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.—­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 instrument is thrown a little to one side or other of the tip of the staff, but in a plane tangent to the circle.  Errors made in setting out a curve with the Trotter curve ranger are not cumulative, as in the method of tangential angles with a theodolite.  No corrections for inaccurate hitting of the final rod can occur, for the curve must necessarily end at that point.  It should be observed that the instrument is not intended to supersede a theodolite, but it has the great advantage over the older instrument that no assistant or chains or trigonometrical tables or any knowledge of mathematics are required.  The data being given, by a theodolite or otherwise, an intelligent platelayer can easily set out the curve, while the trained engineer proceeds