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.--DIAGRAM ENGRAVED ON THE INSTRUMENT.]

Various other cases which may occur in practice can be rapidly met by
one or other of the various scales. Suppose the angle A G B between
the tangents be given, together with the middle point F on the curve,
Fig. 3. Subtract this angle from 180 deg., the difference gives the
angle at the center A O B. Take half this, and set the instrument to
the angle thus found. Walk along the tangent until a rod set up at
some point in the tangent, say E, is seen in coincidence with a rod
set up at B. The position of the instrument then marks the point of
departure A. A rod being placed at A, the first half of the curve may
be set out; or, if B is invisible, the instrument may be reset for the
angle E A B, and the whole curve set out up to B. No cutting of hedges
is necessary, as with theodolite work, for a curve can easily be taken
piece by piece. Inclination of the whole instrument introduces no
appreciable error. If the eye piece be pointed up or down hill, the