The instrument is intended to be thoroughly portable; so much so, indeed, that it is not necessary or even desirable to use a tripod. It may be held in the hand like a sextant, or may be carried on a light staff. The general appearance is shown in Fig. 1. It will be seen that a metal plate, on which two scales are engraved, carries a mirror at one end and an eye piece at the other. The mirror is mounted on a metal plate, which is shaped to a peculiar curve. A clamp and slow motion provide for rapid and for fine adjustment. The eye piece is set at an angle, and contains a half silvered mirror, the upper portion being transparent. This allows direct vision along the axis of the eye piece, and at the same time vision in another direction, after two reflections, one in the eye piece and the other at the adjustable mirror. Fig. 2 is an outline plan of the instrument when closed. In the first form of the instrument only one mirror was provided, but by the double reflection in the improved pattern, any accidental twisting of the rod or handle produces no displacement of the images, since the inclination of one mirror neutralizes the equal and opposite inclination of the other. No cross line is required with the new arrangement, since it is only necessary that the two images should coincide. [Illustration: FIG. 2.--OUTLINE OF INSTRUMENT SHOWING THE PATH OF THE DIRECT AND OF THE REFLECTED RAY.] The dotted line A B represents the direct ray, and the line A C D the reflected one. Fig. 3 shows the different geometrical and trigonometrical elements of the curve, which can be read upon the various scales, or to which the instrument may be set. An observer standing at C sights the point B directly and the point A by reflection. A staff being set up at each point, he will see them simultaneously, and in coincidence if the instrument be properly set for the curve. 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