LESSON NOTE ON 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.

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 crossstaff 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 a 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 backward along the chain line

B. Optical Square

An optical square is also used for setting out right angles. It consist of a small circular metal box of diameter 5 cm and depth 1.25 cm. It has a metal cover which slides round 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. A 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 unsilvered 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. The he should move forward or backward 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.