bearing affected by local magnetic attraction. Figure 146 – Magnetic declination (west).
When a compass bearing for local attraction is corrected, what results is a magnetic bearing. As explained previously, in most areas of the earth, a magnetic bearing differs from a true bearing by the amount of the local magnetic declination (called magnetic variation by navigators). The amount and direction of local declination is shown on maps or charts of the area in a format similar to the following: “Magnetic Declination 26°45°W (1988), Annual Increase 11´”. This means, if you are working in 2008 (20 years later), the local declination is: 26°45’ + (11’ x 20) or 26°45’ +220 = 26°45’ + 3°40’ = 30°25’ To convert a magnetic bearing to a true bearing, apply the declination to the magnetic bearing in precisely the same way that you apply local attraction to a compass bearing. If the declination is east, add it to northeast and southwest magnetic bearings, and subtract it from southeast and northwest magnetic bearings. If the declination is west, add it to southeast and northwest magnetic bearings and subtract it from northeast and southwest magnetic bearings. When you have a compass bearing and know both the local attraction and the local declination, you can go from compass bearing to true bearing in a single process by applying the algebraic sum of local attraction and local declination, Suppose that local attraction is 6°W and declination, 15°E. You could correct for local attraction and convert from magnetic to true in the same operation by applying a correction of 9°E to the compass bearing.
Correct a compass bearing to a magnetic bearing by applying the local attraction. Convert a magnetic bearing to a true bearing by applying the local declination. Use a magnetic bearing to figure the corresponding compass bearing by using both local attraction and local declination. The terms used to describe these calculations are uncorrecting and unconverting. When uncorrecting or unconverting, apply local attraction and local declination in the reverse direction in which you apply them if you were correcting or converting. For example, with a compass affected by a 10°W local attraction, lay off a line bearing S28°W magnetic by compass. If you are correcting, subtract a westerly attraction in the southwest quadrant. However, for uncorrecting, add a westerly attraction in that quadrant. Therefore, to lay off a line bearing S28°W, you would lay off S38°W by the compass. The same rule applies to azimuths. Suppose you have an azimuthreading (measured from north) compass set up where local attraction is 10°W, declination is 25°E, and you want to lay off a line with a true azimuth of 256°. The algebraic sum of these is 15°E. Correcting and converting azimuths, requires the addition of easterly corrections, and subtraction of westerly corrections. Therefore, if you were correcting or converting, you would add the 15° to 256°. Because you are uncorrecting or unconverting, however, you subtract; and, to lay off a line with true azimuth 256°, you read 241° by the compass.
Some transit compasses and most surveyor’s and forester’s field compasses are equipped to offset local attraction, local declination, and/or the algebraic sum of the two (Figure 147). The upper view of Figure 147 shows a compass bearing of N40°W on a compass presumed to be affected by a local attraction of 10°E. In this quadrant, you subtract easterly attraction; therefore, the magnetic bearing should read N30°W. In the lower view, the same compass has been oriented for an error of 10°E by simply rotating the compass card 10°E clockwise. On most orienting compasses, the card can be released for rotating by backing off a small screw on the face of the card. Note that you now read the correct magnetic bearing of N30°W.
As an example of using a surveyor’s compass to perform a small field survey and compose field notes, lets review the scenario depicted in the sketch and remarks of Figure 148. The compass was first setup at station A, then line AE’s bearing is taken for the purpose of later comparison to the forward bearing of engineering tech. Then, line AB’s bearing is taken, and the distance from A to B is chained. The observed bearing of (S62°20´E) is entered beside B in the column headed “Obs. Bearing.” Then the chained distance is entered beside B in the column headed “Dist.” The compass was then shifted to station B, and the back bearing of AB is taken (that is, the bearing of BA) as a check on the previously taken bearing of AB. The back bearing should have the same numerical value (62°20´ in this case) as the forward bearing. A difference in the two would indicate either an inaccuracy in reading one bearing or the other or a difference in the strength of local attraction. Proceeding in this fashion, the survey team continued to take bearings and back bearings, and chain the distances all the way around to the starting point at station A, recording the results after each step. The last forward bearing taken, that of engineering tech, has the same numerical value as the back bearing of engineering tech (bearing of AE) taken at the start. Figure 147 – Orienting a compass for a 10° easterly attraction. 1410 Figure 148 – Sample field notes from a compasstape survey.
As a check on the accuracy of the whole bearingreading process, compute the size of the interior angle at each station from the observed bearings by the method previously described for converting bearings to interior angles. Enter the sizes of these angles in the column headed “Comp. Int. Angle,” and enter the sum below. The sum of the interior angles in a closed traverse should equal the product of 180° (n – 2), n being the number of traverse lines in the traverse. In this case, the traverse has five lines; therefore, the sum of the interior angles should be: 180° (5 – 2) = 180° x 3 = 540° The computed sum is, therefore, the same as the added sum of the angles converted from observed bearings.
If a magnetic compass has a bent needle, there will be a constant instrumental error in all observed bearings and azimuths. To check for this condition, set up and level the compass, wait for the needle to cease oscillating, and read the graduation indicated at each end of the needle. If the compass is graduated for bearings, the numerical value at each end of the needle should be the same. If the compass is graduated for azimuths, the readings should be 180° apart. Similarly, if the pivot supporting the needle on a magnetic compass is bent, there will be an instrumental error in the compass. However, this error, instead of being the same for all readings, will vary. Either of these instrumental errors can be eliminated by reading both ends of the needle and using the average between them. Suppose, for example, that with a compass graduated for bearings you read a bearing of N45°E and a back bearing of S44°W. You would use the average, or: ½ (45° + 44°) = N44°30’E The error in the compass should, of course, be corrected as soon as possible. Normally, this is a job for an expert. Remember the cause of a discrepancy in the reading at both 1411 ends when there is one. It is more probable that the needle, rather than the pivot, is bent. After a bent needle is straightened, if a discrepancy still exists, then probably the pivot is bent too. If a compass needle is sluggish—that is, if it moves unusually slowly in seeking magnetic north—it will probably come to rest a little off the magnetic meridian. The most common cause of sluggishness is weakening of the needle’s magnetism. A needle may be demagnetized by drawing it over a bar magnet. The needle should be drawn from the center of the bar magnet toward the end, with the south end of the needle drawn over the north end of the magnet and vice versa. On each return stroke, lift the needle clear of the magnet. Sometimes the cause of a sluggish needle is a blunt point on the pivot. This may be corrected by sharpening the pivot with a fine file. If the compass is not level when a bearing or azimuth is being read, the reading will be incorrect. A similar error exists if the compass is equipped with sighting vanes and one or more of them are bent. To check for bent compass vanes, set up and level the compass and then sight with the vanes on a plumb bob cord. The most common personal error the observer can make in compass work is MISRengineering techDING. This is caused by the observer’s eye not being vertically above the compass at the time of the reading. Other common mistakes include reading a needle at the wrong end and setting off local attraction or declination in the wrong direction when orienting the compass.
Directions are similarly determined by the use of a transit. This can be done by measuring the size of the horizontal angle between the line whose direction is sought and a reference line. With a transit, however, you are expected to do this with considerably more accuracy and precision than with a surveyor’s compass. Some of the basic procedures associated with the proper operation of the instrument will be discussed in the following paragraphs.
The point at which the LOS, the horizontal axis, and the vertical axis of a transit meet is called the instrument center. The point on the ground over which the center of the instrument is placed is the instrument point, transit point, or station. A wooden stake or hub is usually marked with a tack when used as a transit station or point. To prevent jarring or displacement of the transit, avoid those stations with loose planking, soft or marshy ground, and other conditions that could cause the legs of the tripod to move. The following steps are recommended when you are setting up a transit over a station point:
1. Center the instrument as closely as possible over the definite point by suspending a plumb line from a hook and chain beneath the instrument. Tie the plumb string with a slipknot, so that the height of the plumb is easily adjustable.
2. Move the tripod legs as necessary until the plumb bob is about 1/4 inch short of being over the tack, while maintaining a fairly level foot plate. Spread the tripod legs, and apply sufficient pressure to the legs to ensure their firmness in the ground. Make sure to loosen the wing nuts to release the static pressure before retightening.
3. Turn the plates so that each plate level is parallel to a pair of opposite leveling screws. (It is common practice to have a pair of opposite leveling screws in line with the approximate LOS.) Tighten the leveling screws, and then rotate opposing pairs of leveling screws either toward each other or away from each other until the plate bubbles are centered. If the plumb bob is not directly over the center of the tack, loosen two adjacent leveling screws enough to free the shifting plate. Relevel the instrument if the bubbles become offcenter. During breezy conditions, you may shield the plumb line with your body during setup. Sometimes in windy locations, it may be necessary to construct a wind shield. Setting and leveling the transit rapidly requires a skill that develops through consistent practice. Take advantage of any opportunities to train and increase skills in handling surveying instruments. When setting up or operating a transit, do not forget:
1. The plate bubble follows the direction of the left thumb when you are manipulating the leveling screws.
2. Always check to see if the plumb bob is still over the point after leveling it. If the plumb bob has shifted, recenter the instrument.
3. While loosening the two adjacent leveling screws, shift the transit head laterally.
4. Always maintain contact between the leveling screw shoes and the foot plate.
5. Do not disturb the instrument setup until you are certain that all observations at that point are completed and roughly checked. Move the instrument from that setup only after checking with the party chief.
6. Before the transit is moved or taken up, center the instrument on the foot plate, roughly equalize the height of the leveling screws, clamp the upper motion (the lower motion may be tightened lightly), point the telescope vertically upward, and lightly tighten the vertical motion clamp
The transit contains a graduated horizontal circle, referred to as the horizontal limb. The horizontal limb may be graduated clockwise from 0° through 360° (figure 139, view A), or clockwise from 0° through 360° and also in quadrants (figure 139, view B); or both clockwise and counterclockwise from 0° through 360° (figure 139, view C). 1413 Figure 149 – Three types of horizontal limb graduations. The horizontal limb can be clamped to stay fast when the telescope is rotated (called clamping the lower motion), or it can be released for rotating by hand (called releasing the lower motion). The horizontal limb is paired with another circle (the vernier plate), which is partially graduated on either side of zero graduations located 180° apart on the plate. When the telescope is in the normal (upright) position, the A vernier is located vertically below the eyepiece and the B vernier below the objective end of the telescope. The zero on each vernier is the indicator for reading the sizes of horizontal angles turned on the horizontal limb. To illustrate the method (Figure 1410) of turning an angle from a reference line with a transit:
1. With the transit properly set over the point or station, bring one of the horizontal verniers near zero by hand; clamp the upper motion; and, by turning the upper tangent screw, set one vernier at 0°, usually starting with the A vernier. Train the telescope to sight the marker (range pole, chaining pin, or the like) held on the reference line; clamp the lower motion, and, by using the lower tangent screw, set the LOS on the marker.
2. Release the upper motion and rotate the telescope to bring the zero on the A vernier in line with the 30° graduation on the horizontal limb. To set the vernier exactly at 30°, use the upper tangent screw. You may use a magnifying glass to set the vernier easily and accurately.
3. Mark the next point with a marker and follow the procedures for establishing a point or station. Figure 1410 – Setting the vernier at zerozero (left) and setting an angle exactly on the vernier zero. Similarly, you may use the procedures above to measure a horizontal angle by sighting on two existing points and reading their interior angle. In addition, bear these tips in mind when taking horizontal measurements:
1. Make the centering of the line of sight as close as possible by hand so that you will not turn the tangent screw more than one or two turns. Make the last turn of the tangent screw clockwise to compress the opposing springs.
2. Read the vernier with your eye directly over the top of the coinciding graduations to eliminate the effects of parallax.
3. Take the reading of the other vernier as a check. The readings should be 180° apart.
4. Check the plate bubbles before measuring an angle to see if they are centered, but do not disturb the leveling screws between the initial and final settings of the line of sight. If an angle is measured again, relevel the plate after each reading before sighting again on the starting point.
5. Make sure that the rodman is holding the range pole exactly vertical when you sight at it. When the bottom of the range pole is not visible, let the rodman use a plumb bob.
6. Avoid accidental movement of the horizontal circle; for instance, moving the wrong clamp or tangent screw. If you will observe a number of angles from one setup without moving the horizontal circle, sight at a clearly defined distant object that will serve as a reference mark, and take note of the angle. Occasionally recheck the reading to this point during measurement to ensure no accidental movement has taken place. In an example of a horizontal deflection angle measurement (Figure 1411), the field notes contain data taken from a loop traverse shown in the sketch. The transit was first set up at station A, and the magnetic bearing of AB was read on the compass. Then the deflection angle between the extension of engineering tech and AB was turned in the following manner:
1. The instrumentman released both clamps, matched the vernier to zero by hand, tightened the upper motion clamp, and set the zero exactly with the upper tangent screw.
2. With the telescope plunged (inverted position), the instrumentman sighted the range pole held on station E. Then he tightened the lower motion clamp and manipulated the lower motion tangent screw to bring the vertical cross hair to exact alignment with the range pole.
3. The instrumentman replunged the telescope and trained on the extension of engineering tech. (Notice that the telescope is in its normal position now.) He then released the upper motion and rotated the telescope to the right until the vertical cross hair came into line with the range pole held on station B. He further set the upper motion clamp screw and brought the vertical cross hair into exact alignment with the range pole by manipulating the upper motion tangent screw.
4. The instrumentman then reads the deflection angle size on the A vernier (89°01´). Since the angle was turned to the right, he recorded 89°01´R in the column headed “Defl. Angle.” Likewise, he recorded the chained distance between stations A and B and the magnetic bearing of traverse line AB under their appropriate headings. Figure 1411– Sample fields from a deflection angle transittape survey. 1416 The instrumentman uses the same method at each traverse station, working clockwise around the traverse to station E. The algebraic sum of the measured deflection angle (angles to the right considered as plus, to the left as minus) is 350°59´. For a closed traverse, the algebraic sum of the deflection angles from the standpoint of pure geometry is 360°00´. Therefore, there is an angular error of disclosure here of 0°01´. This small error would probably be considered a normal error. A large variance would indicate a larger mistake made in the measurements. In this example, the general accuracy of all the angular measurements was checked by comparing the sum of the deflection angles with the theoretical sum. The accuracy of single angular measurement can be checked by closing the horizon. The method is based on the theoretical sum of all the angles around a point being 360°00´. The field notes (Figure 1412) show the procedure for closing the horizon. The transit was set up at station A, and angle BAC was turned, measuring 51°15´. Then the angle from AC clockwise around to AB was turned, measuring 308°45´. The sum of the two angles is 360°00´. The angular error of closure is therefore 0°00´, meaning that perfect closure is obtained. Figure 1412 – Sample field notes for closing the horizon.
The vertical circle and the vertical vernier of a transit are used for measuring vertical angles. A vertical angle is the angle measured vertically from a horizontal plane of reference (Figure 1413, view A). When the telescope is pointed in the horizontal plane (when the telescope is level), the value of the vertical angle is zero. When the telescope is pointed up at a higher feature (elevated), the vertical angle increases from zero and is a plus vertical angle or angle of elevation. These values increase from 0° to +90° when the telescope is pointed straight up. As the telescope is depressed (pointed down), the angle increases in numerical value. A depressed telescope reading, showing that it is below the horizontal plane, is a minus vertical angle or angle of depression. These numerical values increase from 00 to –90° when the telescope is pointed straight down. To measure vertical angles, set the transit upon a definite point and level it. The plate bubbles must be centered carefully, especially for transits that have a fixed vertical 1417 vernier. Turn the LOS to approximately the point that the horizontal axis is clamped. Then, bring the horizontal cross hair to the point by means of the telescope tangent screw. Read the angle on the vertical limb using the vertical vernier. On a transit with a movable vertical vernier, the vernier is equipped with a control level. The telescope is centered on the point as previously described, but the vernier bubble is centered before the angle is read. The zenith is an imaginary point overhead where the extension of the plumb line will intersect an assumed sphere on which the stars appear projected. The equivalent point, directly below the zenith, is the nadir. Using the zenith permits reading angles in a vertical plane without using a plus or a minus. Theodolites have a vertical scale reading zero when the telescope is pointed at the zenith instead of in a horizontal plane. With the telescope in a direct position and pointed straight up, the reading is 0°; on a horizontal line, the reading is 90°; and straight down, 180°. When measuring vertical angles with the theodolites (Figure 1413, view B), read the angle of elevation with values less than 90°and the angle of depression with values greater than 90°. These angle measurements with the zenith as the zero value are called the zenith distances. Double zenith distances are observations made with the telescope directly and reversed to eliminate errors caused by the inclination of the vertical axis and the collimation of the vertical circle. Zenith distance is used to measure vertical angles involving trigonometric leveling and in astronomical observations. Figure 1413 – Vertical angles and zenith
1.3.4 Measuring Angles by Repetition
There is a significant distinction between precision and accuracy. A transit on which angles can be measured to the nearest 20 second is more precise than one that can measure only to the nearest 1 minute. However, this transit is not necessarily more accurate. The inherent angular precision of a transit is increased by the process of repetition. To illustrate this principle, suppose that with a one minute transit you turn the angle between two lines in the field and read 45°00´. The inherent error in the transit is 1´; therefore, the true size of this angle is somewhere between 44°59´30´´ and 45°00´30´´. For example, when using repetition, you leave the upper motion locked but release the lower motion. The horizontal limb will now rotate with the telescope, holding the reading of 45°00´. You plunge the telescope, train again on the initial line of the angle, and again turn the angle. You have now doubled the angle. The A vernier should read approximately 90°00´. For this second reading, the inherent error in the transit is still one minute, but the angle indicated on the A vernier is about twice the size of the actual angle measured. The effect of this is to halve the total possible error. This error was originally plus or minus 30 seconds. Now, the error is plus or minus only 15 seconds. If you measure this angle a total of six times, the total possible error will be reduced to onesixth of 30 seconds, or plus or minus 5 seconds. In theory, you could go on repeating the angle and increasing the precision indefinitely. In actual practice, because of lost motion in the instrument and accidental errors, it is not necessary to repeat the angle more than six times. The observation may be taken alternately with the telescope plunged before each subsequent observation. But a much simpler way is to take the first half of the observations with the telescope in the normal position, the other half, in an inverted position. Using the details of the previous example, the first three readings may be taken when the telescope is in its normal position; the last three when it is in its reversed position. To avoid the effect of tripod twist, after each repetition, rotate the instrument on its lower motion in the same direction that you turned it during the measurement; that is, the direction of movement should always be either clockwise or counterclockwise. Measuring angles by repetition eliminates certain possible instrumental errors, such as those caused by eccentricity and by nonadjustment of the horizontal axis. Review the field notes for the angle around a station, repeated six times (Figure 1414). The angle BAC was measured six times, and the angle closing the horizon around station A was also measured six times. The first measurement is not a true repeat, but it is counted as one in the column headed “No. Rep.” (number of repetitions). With the transit first trained on B and the zeros matched, the plate reading was 00°00´. This is recorded beside B in the column headed “Plate Reading”. The upper motion clamp was then released, the telescope was trained on C, and a plate reading of 82°45´ was obtained. This reading is recorded next to the figure ‘‘1” (for “1st repetition”) in the column headed “No. Rep.” The measurement of angle BAC was then repeated five more times. After the final measurement, the plate reading was 136°28´. This plate reading is recorded as the sixth repetition. To get the mean angle, divide some number, or figure, by the total number of repetitions. To determine which figure to use, first multiply the initial measurement by the total number of repetitions. In this case, as follows: 82°45’ x 6 = 496°30’ 1419 Figure 1414 – Notes for the angle around a station, repeated six times. Next, determine the largest multiple of 360° that can be subtracted from the above product. Obviously, the only multiple of 360° that can be subtracted from 496°30´ is 360°. This multiple is then added to the final measurement to obtain the figure that is to be divided by the total number of repetitions. In this example: 136°28’ + 360° = 496°28’ The mean angle then is 496°28’ 6 = 82°44’40” Enter this in the column headed “Mean Angle”. The following computation shows that you should use the same method to obtain the mean closing angle. 277°15’ x 6 = 1663°30’ 360° x 4 = 1440° (largest multiple of 360° 223°32’ + 1440 = 1663°32’ 1663°32’ 6 = 277°15’20” In the example shown above, the sum of the mean angle (82°44´40´´) and the mean closing angle (277°15´20´´) equals 360°00´00´´. This reflects perfect closure. In actual practice, perfect angle closure would be unlikely.
It is often necessary to extend a straight line marked by two points on the ground. Which method is used depends on whether or not there are obstacles in the line ahead, and, if so, whether the obstacles are small or large.
The double centering (or double reversing) method is used to prolong or extend a line. Suppose you are extending line AB (Figure 1415). Set up the transit at B, backsight on A, plunge the telescope to sight ahead, and set the marker at C´. With the telescope still inverted, again sight back on A, but this time, rotate the telescope through 180°. Then replunge the telescope and mark the point C´´. Mark the point C halfway between C´ and C´´. This is the point on the line AB you need to extend. If the instrument is in perfect adjustment (which seldom happens), points C´ and C´´ will coincide with point C. For further extension, move the instrument to C and repeat the procedure to obtain D.
This method is applied when a tree or other small obstacle is in the LOS between two points. The transit or theodolite is set up at point B (Figure 1416) as far from the obstacle as practical. Point C is set off the line near the obstacle and where the line BC will clear the obstacle. At B, measure the deflection angle, a. Move the instrument to C, and lay off the deflection angle 2a. Measure the distance BC, and lay off the distance CD equal to BC. Move the instrument to D, and lay off the deflection angle . Mark the point E. Then, line DE is the prolongation of the line AB.
The bypass an object by perpendicular offset method is used when a large obstruction, such as a building, is in the LOS between two points. The solution establishes a line parallel to the original line at a distance clear from the obstacle (Figure 1417). Set up the instrument at B, and turn a 90° angle from line AB. Carefully measure and record the distance BB´. Move the instrument to B´, and turn another 90° angle. Lay off B´C´ to clear the obstacle. Move the instrument to C, and turn a third 90° angle. Measure and mark distance CC´, which is equal to BB´. This establishes a point C on the original line. Then move the instrument to C, and turn a fourth 90° angle to establish the alignment CD that is the extension of AB beyond the obstacle. Figure 1415 – Double centering. Figure 1416 – Bypassing a small obstacle by the angle offset method. 1421 When the distance to clear the obstacle, BB´ or CC´, is less than a tape length, you can avoid turning four 90° angles. Erect perpendicular offsets from points A and B (Figure 1417) so that AA´ equals BB´. Set up the instrument at B’, and measure angle A´B´B to be sure that it’s 90°. Extend line A´B´ to C´ and then to D´, making sure that point C clears the obstacle. Then, lay off perpendicular offset C´C equal to AA´ or BB´ and perpendicular offset D´D equal to C´C. Then, line CD is the extension of line AB. The total distance of the line AD is the sum of the distances AB, B´C´, and CD. Compute the diagonals formed by the end rectangles and compare the result to the actual measurement, if you can, as a further check.
Sometimes running a straight line between nonintervisible points is necessary when events make the use of other methods impractical. If there is an intermediate point on the straight line from which both of the end points can be observed, you may use the balancing in method (also called bucking in, jiggling in, wiggling in, or ranging in). A problem often encountered in surveying is finding a point exactly on the line between two other points when neither can be occupied, or when an obstruction (such as a hill) lies between the two points. The point to be occupied must be located so that both of the other points are visible from it. The process of establishing the intermediate point is known as wiggling in or ranging in. First, estimate the approximate position of the line between the two points at the instrument station by using two range poles. Line in the range poles alternately in the following manner. As shown (in Figure 1418), view A, set range pole 1 and move range pole 2 until it is exactly on line between pole 1 and point A. Do this by sighting along the edge of pole 1 at the station A until pole 2 seems to be on line. Set Figure 1417– Bypassing a large obstacle by the perpendicular offset method. Figure 1418 – Setting up on a line between two points. 1422 range pole 2 and move pole 1 until it is on line between pole 2 and point C. Now, move pole 2 into line again, then pole 1, alternately, until both are on line AC. The line will appear to pass through both poles and both stations from either viewing position. After finding the approximate position of the line between the two points, set up the instrument on this line. The instrument probably will not be exactly on line, but will be over a point, such as B´, (see Figure 1419, 9iew B). With the instrument at B´, backsight on A and plunge the telescope and notice where the line of sight C passes the point C. Estimate this distance CC´ and also the distance that B´ would be away from C and A. Estimate the amount to move the instrument to place it on the line you need. Thus, if B´ is midway between A and C, and C´ misses C by three feet to the left, B´ must be moved about one and a half feet to the right to reach B. Continue the sequence of backlighting, plunging the telescope, and moving the instrument until the LOS passes through both A and C. When doing this, the telescope is reversed, but the instrument is not rotated. This means that if the telescope is reversed for backlighting on A, make all sightings on A with the telescope reversed. Mark a point on the ground directly under the instrument. Then, continue to use this method with the telescope direct for each backsight on A. Mark a second point on the ground. The point you need on the line AC is then the midpoint between the two marked points. Wiggling in is usually time consuming. Even though the shifting head of the instrument is used in the final instrument movements, you may have to pick up and move the instrument several times. The following method often saves time. After finding the approximate position of the line between the two points, mark two points B´ and B´´ (Figure 1419, 9iew C) one or two feet apart where you know they straddle the line AC. Set up over each of these two points in turn and measure the deflection angles . Also measure the horizontal distance between points B´ and B´´. This enables the ability to find the position B on the line AC by using the following equation: βα α + = aa 1 in which is the proportionate offset distance from B´ toward B´´ for the required point B, and and βα are both expressed in minutes or in seconds.
It is sometimes necessary to run a straight line from one point to another point that is not visible from the first point. If there is an intermediate point on theline from which both endpoints are visible, this can be done by the balancingin method. If no such intermediate point exists, the random line method (Figure 1419, 9iew A) is useful. It is challenging to run a line from A to B, when B is a point not visible from A. It happens, however, that there is a clear area to the left of the line AB, through which a random line can be run to C; C being a point visible from A and B. Figure 1419 – Random line method for locating intermediate stations. 1423 To train a transit set up at A on B, knowing the size of the angle at A is necessary. You can measure side b and side a, and you can measure the angle at C. Therefore, you have a triangle, of which you know two sides and the included angle. You can solve this triangle for angle A by:
• Determining the size of side c by the law of cosines, then determining the size of angle A by the law of sines
• Solving for angle A by reducing to two right triangles Suppose you find that angle A measures 16°35´. To train a transit at A on B, you would simply train on C and then turn 16°35´ to the right. You may also use the random line method to locate intermediate stations on a survey line. As shown in Figure 1419, 9iew B, stations 0 + 00 and 2 + 50, now separated by a grove of trees, were placed at some time in the past. You need to locate stations 1 + 00 and 2 + 00, which lie among the trees. Run a line at random from station 0 + 00 until you can see station 2 + 50 from some point, A, on the line. The transitman measures the angle at A and finds it to be 108°00´. The distances from A to stations 0 + 00 and 2 + 50 are chained and found to be 201.00 feet and 98.30 feet. With this information, it is now possible to locate the intermediate stations between stations 0 + 00 and 2 + 50. The distances AB and AD can be computed by ratio and proportion, as follows: AB x 201.0 40.20 ft. 250 50 = = and AB x 201.0 120.60 ft. 250 150 = = Lay off these distances on the random line from point A toward station 0 + 00. The instrumentman then occupies points B and D; turns the same angle, 108°00´, that he or she measured at point A and establishes points C and E on lines from points B and D through the stations being sought. The distances are computed by similar triangles as follows: B stationto BC x 78.64ft98.3 ft 250 200 )(002 =+ = D stationto DE x 39.32ft98.3 ft 250 100 )(001 =+ =
Determining the horizontal location of a point or points with reference to a station, or two stations, on a traverse line is commonly termed tying the point. The next several paragraphs present various methods used in the process. Figure 1420 – Swing offset method of locating points.
The swing offset is used for locating points close to the control lines (Figure 1420). Measurement of a swing offset distance provides an accurate determination of the perpendicular distance from the control line to the point being located. The swing offset is somewhat similar to the range tie (explained later), but as a rule, requires no angle measurement. To determine the swing offset distance, a chainman holds the zero mark of the tape at a corner of the structure while another chainman swings an arc with the graduated end of the tape at the transit line AB. When the shortest reading on the graduated end of the tape is observed by the chainman, the swing offset or perpendicular distance to the control line is obtained at points a or b. In addition, the horizontal distances between the instrument stations (A and B) and the swing offset points (a and b) may be measured and marked. A tie distance and angle ora θ may be measured from either instrument station to the corner of the structure to serve as a check.
The method of perpendicular offsets from a control line (Figure 1421) is similar to swing offsets. This method is more suitable than the swing offset method for locating details of irregular objects, such as stream banks and winding roads. Establish the control line close to the irregular line to be located, and measure perpendicular offsets, aa´, bb´, cc´, and so on, to define the irregular shape. When the offset distances are short, the 90° angles are usually estimated; but when the distances are several hundred feet long, lay off the angles with an instrument. Measure the distances to the offset points from a to i along the control line.
A point’s location can also be determined by means of a range tie, using an angle and a distance. The method requires extra instrument manipulation and should be used only when none of the previous methods are practical. Actually, range ties establish not only the corner of a structure but also the alignment of one of the sides. Assume that the building (Figure 1422) is not visible from either A or B or that either or both of the distances from A to B to a corner of the building cannot be measured easily. With the instrument set up at either A or B and the line AB established, one member of the party moves along AB until Figure 1421 – Perpendicular offsets. Figure 1422 – Range ties. 1425 he or she reaches point R, which is the intersection of line 12 extended. Move the instrument and set up on R, and measure the distance along the line AB to R. An angle measurement to the building is made by using either A or B as the backsight. Measure the range distance, R2, as well as the building dimensions.
To “set a point adjacent to a traverse line” means to establish the location of a point by following given tie data. This tie data may be (1) a perpendicular offset distance from a single specified station, (2) angles from two stations, or (3) an angle from one station and the distance from another station.
To set a point when given an angle and its distance from a single station, set up the instrument at the station; turn the designated angle, and chain the distance along the LOS. For perpendicular offset, the angle is 90°. To set a point when given a distance from each of two stations, manage by using two tapes if each of the distances is less than a full tape length. To do so, set the zero end of the tapes on both stations; run out the tapes, and match the distance mark on each tape to correspond with the required distance from the stations. When the tape is drawn taut, the point of contact between the tapes will be over the location of the desired point. If one or both of the distances is greater than a full tape length, determine direction of one of the tie lines by correct triangle solution. For example (Figure 1423), set point B 120.0 feet from station A and 83.5 feet from station C. A and C are 117.0 feet apart. Determine the size of the angle at A by using the triangle solution: bc csbs A ))(( 1 cos −− =− 2 s = (120.01/2 117.0 83.5) =++ 160.25 0.24797 (117.0)(120.0) 2(43.25)(40.25) 1 cos A =− = cos A = 1,00000 − 0.24797 − 0.75203 A 41°= 41 ′ To set point B, set up a transit at A, sight on C, turn 41°14´ to the left, and measure off 120.0 feet on that LOS. As a check, measure BC to be sure it measures 83.5 feet.
Figure 1423 – Locating a point by distances from two stations.
To set a point when given the angle from each of two traverse stations under ordinary conditions, use a pair of straddle hubs (commonly called straddlers), as shown in Figure 1424. Here the point is located at an angle of 34°33´ from station 2 + 00 and at an angle of 51°21´ from station 3 + 00. Set up the transit at station 2 + 00, sight it on station 3 + 00, and turn an angle of 34°33´ to the right. For this LOS, drive a pair of straddle hubs, one on either side of the estimated point of intersection of the tie lines. Stretch a cord between the straddlers. Then shift the transit to station 3 + 00, sight it on station 2 + 00, and turn an angle of 51°21´ to the left. Drive a hub at the point where this LOS intercepts the cord between the straddlers. To set a point with a given angle from one station and the distance from another, determine the direction of the distance line by triangle solution. In the example (Figure 14 25) point B is located 100.0 feet from station A and at an angle of 50°00´ from station C. In this example, you can determine the size of the angle at A by first determining the size of angle B, then subtracting the sum of angles B and C from 180°. The solution for angle B is as follows: 100.0 130.0 sin50° 00 ′ sin B = 0.99585 100.0 130.0(0.76604) sin B = Angle B then measures, to the nearest minute, 84°47´. Therefore, angle A measures: 180° ′ °− 74(8400 ′ 50°+ ′)00 45°= 31 ′ Set up a transit at A, sight on C, and turn 45°13´ to the left. Then, set B by measuring off 100.0 feet on this LOS. As a check, set up the transit at C, sight on A, turn 50°00´ to the right, and make sure this line of sight intercepts the marker at B.
Figure 1424 – Setting a point using straddlers.
Figure 1425 – Locating a point by angle and distance from two stations.
Test Your Knowledge 1. What is the size of the deflection angle between traverse lines BC and CD in the figure? Figure Here
2. What is the approximate true bearing of the object if the local declination is 10°W and the local attraction is 20E?
3. What are the respective bearings of the traverse lines OP in A and B in the figure? Figure Here

The exact method used in transittape surveying may vary slightly depending upon the nature of the survey, the intended purpose, the command or unit policy, and the preferences of the survey party chief. The procedures presented in this section are customary methods described in general terms.
All points where a traverse changes direction are marked, usually with a hub that locates the station exactly, plus a guard stake on which the station of the changeofdirection point is inscribed, such as 12 + 35. In the expression “station 12 + 35,” the 12 is called the full station and the 35 is called the plus. The points intended to be tied to the traverse or set in the vicinity of the traverse are usually selected and marked or set as the traverse is run. Select and mark the corresponding tie stations on the traverse at the same time. The first consideration in selecting tie stations is visibility, meaning that tie stations and the point to be tied or set must be intervisible. The next is permanency (not easily disturbed). Last is the strength of the intersection, which generally means that the angle between two tie lines should be as close to 90° as possible. The more acute or obtuse the angle is between tie lines, the less accurate the location of the point defined by their intersection.
A typical transittape survey party contains two chainmen, a transitman, a recorder (sometimes the transitman or party chief doubles as recorder), a party chief (who may serve as either instrumentman or recorder, or both), and axmen, if needed. The transitman carries, sets up, and operates the transit; the chainmen do the same with the tapes and the marking equipment. When the transitman turns an angle, he calls out the identity and size of the angle to the recorder, as “Deflection angle AB to BC, 75°16´, right”. The recorder repeats this and then makes the entry. Similarly, the head chainman calls out the identity and size of a linear distance, as “B to C, 265.72 feet;” then the recorder repeats this back and makes the entry. If the transitman closes the horizon around a point, he calls out, “Closing angle” and the angle measurement itself. The recorder repeats this and then adds the closing angle to the original angle. If the sum of the angles doesn’t come close to 360°, the recorder notifies the party chief. The party chief is in charge and makes all the significant decisions, such as the stations to be marked on the traverse.
The important distinction between accuracy and precision in surveying is that accuracy denotes the degree of conformity with a standard. It relates to the quality of a result whereas precision relates to the quality of the operation by which the result is obtained. The accuracy attained by field surveys is the product of the instructions or specifications to be followed during work and the precision in following those instructions. For example, the “accuracy of a surveyor’s tape” indicates the degree to which an interval of 100 feet, as measured on the tape, actually agrees with the exact interval of a standard 100 foot tape. If a tape indicates 100 feet when the interval it measures is only 99.97 feet, the tape contains an inaccuracy of 0.03 feet for every 100 feet measured. The accuracy of this particular tape, expressed as a fraction, is 0.03/100, or approximately 1/3,300. Precision denotes the degree of refinement in the performance of an operation or in the statement of a result. It relates to the quality of execution and is distinguished from accuracy, which relates to the quality of the result. The term “precision” not only applies to the fidelity of performing the necessary operations but, by custom, has been applied to methods and instruments used in obtaining results of a high order of accuracy. Precision is exemplified by the number of decimal places to which a computation is carried and a result stated. In a general way, the accuracy of a result should determine the precision of its expression. Precision does not have significance unless accuracy is also obtained. In measuring a linear distance with a tape graduated in feet that are subdivided into tenths, you can read (without estimation) only to the nearest tenth (0.1) of a foot. But with a tape graduated to hundredths of a foot, you can directly read distances measured to the nearest hundredth (0.01) of a foot. The apparent nearness of the second tape will be greater; that is, the second tape will have a higher precision. Nature does not allow for perfectly precise measurement. There is always some builtin and/or inherent error, amounting to the size of the smallest graduation. Precision for the first tape above, expressed as a fraction, is 0.1/100 or 1/1,000 and for the second tape, 1/10,000. Precision in measurements is usually expressed in a fractional form with unity as the numerator, indicating the allowable error within a certain limit as indicated by the denominator, such as 1/500. In this case, a maximum error of 1 unit per 500 units measured is acceptable. If the unit of measure is in feet, 1 foot of error for every 500 feet is acceptable. Surveys must be carried out with accuracy, opportunity for errors and mistakes must be avoided. The precision of a survey, however, depends upon the order of precision that is either specified or implied from the nature of the survey. 1429 The various orders of precision are absolute in meaning. Federal agencies control surveys and generally classify surveys into one of four orders of precision; namely, first order, second order, third order, and fourth order control surveys. The first order is the highest and the fourth order is the lowest standard of accuracy. Because of the type of instruments available in the Sengineering techBEEs, most surveys may not require a precision higher than a third order survey. When the order of precision is not specified, use Table 141 as a standard for a horizontal control survey when using the traverse control method. For surveys that call for a higher order of precision, use theodolites to obtain the required precision. Table 141 – Control Traverse Order of Precision. ORDER OF PRECISION MAX # OF AZIMUTH COURSES BETWEEN AZIMUTH CHECKS DISTANCE Mengineering techSUREMENT ACCURATE WITHIN MAXIMUM LINengineering techR ERROR OF CLOSURE MAXIMUM ERRORS OF ANGLES FIRST ORDER 15 35,000 1 25,000 1 2 seconds N or* 1.0 second per station SECOND ORDER 25 15,000 1 10,000 1 10 seconds N or* 3.0 seconds per station THIRD ORDER 50 7,500 1 5,000 1 30 seconds N or* 8.0 seconds per station FOURTH ORDER  3,000 1 1,000 1 2 minutes or compass
• N = the number of stations carrying azimuth.
• * = use whichever is smaller in value. Survey problems may require the use of the triangulation method. In such a case, use Table 142 as a guide for the order of precision if it is not specified in the survey. The practical significance of a prescribed or implied order of precision lies in the fact that the instruments and methods used must be capable of attaining the required precision. The precision of an instrument is indicated by a fraction in which the numerator is the inherent error. (In a one minute transit, the inherent error is one minute.) The denominator is the total number of units in which the error occurs. For a transit, this last then, is 1/5,400, adequate for a third order survey. Precision of a tape is given in terms of the inherent error per 100 feet. A tape that can be read to the nearest 0.01 feet has a precision of 0.01/100, or 1/10,000—adequate for second order work. 1430
For a closed traverse, attain a ratio of linear error of closure that corresponds to the order of precision prescribed or implied for the traverse. The ratio of linear error of closure is a fraction in which the numerator is the linear error of closure and the denominator is the total length of the traverse. To understand the concept of linear error of closure, study the closed traverse shown in Figure 1426. Beginning at station C, this traverse runs N30°E300 feet, thence S30°E300 feet, thence S90°W 300 feet. The end of the closing traverse, BC, lies exactly on the point of beginning, C. This indicates that all angles were turned and all distances chained with perfect accuracy, resulting in perfect closure, or an error of closure of zero feet. Table 142 – Triangulation Order of Precision. PRECISION APPLICATION BASE LINE Mengineering techSUREMENT MAX., PROBABLY ERROR TRIANGLE CLOSURE; MAX. AVERAGE ERROR LENGTH CLOSURE: MAX. DISCREPANCY BETWEEN Mengineering techSURED AND COMPUTED LENGTH BASE LINE FIRST ORDER Case I: For city and scientific study survey 1,000,000 1 1.0 seconds 100,000 1 Case II: Basic network of U.S. 1,000,000 1 1.0 seconds 50,000 1 Case III: All other purposes 1,000,000 1 1.0 seconds 25,000 1 SECOND ORDER Case I: Area networks and supplemental cross arcs in national net. 1,000,000 1 1.5 seconds 20,000 1 Case II: Costal areas, inland waterways, and engineering surveys. 500,000 1 3.0 seconds 10,000 1 THIRD ORDER Topographic mapping 250,000 1 5.0 seconds 5,000 1 1431 However, in reality, perfect accuracy in measurement seldom occurs. In actual practice, the closing traverse line, BC, (Figure 1426), is likely to be some distance from the starting point, C. If this should happen, and the total accumulated linear distance measured along the traverse lines is 900.09 feet, the ratio of error of closure then is .09/900 or 1/10,000. This resulting ratio is equivalent to the precision prescribed for second order work.
The sum of interior angles of a closed traverse will theoretically equal the product of 180° (n – 2), n being the number of sides in the polygon described by the traverse. A prescribed maximum angular error of closure is stated in terms of the product of a given angular value times the square root of the number of interior angles in the traverse. Again, if we use the traverse shown in Figure 1426 as an example, the prescribed maximum angular error of closure in minutes is 01 because the figure has three interior angles. The sum of the interior angles should be 180°. If the sum of the angles as actually measured and recorded is 179°57´, the angular error of closure is 03´. The maximum permissible error of closure is the product of 01´ times the square root of 3, or about 1.73´. The prescribed maximum angular error of closure has therefore been exceeded.
There are several specifications that provide a general idea of the typical precision requirements for various types of transit tape surveys. When linear and angular errors of closure are specified, a closed traverse is involved.
• Requirements for preliminary surveys and land surveys include the following: o Transit angles to the nearest minute, measured once o Sights on range poles plumbed by eye o Tape leveled by eye, and standard tension estimated o No temperature or sag corrections o Slopes fewer than three percent disregarded o Slopes over three percent measured by breaking chain or by chaining slope distance and applying calculated correction o Maximum angular error of closure in minutes is 1.5 o Maximum ratio linear error of closure, 1/1000 o Pins or stakes set to nearest 0.1 foot
• For most land surveys and highway location surveys, typical precision specifications may read as follows: o Transit angles to nearest minute, measured once o Sights on range poles, plumbed carefully o Tape leveled by hand level, with standard tension by tensionometer or sag correction applied Figure 1426 – A closed traverse with a perfect closure. 1432 o Temperature correction applied if air temperature more than 15° different from standard (68°F) o Slopes fewer than two percent disregarded o Slopes over two percent measured by breaking chain or by applying approximate slope correction to slope distance o Pins or stakes set to nearest 0.05 foot o Maximum angular error of closure in minutes is o Maximum ratio linear error of closure, 1/3,000
• For important boundary surveys and extensive topographical surveys, typical precision specifications include the following: o Transit angles by onerein transit, repeated four times o Sights taken on plumb lines or on range poles carefully plumbed o Temperature and slope corrections applied; tape leveled by level o Pins set to nearest 0.05 foot o Maximum angular error of closure in minutes is . o Maximum ratio linear error of closure is 1/5,000. Note that in the first two specifications, onetime angular measurement is considered sufficiently precise. Many surveyors, however, use twoline angular measurement customarily to maintain a constant check on mistakes
It is usually the case on a transittape survey that the equipment for measuring angles is considerably more precise than the equipment for measuring linear distances. This fact leads many surveyors towards a tendency to measure angles with great precision, while overlooking important errors in linear distance measurements. A precision of angular measurement greater than that of linear measurement is useless because angles are only as good as linear distances. Suppose a traverse line BC is run at a right deflection angle of 63°45´ from AB, 180.00 feet to station C. After setting up at B, orient the telescope to AB extended, and turn exactly 63°45´00´´ to the right. But instead of measuring off 180.00 feet, you measure off by 179.96 feet. Regardless of how precisely all of the other angles in the traverse are turned, every station will be dislocated because of the error in the linear measurement of BC. Remember that angles and linear distances must be measured with the same precision.
In transit work, errors are grouped into three general categories; namely, instrumental, natural, and personal errors.
'A transit does not measure angles accurately unless the instrument meets these conditions:
• The vertical cross hair must be perpendicular to the horizontal axis. If the vertical cross hair is not perpendicular, the measurement of horizontal angles will be inaccurate.
• The axis of each of the plate levels must be perpendicular to the vertical axis. If they are not, the instrument cannot be accurately leveled. If the instrument is not level, the measurement of both horizontal and vertical angles will be inaccurate.
• The line of sight through the telescope must be perpendicular to the horizontal axis. If it is not, the line of sight through the telescope inverted will not be 1800 opposite the line of sight through the telescope erect.
• The horizontal axis of the telescope must be perpendicular to the vertical axis. If it is not, the measurement of both horizontal and vertical angles will be inaccurate.
• The axis of the telescope level must be parallel to the line of sight through the telescope. If it is not, the telescope cannot be accurately leveled. If the telescope cannot be accurately leveled, vertical angles cannot be accurately measured.
• The point of intersection of the vertical and horizontal cross hairs must coincide with the true optical axis of the telescope. If it doesn’t, measurement of both horizontal and vertical angles will be inaccurate. Note Any or all of the above conditions may be absent in an instrument that is defective or damaged, or one that needs adjustment or calibration.
Common causes of natural errors in transit include:
• The tripod is set in yielding soil. If the tripod settled evenly—that is, if the tip of each leg settled precisely the same amount—there would be little error in the results of measuring horizontal angles. Settlement is usually uneven, however, which results in the instrument not being level.
• Refraction can be a problem; however, its effect is usually negligible in ordinary precision surveying.
• Unequal expansion or contraction of instrument parts caused by excessively high or low temperature can also be a problem, but for ordinary precision surveying, the effect of this is also usually negligible.
• High wind may cause plumbing errors when you are plumbing with a plumb bob and cord and may also cause reading errors because of instrument vibration.
'Personal errors are the combined results of carelessness and the eye’s physical limitations in setting up, leveling the instrument, and making observations. Common causes of personal errors in transit work include:
• Failure to plumb the vertical axis exactly over the station  Inaccuracy increases drastically as the sight distance decreases (Figure 1427). As shown, an instrument that was supposed to be set up at A was actually set up at A´, 40 feet away from A. (For demonstration purposes the figure was exaggerated to magnify the error; in actual practice the eccentricity amounts only to a fraction of an inch. Remember that mathematically, one inch is the arc of one minute when the radius is 300 feet.). In the upper view, you can see that with B located 300 feet from A, the angular error caused by the displacement is about eight degrees. In the lower view, however, with B located only 100 feet from A, the angular error 1434 caused by the displacement is about 22°. The practical lesson to be learned from this is to always plumb the instrument much more carefully for a short sight than for a long one.
• Failure to center plate level bubbles exactly  The consequent error is at a minimum for a horizontal sight and increases as a sight is inclined. The practical lesson is to always level the instrument very carefully for an incline sight.
• Inexact setting or reading of a vernier  The use of a small, powerful pocket magnifying glass is helpful here. Also, after determining the vernier graduation that most nearly coincides with a limb graduation, check the selection by examining the graduations on either side. These should fall in coincidence with the limb counterparts by about the same amount.
• Failure to line up the vertical cross hair with the true vertical axis of the object sighted  The effect is similar to that of not plumbing exactly over the station, which means that the error increases drastically as the length of the sight decreases.
• Failure to bring the image of the cross hair or that of the object sighted into clear focus (parallax)  A fuzzy outline makes exact alignment difficult. Common mistakes in transit work include:
• Turning the wrong tangent screw  For example, turning the lower tangent screw after taking a backsight, introduces an error into the backsight reading.
• Forgetting to tighten the clamp(s), or allowing a clamp slipping when it is supposed to be tight
• Reading in the wrong direction from the index (zero mark) on a double vernier
• Reading the wrong vernier; for example, reading the vernier opposite the one that was set
• Reading angles in the wrong direction; that is, reading from the outer row rather than the inner row, or vice versa, on the horizontal scale
• Failure to take a fullscale reading before reading the vernier  For example, you may drop 20 to 30 minutes from the reading, erroneously recording only the number of minutes indicated on the vernier, such as 15°18´ instead of 15°48´. Do not be so intent on reading the vernier that you lose track of the fullscale reading of the circle.
'The accuracy and quality of a survey depends upon the condition of the surveying instrument and the experience of the surveyor. The life expectancy and usefulness of Figure 1427 – Exaggerated illustration of error caused when the transit is not centered exactly over the occupied station. 1435 an instrument can be extended considerably by careful handling, stowing, and maintenance. Every instrument is accompanied by an instruction manual that indicates not only the proper operation and components of the instrument but also procedures for its care and maintenance. Study this instruction manual thoroughly before attempting to use any instrument.
Every transit, theodolite, and level comes equipped with a carrying box or case. The instrument and its accessories can be stowed in the case in a manner that ensures a minimum of motion during transportation. Always stow instruments in their carrying cases when not in use.
In general, all surveying instruments, equipment, and tools must be cleaned thoroughly immediately following use. For example, dust off the transit or theodolite and wipe it dry before placing it back in its case after each use. Remove all dust with a clean cloth. This applies particularly to the optical parts. Chamois leather is suitable for this purpose, but a clean handkerchief is better than a soiled chamois leather. Do not use liquid for cleaning — no water, petroleum products, or oil. If necessary, breathe on the lenses before polishing them. When the instrument becomes wet, remove its case and dry it thoroughly at room temperature as soon as is convenient. If you leave the instrument in the closed case, the air inside the hood will take up humidity by increasing temperature and will in time diffuse inside the instrument. While cooling off, the water will condense and form a coating or tarnish that may make any sighting with the telescope and reading of the circles difficult. Remove any mud or dirt that may adhere to the tripod, range pole, level rod, and so forth, after each use. Clean each piece of equipment after each use to eliminate the chance of forgetting to later. This is important, especially when the surveying gear is made of a material susceptible to rust action or decay. When lubricating the instruments, use the recommended lubricant for each part in conjunction with the climatic condition in your area. For instance, graphite is the recommended lubricant for transit moving parts when the transit is to be used in subzero temperatures as opposed to the typical light film of oil (preferably watch oil) used in normal weather conditions. Apply the lubricant thinly to avoid making easy repositories for dust. Consult the manufacturer’s manual or your senior engineering tech whenever you are in doubt before doing anything to an instrument.
Test Your Knowledge 4. When typing in a point to a station on a traverse, which of the following conditions should you carefully consider?
5. What is the recommended lubricant for surveying instruments at subzero temperatures?
6. A temperature correction applied to tape measurements is considered to be a typical precision specification for which of the following surveys?

A survey traverse is a sequence of lengths and directions of lines between points on the earth, obtained by or from field measurements and used in determining positions of the points. A survey traverse may determine the relative positions of the points that it connects in series; and, if tied to control stations based on some coordinate system, the positions may be referred to that system. From these computed relative positions, additional data can be measured for layout of new features, such as buildings and roads. Traverse operations (commonly called traversing) are conducted for basic area control, mapping, large construction projects such as military installation or air bases; road, railroad, and pipeline alignment, control of hydrographic surveys, and for many other projects. In general, a traverse is either a closed traverse or an open traverse. A closed loop traverse (Figure 14 28, view A), as the name implies, forms a continuous loop, enclosing an area. This type of closed traverse starts and ends at the same point, whose relative horizontal position is known. A closed connecting traverse (Figure 1428, view B) starts and ends at separate points, whose relative positions have been determined by a survey of an equal or higher order accuracy. An open traverse (Figure 1428, view C) ends at a station whose relative position is not previously known, and unlike a closed traverse, provides no check against mistakes and large errors. Open traverses are often used for preliminary survey for a road or railroad. Figure 1428 – Types of traverses. 1437 The order of accuracy for any traverse is determined by the equipment and methods used in the traverse measurements, by the accuracy attained, and by the accuracy of the starting and terminating stations. Hence, the order of accuracy is specified before the measurements are started. For engineering and mapping projects, the distance measurement accuracy for both electronic and taped traverses for first, second, and third order are 1/35,000, 1/15,000, and 1/7,500, respectively. For military use such as field artillery, lower order accuracies of fourth, fifth, and sixth are 1/3,000, 1/1,000, and 1/500, respectively. The order referred to as lower order is applied to all traverses of less than third order. To accomplish a successful operation, the traverse party chief must ensure that initial preparations and careful planning are done before the actual traversing begins.
A traverse party may vary in size anywhere from two to twelve personnel, all under the supervision of a traverse party chief. A traverse party usually consists of a distance measuring crew, an angle crew, sometimes a level crew, and other support personnel. This breakdown of personnel is ideal, but on many occasions, the same personnel will have to perform a variety of tasks or functions. Therefore, each party member is trained to assume various duties and functions in several phases of the work survey.
Whenever possible, make a reconnaissance to determine the starting point, the route to be followed, the points to be controlled, and the closing station. When selecting the starting and closing points, select an existing control station that was determined by a survey whose order of accuracy was equal to or greater than the traverse to be run. When running a traverse in which the direction of the traverse lines are not fixed before the start, select a route that offers minimum clearing of traverse lines. Use the best available maps and aerial photographs during the office and field reconnaissance. By selecting a route properly, you can lay out the traverse to pass relatively close to points that have to be located or staked out. On other surveys, such as road center line layout, predetermine the directions of the traverse lines, and clear all obstructions, including large trees, from the line. Often the assistance of the equipment and construction crews is needed at this point. For the lower order surveys and where you use taping, select the exact route and station locations as the traverse progresses. Always select these stations so that at any one station, both the rear and forward stations are visible, and only a minimum number of instrument setups is kept, reducing the possibility of instrument error and the amount of computing required. Furthermore, the Electronic DistanceMeasuring (EDM) devices have made traverse reconnaissance even more important. Consider the possibility of using an EDM after the general alignment in direction and the planned positioning of stations. A tower or platform installed to clear surface obstruction will permit comparatively long optical sights and distance measurements, hence avoiding the necessity of taping it in short increments.
ome station marks are permanent markers, and some are temporary markers, depending upon the purpose of the traverse. A traverse station that will be reused over a period of several years is usually marked in a permanent manner. Permanent traverse 1438 station markers take various forms, including iron pipe filled with concrete, a crosscut in concrete or rock, or a hole drilled in concrete or rock and filled with lead, with a tack to mark the exact reference point. Temporary markers are used on traverse stations that may never be reused, or perhaps will be reused only a few times within a period of one or two months. Temporary traverse station markers are usually twoinch by twoinch wooden hubs, 12 inches or more in length. They are driven flush with the ground and have a tack or small nail on top to mark the exact point of reference for angular and linear measurements. To assist in recovering the hub, a oneinch by twoinch wooden guard stake, 16 inches or more in length is driven at an angle so that its top is about one foot over the hub. Keel (lumber crayon) or a large marking pen is used to mark letters and/or numbers on the guard stake to identify the hub. The marked face of the guard stake is toward the hub. Since many of the hubs marking the location of road center lines, landing strips, and other projects will require replacement during construction, reference marks are placed several hundred feet or meters away from the station they reference. Reference marks, usually similar in construction to that of the station hub, are used to reestablish a station if its marker has been disturbed or destroyed.
As previously discussed, the starting point of a closed traverse must be a known position or control point; and, for a closed loop traverse, this point is both the starting and closing point. Closed connecting traverses start at one control point and tie into another control point. A traverse starting point should be an existing station with another station visible for orienting the new traverse. The adjacent station must be intervisible with the starting point to make the tie easy. If you do not find the adjacent station easily, observe an astronomic azimuth to orient the starting line, and then continue the traverse. Any existing control near the traverse line should be tied into the new work.
As traversing progresses, conduct linear measurements to determine the distance between stations or points. Generally, the required traverse accuracy will determine the type of equipment and the method of measuring the distance. For the lower orders, a single taped distance is sufficient. However, as the order of accuracy gets higher, DOUBLE TAPING (once each way) is required. Compare ordinary steel tapes to an Invar or Lovar tape at specified intervals. For the highest accuracy, use electronic distancemeasuring devices (EDM) to measure linear distances. Linear measurements may also be made by indirect methods, using an angle measuring instrument like the transit or theodolite with stadia. When determining the distances by stadia readings, read the vertical angles and use them to convert slope distances to horizontal distances. If double taping or chaining is required, follow these procedures:
Horizontal angles formed by the lines of each traverse station determine the relative directions of the traverse lines. These angles are measured using a transit or a theodolite, and can also be determined graphically with a plane table and alidade. In a traverse, three traverse stations are significant: the rear station, the occupied station, and the forward station (Figure 1429). Figure 1429 – Traverse stations and angles. The rear station is the station from which the crew performing the traverse has just moved, or is a point, the azimuth to which is known. The occupied station is the station at which the crew is now located and over which the surveying instrument is set. The forward station is the next station in succession and constitutes the immediate destination of the crew. The stations are numbered consecutively starting at one and continuing throughout the traverse. In addition to the number of the station, an abbreviation indicating the type of traverse is often times included; for example, ET for electronic traverse or TT for theodolite or transittape traverse. Always measure horizontal angles at the occupied station by pointing the instrument toward the rear station and turning the angle clockwise to the forward station for the direct angle and clockwise from the forward to the rear station for the explement (Figure 1430). If you use a deflection angle, plunge the instrument telescope after sighting the rear station, and read the angle left or right of the forward station. 1440 Figure 1430 – Kinds of angles measured at the occupied station.
Test Your Knowledge 7. In double taping between traverse stations, you should use which of the following procedures? A. Use only tapes that are calibrated. B. Ensure the stations are spaced so that the distance between stations is less than a fulltape length. Continue taping until the tiein control point is reached; then retape all measurements C. D. Retape line measurements not within allowable limits. 8. Closed traverses are often used for preliminary surveying of roads and railroads. A. True B. False 9. Which of the following traverse stations may be a point with a known azimuth location? A. Forward B. Rear C. Occupied 
This lesson presented you with information relating to the determination of distance and direction. Specifically, you were introduced to conversion methods for bearings, deflections, and interior and exterior angles, through arithmetic and the use of a compass. After being familiarized with distance and direction, you were presented with the procedures used to conduct transit tape surveys, which includes such tasks as meeting the required order of precision, identifying errors and mistakes, as well as caring for equipment and instruments. Finally, the steps necessary to conduct accurate traverse operations was covered, including organizing the survey party, conducting reconnaissance, and performing the surveying tasks.
1. A traverse that has been established and is used to locate detail points and objects are located is a _______.
2. In true geographical direction, the reference line is the meridian passing through the point where the observer is located, and the direction of a line passing through that point is described in terms of the horizontal angle between that line and the meridian.
3. The bearing of line AB in the traverse is S2726’W and the bearing of the line BC is N10°17’W. What is the deflection angle between AB and BC in the figure?
4. The directions of traverse lines AB and BC are indicated by deflection angles. Determine the bearing of BC by using the figure.
5. How many degrees are there in the exterior angle ABC as shown in the figure?
6. How many degrees are here in the interior angle ABC as shown in the figure?
7. To convert a bearing in the SE quadrant to the equivalent azimuth, you must use which of the following calculations?
8. Assume that a measured forward bearing on a compasstape survey was N15°35’W and the back bearing on the same line was S15°15’E. The difference was probably caused by which of the following conditions?
9. The magnetic declination at a given point on the surface of the earth is the horizontal angle that the magnetic meridian makes with what line?
10. What is the appropriate compass bearing of the object in the figure?
11. What is the approximate magnetic bearing of the object if the local attraction is 20°E?
12. What method should you use to correct or convert a compass azimuth reading to a true azimuth reading when both local attraction and local declination are easterly?
13. When making a closed traverse compasstape survey, why should you first read and record the back bearing of a traverse line from the first setup point?
14. What is the sum of the interior angles in a closed traverse consisting of size traverse lines?
15. If a compass is in error when you are taking bearings at several different places and each error varies from the preceding one, the errors are probably due to which of the following factors?
16. The only compass available for taking bearings has an instrument error. What forward bearing should you use when the compass needle indicates a forward bearing of N22°W and a back bearing of S24°E?
17. You are using a compass that has an instrument error and is graduated for azimuths. What forward azimuth should you record when the compass needle indicates a forward azimuth of 37° and a back azimuth of 219°?
18. Which of the following defects is most likely to cause a compass to read incorrectly at both ends of its needle?
19. A compass needle that is weak magnetically should be strengthened by which of the following methods?
20. A compass needle acts sluggishly although it has retained its full magnetism. Which of the following methods should be used to make the needle act as it should?
21. In setting up and leveling a transit, you have followed all of the correct procedures. You discover, however, that the plumb bob is still not quite directly over the station point. Which of the following actions should be taken next?
22. Before taking up the transit, which of the following actions should you take concerning the telescope and the vertical motion clamp?
23. In which of the following ways are the horizontal limbs of transits numbered?
24. When you are turning a 40° horizontal angle by transit, what part will normally point to the number of degrees turned?
25. Releasing the upper motion of a transit enables you to take which of the following actions?
26. Which of the following steps should you normally take when turning a 20° horizontal angle from a reference line with a transit?
27. To fix the exact position of the horizontal limb with respect to the Avernier, what transit screw, if any, should you use?
28. The closingthehorizon method of checking the accuracy of angular measurements is based on the geometric fact that the sum of the:
29. A vertical angle was recorded at +36°. This angle is a measurement of what type?
30. You are measuring a 30° angle with a oneminute transit. To improve the precision of this measurement, you turn the angle a total of four times. If the plate reading after the fourth measurement is 119°59’, what is the size of the angle turned?
31. You have measured an angle using the repetition procedure. If the original measurement was 37°22’ and your sixth and last repeat was 224°12’42”, what is the mean angle?
32. Which of the following procedures is a method for extending a straight line?
33. What step in the doublecentering procedure is taken just before the instrument is rotated through 180° in the horizontal plane?
34. When double centering resets in two different extension points, what procedure should you use?
35. After recording the deflection angle at D as shown in the figure, what is the next step?
36. If you use the angle offset method of bypassing an obstacle, what is the size of the deflection angle at C as shown in the figure?
37. Which of the following distances is equal to CD as shown in the figure?
38. What is the deflection angle at point D as shown in the figure?
39. The angle offset and the perpendicular offset methods are useful in establishing a survey line under which of the following conditions?
40. The “balancing in” process should be used to locate an intermediate point between two control points on a survey line under which of the following conditions? approximately equal
41. If deflection angles α and β as shown in the figure are four and six minutes, respectively, and distance a is four feet, how far should you set up the instrument from B’ so that it is exactly in line with points A and C?
42. For which of the following situations should the random line method be used?
43. What typingin method should you use when locating the configuration of an irregular shoreline from a traverse line?
44. What meaning is generally given to the term “settling a point”?
45. You can tiein a point or set a point to two stations on a traverse by taking which of the following measurements?
46. Surveyors use straddlers for what purpose?
47. You must set a marker at a certain point from traverse station 3 + 00 and 4 + 25. The angle from the traverse line to station 3 + 00 and the distance between the point and station 4 + 25 are given. How should you proceed to set the point?
48. A closed traverse was to be 15,000 feet in length. The last course was to be 3,000 feet in length. After you turn the last deflection angle and progress 3,000 feet on the last course, you find that you are three feet from the starting point of the traverse. What is the order of precision?
49. If precision of 1/20,000 is required, what is the maximum allowable error of closure for a traverse of 10,560 feet?
50. Which of the following errors in a transit affects both horizontal and vertical angle measurements?
51. Which of the following personal errors results in a larger error for inclined sights than for horizontal sights?
52. Which of the following situations is considered a mistake in transit work?
53. The carrying case for a transit or a theodolite is specifically designed for which of the following conditions?
54. Which of the following actions should you take after an instrument has been exposed to rain and has been wiped down with a clean cloth or chamois leather?
55. Which of the following statements describes the characteristics of an open traverse as compared to a closed connecting traverse?