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.

To set out a tangent to the curve at A, Fig. 3, set up a rod at A and
another at any point C, and take up a position on the curve at some
point between them. Adjust the mirror until the rods are seen
superimposed. Then moving back to A, observe C direct, and set up a
rod at E in the line observed by reflection. Then A E is the tangent
required. Similarly, on completing the setting out of a curve, and
arriving at the end of the chord, the remote end being seen by
reflection, the direction observed along the axis of the eyepiece is
the new tangent.

Any of the angles or other ratios already mentioned may be used for
setting the instrument, but if no data whatever are given, as in the
rough surveys for colonial railways where no previous surveys exist,
it is only necessary to select points through which the curve must
pass, to set up ranging rods either at the extremities of the desired
curve, or at any points thereon, to take up a position on the desired
curve between two rods, and to adjust the instrument until they are
seen in coincidence. The curve can then be set out, and fully marked,
and the elements of the curve can be read on the scales and recorded
for reference.

[Illustration: FIG. 4.--DIAG