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

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

use.

Fig. 7 is a sectional plan of the instrument. A and B are 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.

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°. 60° also.

=

Therefore FEG = 180° - (2 × 60°) =

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.

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

in the mirrors, as shown in Fig. 9. To use the instrument, move it back or forward until the lining rods appear as shown in Fig. 9. A point vertically under the instrument will then be in the straight line AB. It is useful for finding an intermediate point in a long line without the time and labour involved in going to one end to line it out. It is also possible to get into the line by setting up two ranging rods so that they range in with the pole at one extremity of the line. Then try if they also range in with the poles at the other extremity of the line. If they do, they are in the line; and if not, they must be shifted until they range in with the poles at both extremities of the line, their correct position being found by trial and error.

Use of the Chain.--The method of chaining a line is as follows:- Having stretched out the chain, the follower holds his end of it at the ranging rod marking the beginning of the chain line, while the leader moves forward to the full extent of the chain, having with him the ten chaining arrows. The follower, having the ranging rod at the other end of the chain line in view, directs the leader to right or left until he has got the chain into line. The leader then inserts the first arrow to mark the end of the chain. The chain is then moved forward until the follower reaches the arrow, at which he holds the end of the chain, and again directs the leader until he gets him into line. A second arrow is then inserted by the leader to mark the end of the second chain length. The follower picks up and brings with him each arrow after the leader has inserted the one in front, and the operation is repeated in the same way until the ten arrows have been inserted by the leader. This, of course, occurs at the end of 10 chains, at which point the follower delivers up all the ten arrows to the leader, meantime marking the end of the 10 chains by a ranging rod or other temporary mark, until the next arrow has been inserted by the leader. Thus the ten arrows are a valuable check upon the counting of the number of chains.

When offsets (see page 17) are required, the chain is simply allowed to lie stretched out on the ground, in the line, between the chaining arrows until the offsets have been measured to it. When fences, hedges, or boundaries have to be crossed, the chain is pulled through them, and the distance on the chain at which they cross is noted.

~~1004 chs

Chaining on Slopes.-As the survey when plotted on paper is a horizontal projection of the ground surveyed, all distances must be measured horizontally. When the ground is sloping, if the distance is measured along the sloping surface it will be too great, as may be seen from Fig. 10, where, if the slope is at an angle of 5°, the distance AB as measured on the slope is 10.04 chains, or 10 chains

10 che

Fig. 10.-Chaining on Slopes.

4 links, whereas the required horizontal distance AC is only 10 chains.

In all cases, therefore, when the ground slopes there is a certain deduction to be made from the distance as measured on the slope to reduce it to the horizontal distance.

The following table shows the difference per chain of 66 ft. between the hypotenusal or slope measurement and the horizontal

measurement:

TABLE FOR REDUCING MEASUREMENTS ON SLOPE TO
HORIZONTAL: 66 FT. CHAIN.

The following table gives deductions per 100 ft. to be made from measurements taken on slope to reduce them to the horizontal measurements. This table is useful when a 100 ft. chain is

used.