1.15. MEASUREMENT OF DIRECTIONAL ANGLES ON THE MAP

Protractor measurement. With a finely sharpened pencil, carefully along the ruler, draw a line through the main points of the conventional signs of the starting point and landmark. The length of the drawn line must be greater than the radius of the protractor, counting from the point of its intersection with the vertical line of the coordinate grid. Then combine the center of the protractor with the intersection point and rotate it, in accordance with the angle, as shown in Fig. 27. Counting against the drawn line at the position of the protractor indicated in fig. 27, a, will correspond to the value of the directional angle, and with the position of the protractor indicated in fig. 27.6, 180° must be added to the reading.

When measuring the directional angle, it must be remembered that the directional angle is measured from the north direction of the vertical grid line in a clockwise direction.

The average error in measuring the directional angle with a protractor on the commander's ruler is approximately 1°. Large protractor (with a radius of 8-10 cm) the angle on the map can be measured with an average error of 15".

Rice.27. Measurement of directional angles with a protractor

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Chordugometer measurement (Fig. 28). Through the main points of the conventional signs of the starting point and landmark, draw a thin straight line on the map with a length of at least 12 cm. From the point of intersection of this line with the vertical grid line of the map, with a compass, serifs are made on them with a radius equal to the distance on the chordo-angle measure from 0 to 10 large divisions. Serifs are made on the lines forming sharp corner.

Then the chord is measured - the distance between the marks of the pending radii. To do this, the left needle of the measuring compass with a delayed chord is moved along the extreme left vertical line of the scale of the chordouglometer until the right needle of the compass coincides with any intersection of the inclined and horizontal lines. In this case, the right needle must be moved strictly at the same level as the left one. In this position, the compass is counted against its right needle. On the upper part of the scale, large and tens of small divisions are counted. On the left side of the scale with the price of divisions 0-01 specify the value of the angle. An example of measuring an angle with a chordo-goniometer is shown in the figure.

An acute angle is measured from the nearest vertical grid line using a chord-angle meter, and the directional angle is measured from the north direction of the grid line in a clockwise direction. The value of the directional angle is determined by the change

Rice.28. Measuring the directional angle with a chord goniometer

angle, depending on the quarter in which the landmark is located. Relationship between measured angle a" and directional angle a is shown in Fig. 29.

Angles can be measured with a chord goniometer with an average error of 0-01-0-02 div. ang. (4- 8").

Rice. 29.The transition from the angle a "measured with a chord goniometer to the directional angle a

Measurement by an artillery circle. The center of the circle is combined with the starting point (the main point of the conventional sign) and the circle is set so that its diameter 0-30 is parallel to the vertical lines of the coordinate grid, and zero is directed to the north. Then the scale bar is aligned with the main point of the conventional landmark sign, and at the intersection of the edge of the ruler with the scale of the circle, the angle is read.

An artillery circle can measure the directional angle without a scale bar (Fig. 30). In this case, a line is first drawn on the map through the main points of the conventional signs of the starting point and landmark. Then the artillery circle is set, as indicated above, and against the drawn line, the value of the directional angle is read on the scale of the circle.

The initial directional angle is calculated in accordance with the task. According to the initial directional angle, which, for example, for side 1-2 is equal to 49 0 30′ , we calculate the directional angles of the remaining sides of the theodolite traverse. Calculations are carried out according to the rule: the directional angle of the next side is equal to the directional angle of the previous side plus 180 0 and minus the corrected horizontal angle lying to the right along the course:

last . = prev.+ 180 0 - β (23)

For example:

2-3 = 49 0 30′ + 180 0 - 98 0 07′ =131 0 23′ ;

3-4 = 131 0 23′ + 180 0 - 153 0 27′= 157 0 56′ ;

.........................…………………

6-1 = 224 0 44 ′+ 180 0 - 52 0 44 ′ =352 000′ ;

1-2 = 352 0 00 ′+ 180 0 - 122 0 30 ′ =4 9 0 30 ′ .

If during the calculation the reduced angle turns out to be less than the subtracted one, then 360 0 must be added to the reduced angle. If the calculated directional angle is greater than 360 0 , 360 0 is subtracted from it. The directional angle of the original side 1-2, obtained at the end, serves as a calculation control.

Using the formulas for the relationship of directional angles and points (table 5), the values ​​of the directional angles calculate the points.

Table 5

In the statement of calculation of coordinates, records of horizontal distances and their directional angles and points are made in the line between the end points of the line to which they refer.

2.1.4 Calculation of coordinate increments and adjustment of linear measurements

The next stage of processing is the calculation of the increments of the coordinates of each front vertex of the line relative to the back. Coordinate increments ΔX and ΔY are calculated using a microcalculator with an accuracy of 0.01 m according to the formulas:

∆X=Dcos , ∆Y=Dsin ;

∆X= Dcos g, ∆Y= Dsin g;

Coordinate increments are recorded with their signs in columns 7 and 8 on the same line with the corresponding horizontal distance D and directional angle . The sign of the increment of coordinates is determined in the direction of the rhumb along (Table 6.)

Table 6

For a closed traverse, the theoretical values ​​of these quantities must be zero:

Σ∆X m =0, Σ∆Y m =0. (25)

But due to errors in the measurements of the lines, the values ​​of the sums are obtained other than zero. ƒ x and ƒ values y are called residuals of increments of coordinates along the X and Y axes and calculate:

Σ∆X= ƒ x , Σ∆Y= ƒ y. (26)

Before distributing these discrepancies, it is necessary to make sure that they are admissible, for which it is necessary to calculate the absolute discrepancy of the traverse perimeter.

The absolute discrepancy of the perimeter of the theodolite traverse is calculated using the Pythagorean theorem:

ƒ p =√(ƒ x 2 + ƒ y 2).(27)

The accuracy of the theodolite traverse is estimated by the value of the relative discrepancy, which should not exceed 1/2000 of the perimeter, i.e.: ƒ R/p 1/2000, where P is the perimeter of the polygon.

If the residual in the perimeter is admissible, then the residuals ƒ x and ƒ y distribute with the opposite sign to all increments ∆X i and ∆Y i ; directly proportional to the line lengths rounded to 0.01 m. The corresponding corrections are calculated using the formulas:

V ∆X i = (-ƒ x / P) D i , V ∆ yi = (-ƒ y / P) D i (28)

The control for calculating corrections is equality: the sum of corrections in increments along the abscissa and ordinates must be equal to the corresponding discrepancy with the opposite sign.

By adding the calculated corrections to ∆X i and ∆Y i , the corrected values ​​of the coordinate increments are obtained, which are recorded in columns 9 and 10.

The control for calculating the corrected increments of coordinates will be equalities:

∆X Spanish=0

The position of any object on the ground is most often determined and indicated in polar coordinates, that is, the angle between the initial (given) direction and the direction to the object and the distance to the object. The direction of the geographical (geodesic, astronomical) meridian, magnetic meridian or vertical line of the coordinate grid of the map is chosen as the initial one. The direction to some remote landmark can also be taken as the initial one. Depending on which direction is taken as the initial one, there are geographical (geodesic, astronomical) azimuth A, magnetic azimuth Am, directional angle.

The relationship between magnetic azimuth, bearing angle, and geodetic (true) azimuth is shown in Fig. 24.

Magnetic azimuth Am– horizontal angle counted from the north direction of the magnetic meridian in a clockwise direction to the direction towards the object.

Directional angle α– the angle between the north direction of the vertical line of the coordinate grid of the map and the direction to the local object (landmark), counted clockwise.

Geodetic (true) azimuth Ai- the angle between the north direction of the geodetic (true) meridian (the side of the map frame or a line parallel to it) and the direction to the object, counted clockwise. The direction of the geodesic meridian on the topographic map corresponds to the sides of its frame, as well as straight lines that can be drawn between the minute divisions of the same name.

Magnetic, geodetic azimuth, as well as directional angle, can have values ​​from 0° to 360°.

Rice. 24. Relationship between magnetic azimuth,

directional angle and geodetic azimuth

Approach of meridians γ is the angle between the north direction of the geodetic meridian and the vertical line of the coordinate grid. The convergence of the meridians is measured from the north direction of the geodetic meridian along or counterclockwise to the north direction of the vertical grid line. For points located to the east of the geodetic meridian, the proximity value is positive, and for points located to the west, it is negative. On topographic maps of the Republic of Belarus, the convergence of the meridians does not exceed ±3°. The essence of the convergence of the meridians is shown in fig. 25.

Rice. 25. The essence of convergence of meridians

The value of convergence of the meridians, indicated on the topographic map in the lower left corner, refers to the center of the map sheet.

Magnetic declination δ is the angle between the north direction of the geodesic meridian and the direction of the magnetic meridian (magnetic needle). If the northern end of the magnetic needle deviates from the geodetic meridian to the east, the magnetic declination is considered positive, and to the west - negative.

Heading Correction (PN) is the angle between the direction of the vertical line of the coordinate grid and the magnetic meridian. It is equal to the algebraic difference between the magnetic declination and the approach of the meridians:

PN = (± δ ) – (± γ ).

Data on magnetic declination, convergence of meridians and the value of the directional correction are placed under the south side of the frame of each sheet of a large scale topographic map. The transition from the directional angles and geodetic azimuths measured on the map to magnetic azimuths is carried out according to the formulas

Am \u003d α - (± PN);

Am \u003d A - (± δ ).

Measurement on the map of directional angles. Directional angles of directions to local objects (landmarks) are measured on the map with a protractor, an artillery circle and a chord goniometer.

With a protractor, the directional angle on the map is measured in the following sequence:

the landmark on which the directional angle is measured is connected by a straight line to the standing point so that this straight line is greater than the radius of the protractor and crosses at least one vertical line of the coordinate grid;

combine the center of the protractor with the intersection point, as shown in Fig. 26, and the value of the directional angle is counted along the protractor.

Rice. 26 . Measurement of directional angles on the map with a protractor

In our example, the directional angle from the origin to the pit is 65°, and the directional angle from the origin to the bridge is 274°.

Artillery Circle is a celluloid plate, on the outer edge of which a scale is applied in divisions of the goniometer. The price of one division is 0-10. Major divisions corresponding to 1-00 are digitized from 0 to 60; at the same time, a number of red numbers are applied in ascending order clockwise, and a number of black numbers - counterclockwise.

When measuring the directional angle, the artillery circle is set on the map so that its center coincides with the point of intersection of the line of the determined direction and the vertical line of the coordinate grid, and the zero stroke is with the northern direction of this line. Then the reading is taken on the red scale of the circle against the line of the determined direction.

Measurement of the angle using a chordo-goniometer is performed in this order. Through the main points of the conventional signs of the starting point and the local object, on which the directional angle is determined, a thin straight line with a length of at least 15 cm is drawn on the map. From the point of intersection of this line with the vertical line of the coordinate grid of the map, a compass-measuring instrument makes serifs on the lines that form an acute angle with a radius equal to the distance on the chord-angle meter from 0 to 10 large divisions. Then measure the chord - the distance between the marks. Without changing the solution of the measuring compass, its left needle is moved along the extreme left vertical line of the scale of the chordoangular meter until the right needle coincides with any intersection of the inclined and horizontal lines. The left and right needles of the measuring compass must always be on the same horizontal line. In this position, the needles are read off by the chord-angle meter.

If the angle is less than 15-00 (90°), then large divisions and tens of small divisions of the goniometer are counted on the upper scale of the chordogoniometer, and units of goniometer divisions are counted on the left vertical scale.

The position of any object on the ground is most often determined and indicated in polar coordinates, that is, the angle between the initial (given) direction and the direction to the object and the distance to the object. The direction of the geographic (geodesic, astronomical) meridian, magnetic meridian or vertical line of the coordinate grid of the map is chosen as the initial one (Figure 106). The direction to some remote landmark can also be taken as the initial one. Depending on which direction is taken as the initial one, there are geographical (geodesic, astronomical) azimuth A, magnetic azimuth Am, directional angle α and position angle 0.

Geographic (geodetic, astronomical) azimuth- this is the dihedral angle between the plane of the meridian of a given point and the vertical plane passing in a given direction, counted from the north direction in a clockwise direction. The geodetic azimuth is the dihedral angle between the plane of the geodesic meridian of a given point and the plane passing through the normal to it and containing the given direction. Dihedral angle between the plane of the astronomical meridian of a given point and the vertical plane passing in a given direction is called the astronomical azimuth.

Magnetic azimuth- horizontal angle measured from the north direction of the magnetic meridian in a clockwise direction.

The directional angle α is the angle between the passing through given point direction and a line parallel to the x-axis, counted from the north direction of the x-axis in a clockwise direction.

All of the above angles can have values ​​from 0 to 360°.

Position angle 0 is measured on both sides of the direction taken as the initial one. Before naming the position angle of the object, indicate in which direction (to the right, to the left) from the initial direction it is measured.

Protractor directional angles measured in this order (Figure 107). The starting point and the local object are connected by a straight line; the length of which from the point of its intersection with the vertical line of the coordinate grid must be greater than the radius of the protractor. Then the protractor is combined with the vertical line of the coordinate grid, in accordance with the angle. The reading on the protractor scale against the drawn line will correspond to the value of the measured directional angle. The average error in measuring the angle with a protractor is 0.5°

Figure 107 - Measurement of directional angles on the map with a protractor: a- directional angle of direction to the bridge is 274 o; b- directional angle to the pit is 65.

To draw on the map the direction specified by the directional angle in degrees, it is necessary through main point symbol of the starting point, draw a line parallel to the vertical line of the coordinate grid. Attach a protractor to the line and put a dot against the corresponding division of the protractor scale (reference), equal to the directional angle. After that, draw a straight line through two points, which will be the direction of this directional angle.

convergence of meridians. Transition from geodetic azimuth to directional angle. Convergence of meridians (see subsection 1.2.4).

The essence of the convergence of the meridians in expanded form is shown in Figure 108.

direction The geodesic meridian on the topographic map corresponds to the sides of its frame, as well as straight lines that can be drawn between the minute longitude divisions of the same name.

The geodetic azimuth of the direction differs from the directional angle by the amount of convergence of the meridians (Figure 109).

Magnetic declination. Transition from magnetic azimuth to geodetic azimuth. The property of a magnetic needle to occupy a certain position at a given point in space is due to the interaction of its magnetic field with the earth's magnetic field.

Negative convergence of meridians. Positive convergence of meridians.

Figure 108 - Essence of convergence of meridians.

Figure 109 - Dependence between geodetic azimuth, directional angle and convergence of meridians.

The direction of the steady magnetic needle in the horizontal plane corresponds to the direction of the magnetic meridian at the given point. The magnetic meridian generally does not coincide with the geodesic meridian.

The angle between the geodesic meridian of a given point and its northward magnetic meridian is called the declination of the magnetic needle or magnetic declination.

The magnetic declination is considered positive if the northern end of the magnetic needle is deflected east of the geodetic meridian (Eastern declination), and negative if it is deflected west (Western declination).

The relationship between geodetic azimuth, magnetic azimuth and magnetic declination (Figure 110) can be expressed by the formula:

Magnetic declination changes with time and place. Changes are either permanent or random. This feature of the magnetic declination must be taken into account when accurately determining the magnetic azimuths of the directions of measures, when preparing the movement along azimuths, etc.

Figure 110 - Relationship between geodetic azimuth, magnetic azimuth and magnetic declination

Changes in magnetic declination are due to the properties of the Earth's magnetic field.

Earth's magnetic field- space around earth's surface, in which the effects of magnetic forces are found. Their close relationship with changes in solar activity is noted.

Vertical plane b, passing through the magnetic axis of the arrow, freely placed on the tip of the needle, is called the plane of the magnetic meridian. The magnetic meridians converge on Earth at two points called the north and south magnetic poles (Mi Mi), which do not coincide with the geographic poles. The north magnetic pole is located in northwest Canada and moves northwest at a rate of about 16 miles per year. The south magnetic pole is located in Antarctica and is also moving. In this way; they are wandering poles.

There are secular, annual and daily changes in magnetic declination.

century changes magnetic declination is a slow increase or decrease in its value from year to year. Having reached a certain limit, they begin to change in the opposite direction. For example, in London 400 years ago the magnetic declination was + 11°20". Then it decreased and in 1818 it reached - 24°38". After that, it began to increase and currently is about 1 - 11 °. It is assumed that the period of secular changes in magnetic declination is about 500 years.

To facilitate accounting magnetic declination at different points on the earth's surface are special maps of magnetic declination, on which points with the same magnetic declination are connected by curved lines. These lines are called isogons. They are applied to topographic maps at scales of 1:500,000 and 1:1,000,000.

The maximum annual changes in magnetic declination do not exceed 14 - 16. Information about the average magnetic declination for the territory of the map sheet, related to the moment of its determination, and the annual change in magnetic declination are placed on topographic maps at a scale of 1: 200,000 and larger.

During the day magnetic declination makes two oscillations. By 8 o'clock the magnetic needle occupies the last eastern position, after which it moves to the west until 14:00, and then until 23:00 it moves to the east. Until 3 o'clock it moves to the west for the second time, and by sunrise it again occupies the extreme eastern position. The amplitude of such fluctuations for middle latitudes reaches 15. With an increase in the latitude of the place, the amplitude of the fluctuations increases.

It is very difficult to take into account daily changes in the magnetic declination.

Random changes in magnetic declination include perturbations of the magnetic needle and magnetic anomalies.

Magnetic needle perturbations, covering vast areas, are observed during earthquakes, volcanic eruptions, auroras, thunderstorms, the appearance of a large number spots on the Sun, etc. At this time, the magnetic needle deviates from its usual position, sometimes up to 2 - 3 °. The duration of disturbances ranges from several hours to two or more days.

Deposits of iron, nickel and other ores in the bowels of the Earth have a great influence on the position of the magnetic needle. Magnetic anomalies occur in such places. Small magnetic anomalies are quite common, especially in mountainous areas. In areas of magnetic anomalies, it is impossible to use a magnetic needle to determine orientation directions. Districts; magnetic anomalies are marked on topographic maps with special symbols.

Transition from magnetic azimuth to directional angle. On the ground, with the help of a compass (compass), the magnetic azimuths of the directions are measured, from which they then go to the directional angles. On the map, on the contrary, directional angles are measured and from them they are transferred to the magnetic azimuths of directions on the ground. To solve these problems, it is necessary to know the magnitude of the deviation of the magnetic meridian at a given point from the vertical line of the coordinate grid of the map.

Angle formed by a vertical line coordinate grid and the magnetic meridian, which is the sum of the convergence of the meridians and the magnetic declination, is called the deviation of the magnetic needle or the direction correction (PN). It is measured from the north direction of the vertical grid line, and is considered positive if the north end of the magnetic needle deviates to the east of this line, and negative if the magnetic needle deviates west. In Figure 111, the directional correction is 2° 16"+5° 16"=+7°32".

The correction by directions, the convergence of the meridians and the magnetic declination that make it up, is given on the map under the south side of the frame in the form of a diagram with explanatory text.

The correction of direction in the general case can be expressed by the formula:

PN=(+/-δ)-(+/-γ)

If the directional angle of the direction is measured on the map, then the magnetic azimuth of this direction on the ground

Am=α-(+/-PN).

The magnetic azimuth of any direction measured on the ground is converted into the directional angle of this direction according to the formula:

α=Am+(+/-PN).

To avoid mistakes when determining the magnitude and sign of the direction correction, it is necessary to use the direction scheme of the geodetic meridian, magnetic meridian and vertical grid line placed on the map.

With precise measurements the transition from directional angles to magnetic azimuths and vice versa is performed taking into account the annual change in magnetic declination. First, the declination of the magnetic needle is determined for a given time (the annual change in the declination of the magnetic needle indicated on the map is multiplied by the number of years that have passed since the creation of the map), then the resulting value is algebraically summed with the declination of the magnetic needle indicated on the map. After that, they pass from the measured directional angle to the magnetic azimuth according to the above formulas.

Control questions and exercises:

1. What is the map scale value? What is the scale of maps of scales 1:500,000 and 1:1,000,000?

2. List the scale range of topographic maps and indicate with what accuracy distances can be measured using maps of different scales?

3. The distance on a 1:100,000 scale map between two points is 5.28 cm. What is this distance on the ground?

4. A distance of 1450 m was measured in a straight line on the ground. Determine the length of this distance on maps of scales 1:25,000 and 1:100,000.

5. Measured by a curvimeter on a map of scale 1: 200,000, the length of the route of movement turned out to be 78.5 cm. Half of the route passes in hilly, and the second half in mountainous areas. Determine the Route Length on the ground.

6. The radius of weak destruction on the ground from the earthquake is 15.3 km. What is the area of ​​destruction?

7. Measured on a 1:50,000 scale map, the distance from T1 to T2 turned out to be 1.52 cm, where it is located on the slope of the mountain. Target elevation angle 30°. What is the distance T2 on the ground?

8. Define; geodetic azimuth and directional angle. Specify the difference between geodetic and astronomical azimuths.

9. The magnetic azimuth of the direction to a distant landmark, measured by a compass on the ground, is 102 ° 31 ". The declination of the magnetic needle is 5 ° 28", and the convergence of the meridians is 1 ° 16 ".

10. The directional angle of the direction on T2 measured on the map with a protractor is 18 o 46 ". The correction of the direction indicated on the map is + 1 o 32". The map was made seven years ago. Annual change in magnetic declination - 0 o 02 "Determine the value of the magnetic azimuth of the direction on the ground.

The work of determining the directional angle of the orientation direction in an astronomical way is greatly simplified if it is possible to determine the direction of the true meridian at a given point mechanically.

To implement this method, an azimuth nozzle ANB-1 was developed for the PAB-2A compass. In 7.3.4.1, it was indicated that this nozzle is used in determining the directional angle of the orientation direction from the hour angle and declination of a luminary whose height is more than 3-00. But it also has another purpose - to determine the direction of the true meridian at the point of standing of the compass in a mechanical way, hence the name "azimuth".

The application of the mechanical method of astronomical orientation is based on the fact that the place of the celestial pole on the celestial sphere is completely determined by the angular distance from it to the Polar Star (α Ursa Minor) and the difference in the hourly angles of the Polar and Kokhab stars (β Ursa Minor). Visually, the Polar Star is found in the sky with the help of the two extreme stars of the “bucket” of the constellation Ursa Major (Figure 7.9a). To do this, mentally connect these stars with a straight line and continue it for about five times the distance to the same bright star. This will be the star α of the constellation Ursa Minor, also having the shape of a bucket. The star β (Kochab) is located on the other side of the "bucket" of the constellation and is the second brightest star in this constellation after the star α (Polar).

The sighting axis of the nozzle according to the position of the stars α and β Ursa Minor is mechanically oriented to the celestial pole. Thus, the north direction of the true meridian is fixed, and the task of determining the azimuth of the orientation direction is reduced to measuring the horizontal angle between the direction of the meridian and the direction to the landmark. And if the compass is pointed at the celestial pole with zero readings on the compass scales, then after pointing the reference mechanism at the reference point, it will be possible to take the value of the true azimuth of the reference direction from these scales.

The angular distances of the stars α and β from the celestial pole, although slightly, change as a result of the precession of the celestial axis. The relative position of these stars also changes as a result of their own motion. Therefore, it is inappropriate to mark places on the grid where images of stars should be entered with constant points. These places on the grid are indicated as two bisectors (Figure 7.9b).

The bisector for the introduction of the North Star has a scale that takes into account the annual change in its polar distance for the period up to 2050, as well as the change in the difference between the hourly angles of the stars α and β.

The determination of the directional angle of the orientation direction is carried out in the following sequence:

install the compass, put the azimuthal nozzle on the nozzle of the monocular and fix it;

connect and turn on the lighting;

set the reference worm of the compass to zero readings on the compass ring and drum;

by rotating the drum of the vertical aiming mechanism of the compass monocular, bring the nozzle level bubble to the middle;

open the cover of the head of the reticle and, observing through the eyepiece of the reticle, rotate the diopter ring to set a sharp image of the reticle. Close the lid;

by rotating the handwheel of the adjusting worm of the compass and turning the sight of the nozzle vertically by hand (previously opening the clamping screw), use the rear sight and front sight of the sight to point it at the North Star. Watching through the eyepiece, make sure that it is in the field of view. Tighten the clamping screw;

open the cover of the sight head and by rotating the handwheel for turning the sight head, observing through the eyepiece, enter the star β of the constellation Ursa Minor into the field of view;

using the adjusting worm of the compass, the screw of the vertical aiming mechanism of the reticle and the handwheel for turning the reticle head, set the reticle so that the image of the star α is placed in the small bisector against the scale of the corresponding year, and the star β is placed in the large bisector. In this case, the optical axis of the sight (grid crosshair) will coincide with the direction of the true meridian (the true azimuth of this direction is zero);

turning the handwheel of the reference worm of the compass and turning the sight of the nozzle vertically, aim the crosshair of the sight grid at the selected landmark, which is not closer than 200 m (Figure 7.9c);

remove from the compass scales the value of the true azimuth A of the direction to the landmark;

determine the value of convergence of the meridians γ (see 7.2);

calculate the directional angle to the landmark using the formula

αOr = A - (±γ). (7.22)

When determining the azimuth of the direction to a landmark remote from the instrument at a distance of less than 200 m, it is necessary to introduce a correction taken from Table 7.4 into the obtained value of the azimuth or directional angle.