CROSS-STAFF AND OPTICAL SQUARE

CROSS-STAFF AND OPTICAL SQUARE

A. Cross-staff

The cross-staff is a simple instrument for setting out right angles. There are three types of cross-staves.

1. Open
2. French
3. Adjustable

The open cross-staff is commonly used.

1) Open cross-staff

The open cross-staff consists of four metal arms with vertical slits. The two pairs of arms (AB and BC) are at right angles to each other. The vertical slits are meant for sighting the object and the ranging rods. The cross-staff is mounted on a wooden pole of length 1.5m and diameter 2.5 cm. The pole is fitted with an iron shoe.

For setting out perpendicular on a chain line, the cross-staff is held vertically at the approximate position. Suppose slits A and B are directed to the ranging rods (R, R₁) fixed at the end stations. Slits C and D are directed to the object (O). Looking through slits A and B, the ranging rods are bisected. At the same time, looking through slits C and D, the object O is also bisected. To bisect the object and the ranging rods simultaneously, the cross-staff may be moved forward or backwards along the chain line

2) French cross-staff:

It consists of an octagonal brass tube with slits on all the eight sides. It has an alternate vertical sighting slit and an opposite vertical window with a vertical fine wire or horsehair on each of the four sides. These are used for setting out right angles. On the other sides are vertical slits, which are at 45° to those mentioned above for setting out angles of 45°. The sights are about 8 cm apart.

It carries a socket at the base so that it may be mounted on the pointed staff when in use. The sights being too close, it is not as accurate as of the open cross-staff.

French Cross staff

 

For setting out a right angle at a given point on a chain line, it is held vertically over the given point and turned until one of them saw cuts or (the pair of sights) is ranged along the chain line. Then the line of sights through the other saw cut or the pair of sights) is at right angles to the chain line and a ranging rod can be fixed in this direction at a convenient position.

To find the foot of the perpendicular from an object on a chain line, the cross-staff is held vertically at an approximate position of the required object and turned until one of the saw cuts or (the pair of sights) is ranged along the chain line.

If on looking through the another saw cut or (the pair of sights) is seen the object from which the foot of the perpendicular is to be drawn, then the point where the cross-staff is held is the correct position of the foot of the perpendicular from the given object. If not, the cross-staff is moved forward or backwards along the chain line until the line of sight through the saw cut or (the pair of sights) at right angles to the chain line bisect the given object.

3) Adjustable cross-staff:

It consists of a brass metal cylindrical tube about 8 cm in diameter and 10 cm in deep (divided in the centre). The upper cylinder can be rotated relatively t the lower one by a circular rack and pinion arrangement actuated by mill headed screw. Both are provided sighting slits.

The lower part is graduated to degree and subdivision, which the upper one carries a vernier.it has a magnetic compass at the top which may serve to take the bearing of the line.

It is used for setting out angles of any magnitude.

B. Optical Square

An optical square is also used for setting out right angles. It consists of a small circular metal box of diameter 5 cm and depth 1.25 cm. It has a metal cover which slides around the box to cover the slits. The following are the internal arrangements of the optical square.

1. A horizon glass H is fixed at the bottom of the metal box. The lower half of the glass is unsilvered and the upper half is silvered.

2. An index glass I is also fixed at the bottom of the box which is completely silvered.

3. The angle between the index glass and horizon glass is maintained at 45⁰.

4. The opening ‘e’ is a pinhole for eye E, ‘b’ is a small rectangular hole for ranging rod B, ‘P’ is a large rectangular hole for object P.

5. The line EB is known as horizon sight and IP as index sight.

6. The horizon glass is placed at an angle of 120⁰ with the horizon sight. The index glass is placed at an angle of 105⁰ with the index sight.

7. The ray of light from P is first reflected from I, then it is further reflected from H, after which it ultimately reaches the eye E

Principle

According to the principle of reflecting surfaces, the angle between the first incident ray and the last reflected ray is twice the angle between the mirrors. In this case, the angle between the mirrors is fixed at 45⁰. So, the angle between the horizon sight and index sight will be 90⁰.

Setting up the perpendicular by optical square

1.      The observer should stand on the chain line and approximately at the position where the perpendicular is to be set up.

2.      The optical square is held by the arm at the eye level. The ranging rod at the forward station, B is observed through the unsilver portion on the lower part of the horizon glass.

3.      Then the observer looks through the upper silvered portion of the horizon glass to see the image of the object P.

4.      Suppose the observer finds that the ranging rod B and the image of object P do not coincide. Then he should move forward or backwards along the chain line until the ranging rod B and the image of P exactly coincide

5.      At this position, the observer marks a point on the ground to locate the foot of the perpendicular.