If any intermediate position be taken up on the curve, both A and B will be seen in coincidence.  If the two rods do not appear superimposed, the operator must move to the right or the left until this is the case.  The instrument will then be over a point in the curve.  Any number of points at any regular or irregular distances along the curve can thus be set out.  One of the simplest elements which can be taken as a datum is the ratio of the length of the chord to the radius, AB/AO, Fig. 3.  This being given, the value of the ratio is found on the straight scale on the body of the instrument, and the curved plate is moved until the beveled edge cuts the scale at the desired point.  The figure of this curve is a polar curve, whose equation is r = a +- b sin. 2 [theta], where a is the distance from the zero graduation to the axis of the mirror, and b is the length of the scale from zero to 2, and [theta] is the inclination of the mirror.  In the perspective view, Fig. 1, the curved edge cuts the scale at 1.  The instrument being thus set, the following elements may be read either directly on the scales or by simple arithmetical calculation: 

[Illustration:  FIG. 3]

    The radius = 1.

    AB, the chord, read direct on the straight scale.

    AFB, the length of the arc, read direct on the back or under
    surface of the plate.

    FH, the versed sine, read direct on the curved scale.

    ACB, the angle in the segment, read direct on the graduated
    edge.

    EAB, the angle between the chord and the tangent, read direct
    on the graduated edge.

    GAB, the tangential angle = 180 deg. — ACB.

    AOB, the angle at the center = 2GAB.

    AGB, the angle between the tangents = 180 deg. — AOB.

    OAB, the angle between the chord and the radius = EAB — 90
    deg.

AH_{2}
GF = --------- - FH. 
HO

The foregoing elements are contained in a very simple diagram, Fig. 4, which is engraved on the instrument, together with the following references: 

        B = 180 deg. — A.
        C = 2B. 
        D = 180 deg. — C.
        E = A — 90.

Only one adjustment is necessary, and this is provided by means of the screws which fix the inclination of the eyepiece.  This is set at such an angle that the instrument, when closed and reading 90 deg. on the divided limb, acts as an optical square.

It is not necessary, as in the ordinary method with a theodolite, that one end of the curve should be visible from the other.  If an obstacle intervenes, all that part of the curve which commands a view of both ends can be set out, and a ranging rod can be set up at any point of the curve so found, and the instrument may be reset to complete the curve.