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Arrows. Accompanying the chain are ten arrows or marking pins (Fig. 2). These are inserted in the ground to mark the end of each chain. When the ground is too hard to insert the arrow, a scratch may be made with the point for a mark, or the arrow may be simply laid down flat, care being taken that it is not moved while dragging the chain forward.

Ranging Rods and Flags.-These are iron-shod wooden poles, slightly tapering from the bottom, which are used to range out lines and mark points. They are usually 5 or 6 ft. long, and are painted in divisions alternately black and white or red and white, to render them visible at a distance. When they are at a considerable distance, they should have a piece of white or red cotton cloth tied on the top as a flag, to make them conspicuous. A very convenient length is 10 links, painted in ten divisions. These rods come in very useful for measuring short offsets. Three rods are necessary to range out a straight line, but the surveyor should have from six to twelve ranging rods to mark the ends of the chain lines and important points of the survey. For very long lines it is necessary to have poles of greater length, 10 to 15 ft. long or more, according to circumstances. In wet weather for flags use woollen cloth instead of cotton, which clings to the pole when wet.

Laths. A bundle of laths sharpened to a point sometimes comes in useful in ranging long lines and marking points to be levelled in taking cross sections. They are cheap and easily procurable, and are easily sharpened to a point or cut to any desired length. Being white, they are easily seen, and they may be discarded when done with, without serious loss.

Whites. When laths are not to be had, small twigs sharpened to a point and cleft in the head, with a piece of paper inserted in the cleft, are good marks.

Steel Tapes. For accurate measurements a steel tape must be used. This consists of a steel band about in. wide, with feet, inches, and eighth parts of an inch marked on one side, and links or decimals of 66 ft. on the other, in the case of a tape 66 ft. long. Steel tapes may be had of any desired length, and are made to roll up inside a small circular leather case.

Linen Tapes. For ordinary measurements a linen tape is used. The chief use of the linen tape is the measurement of offsets, the chain being allowed to lie on the ground in the chain line while the offset is measured from it with the tape. Linen interlaced with fine metallic wire has been used as an improvement in point of strength and stretching. It is, however, inferior to a good plain linen tape. New tapes may be bought separately, and are easily inserted in the leather case when the old tape is worn out.

Linen tapes are not to be depended on for accurate or important measurements on account of their stretching, especially if wet, while on a windy day the tape is useless for long measurements, as it catches the wind, sags and pulls. If the tape gets wet and dirty, it should never be rolled up until it has been cleaned and dried. It should be coiled loosely until it can be washed in clean water. It may then be hung up to dry, and afterwards rolled up in the leather case.

Steel Band. As a substitute for the chain a steel band may be used. This consists of a steel band with a brass handle at each end, similar to the ordinary chain handles. The advantage of the steel band is that it is practically unalterable in length (for ordinary small surveys); while the chain is liable to be stretched or to have its links bent, and must therefore be tested occasionally and adjusted.

The steel band does not accommodate itself to the inequalities of the ground when laid down, as well as the chain. It is, however, no doubt better and more accurate for measuring long lines, especially when not many offsets are required, and it is consequently not necessary to allow the chain to lie on the ground; in such work, for instance, as chaining out the centre line of a railway.

Adjusting the Chain. This is effected by removing some of the rings connecting the straight links if the chain is too long; or by straightening out the links and inserting some of the additional rings furnished on the chain if it is too short. The chain may be tested by comparing it with a steel tape.

Cross Staff. This is used for setting out long offsets at right angles to the chain line. The simplest form of cross staff

is that shown in Fig. 3, consisting of four arms with vertical slits for sighting through, at right angles to each other. These are fixed upon an iron-shod ranging rod which is inserted into the ground on the chain line at the point where it is desired to set off an offset line at right angles to the chain line. It is turned round until one pair of opposite slits is in line with the chain line. By then looking through the other pair of slits an offset line at right angles to the chain line may be lined out.

Fig. 4 shows an octagonal form of cross staff with slits on all eight sides. By means of this, lines at an angle of 45° as well as 90° with the chain line may be set off.

Fig. 5 is another form which may be used for setting off or measuring angles approximately. There are graduations round

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the circumference; the top part slides over the under part, and may thus be set to any required angle by means of the graduations. The forms of cross staff shown in Figs. 3, 4, and 5 are those made by Stanley, Great Turnstile, Holborn, London, and any of these may be obtained with compasses fixed on them for taking bearings. The simplest form of cross staff is the best, as the additions only complicate matters, and are better provided for in other instruments specially made for measuring angles. As, in general, long offsets are to be avoided, the cross staff should only be sparingly used.

Optical Square. This is another instrument for setting out right angles. It consists of a small circular metal box (Fig. 6), which shows the instrument as made by Stanley. It is usually protected by a metal cover as shown in the figure. This slides round so as to cover the openings and protect the mirrors when not in

A and B are


Fig. 7 is a sectional plan of the instrument. slits for the eye, c is the opening through which the lining rod at D is reflected on to the mirror. E and F are two mirrors placed at 45° to each other, the under half of the mirror E being unsilvered. The instrument is used by placing the eye at the slit A and looking through the slit в along the chain line, at right angles to which it is desired to lay off the offset line. The slits A and B being thus properly placed in line, if a ranging rod be held at D, when it is at right angles to AB it will be reflected in the mirror F, and thence to the mirror E, where its reflection will coincide with the ranging rod at K, as

Fig. 6. Optical Square.

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seen through the unsilvered lower half of the mirror E. The chainman being sent out with the ranging rod in the direction of D, must be directed to move it to right or left until its reflection in the mirror E coincides with the ranging rod on the chain line

at K.

The theory of the instrument is as follows:-The mirror E is placed at an angle of 60° with the line ABK, and the mirror F is at an angle of 45° with the mirror E. Angle of reflection AEM =

angle of incidence pEF = 60°. Therefore FEG = 180° - (2 x 60°) =

60° also.

Then in the triangle PEF we have pEF=60°, EF = 45°, and therefore pFE 75°. The angle of incidence NFG is therefore also 75°, and consequently the angle EFG = 180° - (2 × 75°) = 30°. In the triangle EFG we have then FEG = 60°, EFG = 30°, and therefore FGE = 90°, or the line FGD is at right angles to the line ABK.

It is almost impossible to use the optical square when the ground is not level and one ranging rod is higher than the other, although it may be done by twisting the instrument into a plane approximately parallel to the surface of the ground. The right angle will then, however, be set off in this plane, and its horizontal projection will not be a right angle. Altogether it may be said that the use of the instrument is limited to cases where the ground is practically level. These remarks also apply to the box sextant, page 73, Chapter II.



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Fig. 8.-Line Ranger.

Line Ranger.-This instrument (Figs. 8 and 9) consists of two square prisms E and F having their hypotenusal sides ef and gh silvered and at right angles to each other, Fig. 8 being a plan of the instrument. These are placed one above the other in a small box similar to the optical square, having openings at a and b and slits at c and d. Upon looking through the slits c, d, in the direction GH, if the instrument is in the line AB the reflections of the ranging rods at A and B will appear to be in the same vertical line at c

Fig. 9.-Line Ranger.

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