The object of this instrument is to determine:
1. When the observer is on the line joining two points when he is between them or to show when the angle between the objects measured at the position of the observer is 18° degrees.
2. To prolong a line in any direction through the position of the observer. These two functions of the instrument render it at times of great value in navigation, hydrographic and land surveying and also in railroad engineering.
TYPE I
In its simplest form the instrument consists of a prism or of two plane mirrors set perpendicular to a metallic or wooden base with their silvered faces at an angle of 90 degrees as shown in the figure. Mirrors are recommended on account of their cheapness, though the prism has some advantages. With two sextant index glasses almost any one can make the instrument here shown. When the backs of the mirrors are covered with a heavy coating of sealing wax dissolved in alcohol and encased in thin tin or brass, they will stand moisture well. The distance between the centers of the mirrors should not be less than four (4) inches, in order for the ray of light from the rear object to clear the observer's head when the instrument is held to the right eye. The mirrors are set perpendicular to the base and the heavy line in each case shows the face of the mirror. The mirrors A and B may be secured to small blocks or a light casting which could hold the telescope or eye-tube and the whole be attached to a wooden base. In making a home-made instrument secure block carrying mirror A to the wooden base and set B as shown under sextant attachment. When using the instrument it is held horizontally, of course, like a sextant in taking horizontal angles. The telescope or sight tube should be arranged to move up and down as on a sextant.
TYPE II
3. In Type II, the mirror A is at right angles to the line of sight and C is parallel to B. This type approaches mathematical accuracy closer than Type I, as the mirrors A and B may be placed closer together than in Type I about 2 inches apart, distance from A to B about 9 inches. This type has a little wider range than Type I, as by removing mirror C a beam bearing may be taken with A and B and by having B arranged so that it may be easily set at 22 1/2 degrees we can easily take a bow bearing also.
BC = 1 ½ inches
O’B = 4 inches
TYPE III
4. From an examination of the figure, it will be seen that if the axis of the telescope or eye-piece makes an angle of 10 degrees with the perpendicular to the mirror A through the line of sight and the plane of B makes an angle of 45 degrees with the plane of A, and the plane of C makes an angle of 10 degrees with B then when the observer is on the line joining P and O and directs his line of sight to flag P he will see the reflected image of O at O' in the mirror A, conversely, if he directs his line of sight toward P and sees the image of O at O', then he must be on the line joining P and O. Of course it is assumed that the rear object O is at a sufficiently great distance to render the error due to parallax inappreciable. The range of the instrument for accuracy in this respect is about the same as that of a sextant.
5. Referring to Type I. In order to attain mathematical accuracy as near as possible a vertical line should be shown on the silver side of the mirror B at b where the reflection of the intersection of the vertical plane through the axis of the telescope with the silver side of the mirror A is shown on the mirror B. A pin or notch is shown at P. If the back object be 100 yards distant and its image, falling on the vertical line b, be seen in the mirror A directly under the pin or notch P, when directed toward the front object, then the difference between the angle as shown by the instrument and 180 degrees will be less than 4' of arc, if the back object be 500 yards distant, then the error will be less than 1' of arc, assuming a distance of 4" between the mirrors, which is an inappreciable quantity when compared with the beam of a ship or even that of a sounding boat.
TYPE IV
SEXTANT ATTACHMENT
6. By adding a third mirror to an ordinary sextant we have an arrangement with which an angle of 180 degrees and over may be measured. The angle in this case is equal to the reading of the vernier plus 90 degrees. When the sextant is set at 90 degrees we have a range indicator. At times it may be desirable to be able to measure an angle of 180 degrees and over with a sextant, but for ordinary use the instrument made as described under Type I, will be found more convenient. If an extra glass be used on a sextant, it should be made to ship on the index arm outside of the regular index glass as shown in the figure in par. 4.
7. To do this practically, after the third mirror has been fitted to a proper frame of brass or aluminum, a hole should be tapped in the index arm to correspond with the one for the thumbscrew in the mirror frame. In the sketch the circle BPT represents the end of the index arm, B the index glass, C the third
mirror, T, thumb-screw and P hole for pin, drilled in the mirror frame. Ship the mirror C and set up on T hard enough to hold the frame in place, then having selected two objects at a sufficiently great distance apart so that the distance from the observer to the back object will be not less than about 1000 yards, take station exactly on the line between the objects and having clamped the sextant at 90 degrees look toward the front object and turn the third mirror C about the pivot T until the image of the back object is seen directly under the front object. The third glass, C is now set at the proper angle and the position for the second hole in the index arm for the pin P should be marked through the hole at P. The hole in the frame should be tapped and a pin inserted to fit the hole in the index arm. This arrangement will allow the mirror C to be easily shipped and unshipped.
USE OF THE INSTRUMENT IN NAVIGATION
8. When circumstances permit, the observer should stand with his back to the nearer object. This not only makes the reflected image more distinct but the range is also rendered more sensitive. In using the instrument for a range if the line of sight falls to the right of the object in front of the observer when he sees the reflected image of the rear object in the mirror A, then he is to the right of the line.
(a) In Types II, III, and IV, by removing the mirror C and having the glass B so arranged as to be easily set at 22 1/2 degrees we have a convenient instrument for taking bow and beam bearings.
(b) To avoid a rock or shoal by keeping on a line between two objects when no ordinary range is available.
A strong tide renders the channel between the rocks dangerous, no range lights can be placed in the ordinary way, as the land at B is too high. By placing a second light or beacon at B a vessel may be safely steered between the rocks by day or night in any stage of the tide, as with ordinary range lights.