is accurately adjusted in a truly vertical position on the line-may serve to take the bearing of the line with magnetic truth. There is a form of cross-staff, as in Fig. 47, which is so constructed that

one or more points, but this can only be regarded as approximate. Some writers affirm that this instrument is valuable for setting out base-lines,. . . . more particularly for crossing any high ground with a sharp ridge." I can only say that I should place very little reliance on the accuracy of any survey which depended upon a crossstaff, either for the prolongation of lines across ridges or even for setting out right angles.

Optical Square. This is at once a most accurate and useful little instrument for its purpose, but it also must be used with great caution. All appliances of this character are liable to be used to save trouble-I mean they facilitate long offsets. The optical square (Fig. 50) consists of a metal box of from 1 to 2 in. diameter, formed by an outer Fig. 50. and inner tube working one within the other, so that by a slight movement right or left the slots upon the outer tube are made identical with similar slots on the inner case, but which latter are so placed in fixing the two together that although capable

of a slight movement they are held in position by a screw. enables the instrument to be protected from dust or dirt when not

This

in use. Within this circular box are contained two mirrors (one of which is only half silvered, the lower portion being plain) placed at an angle of 45 deg. with each other. Referring to Figs. 51 and 52 it will be seen that the glass E is placed at an angle of 120 deg. with the line of sight or diameter of the box, and the mirror F is at 45 deg. with this. Now, by a well-known law, a ray of light in direction of A B falling on E will be reflected on to F at an angle of 60 deg. (F E c), which will be again reflected in the line F c, whereby F C is 90 deg. with a B. Thus, a person wishing to establish a point on his chain-line A B at right angles with some particular point, right or left, has simply to walk along the line in direction of B until the object at D becomes coincident with the forward station B. Thus supposing a white flag is placed at в, Fig. 53, and

another flag at some distance further ahead, say B' (for this is most important, as will be explained hereafter), and at the point D a red flag is fixed; then, provided the observer is in absolute line with B and B' when D appears coincident on the upper half of the mirror E, the red and white flags will be as on Fig. 54. Again, if at any point on the chain-line, as c, Fig 53, it be necessary to establish a point at right angles, as D, instruct an assistant to move backwards and forwards until his flag is coincident with the points в and в'.`

The Line Ranger. This is a very useful little appliance for obtaining an intermediate station upon a line. It consists of two reflecting glass prisms placed one over the other, having two sides in the same plane so that the hypotenuse of the one is at right angles to that of the other. The observer holding the ranger in his hand and looking into the prisms in direction of G H (Fig. 55), if he is in a true line, the reflected image of a rod at his right hand on в on the prism E, whilst a pole at A on his left will be reflected in the prism F, so that when these images are in the same straight line the instrument is also exactly in the same straight line with the objects A and B."

66

Clinometer. The clinometer in its primitive state was simply an appliance for ascertaining the angle of a slope with the horizon,

the most simple being a card in the form of a semicircle, divided right and left of the line of quadrant into degrees and subdivisions

H

E

Fig. 55.

of a degree. With a small plumb-bob attached to the centre it is possible, by elevating or depressing the line of diameter, to read off the number of degrees, &c.

Merrett's Quadrant.-A modification of the quadrant was invented by the late Mr. H. S. Merrett. It is made of boxwood, having two arcs (right and left) of 90 deg., divided into degrees and half-degrees, being sufficiently clear for the purposes for which it would be required. It has two tables engraved on it, one to ascertain the height of any object, the other for shortening the hypotenusal line to the horizontal line, when required in surveying hilly districts the same as a theodolite.

There are also angles of slopes usually adopted in railway cuttings and embankments.

It is governed in its operations by a spirit-level on the top, having two sights. The arc is divided both ways so as to enable the observer to read either for angles of acclivity or declivity. It is fixed upon a small tripod, whereby greater accuracy is obtained.

I have thought it necessary to explain briefly this instrument, but neither has it come into very general use, nor can it in fact compare with the many excellent instruments of modern days.

Clinometer Rule.--This is possibly one of the most simple and compact of the absolute instrument types. It consists (Fig. 56) of a box-wood rule in two parts, with a hinged joint (like a sector) about 6 in. long when closed. In the upper arm a small spirit

level c is inserted, whilst at either end are fixed sights A and B with cross wires. Attached to the hinge is a brass quadrant F, which is divided into 90 deg. and minutes. A spirit-level D is also inserted in the upper portion of the lower arm G, whilst upon one

of the sides is engraved a scale and table of hypotenusal allowances, and the more complete clinometers are accompanied by a small compass F.

In using this instrument for acclivity you sight from A to B, and for declivity from в to A.

The price, in morocco case, varies from £1 1s. to £3 3s.

The Abney Level.-This portable and neat little instrument

(Fig. 57) is a reflecting level and clinometer combined, and is deservedly very popular amongst engineers and surveyors, for it

D

will almost go inside the waistcoat pocket. It was invented by Captain Abney (of photographic renown), and consists of a hollow arm A, in which is contained a telescope. Attached to this arm is a vertical arc в, each quadrant of which is divided right and left into 60 degrees and subdivisions. This arm is of sufficiently stout metal to enable at its centre a horizontal spindle to be fixed (which is actuated by a milled-headed wheel D') carrying a spiritlevel E, the case of which has a slot underneath, so as to expose the bubble, similarly constructed to the hand-level, so that in whichever position the arm is held the bubble will be reflected on to the mirror. A vernier * fixed to the spindle and at right angles to the arm of the bubble indicates the relative angles of acclivity or declivity on the vertical arc, the observation

Axis of

Axis of

Fig. 58.

Bubble

being complete when the bubble is coincident with the horizontal line of the half

Telescope silvered mirror at its intersection with the distant point. Referring to Fig. 58, it will be observed that the instru

ment in its entirety is in a truly horizontal position. Fig. 59 shows the instrument being used for the angle of acclivity (which in this case is 34 deg. 15 min.), and Fig. 60 that of declivity, or 19 deg. 30 min. with the horizon. Thus the level tube is always horizontal, and the arm of the vernier vertical, whilst the telescope assumes whatever

angle it may be desired to observe, and the vertical are consequently has its zero varying in position accordingly. The cost of this little instrument is £2 2s. The Abney level may be made to fit on to a tripod with a ball-and-socket movement, whereby greater steadiness and consequently more accuracy may be attained.

Reflecting Clinometer Scale.-This (Fig. 61) is somewhat on the principle of the Abney level, and has the advantage of being half the cost. It consists of a telescope with a mirror half silvered, to reflect the bubble into the slot. The vertical arc to which

* A vernier is fully described on p. 52.