For Plotting a Ship's Position by the Three-Point Problem.
1. This instrument is intended to take the place of the three-armed protractor or station pointer, when the scale of the chart is so small that the hub, circle and arms, of the latter instrument are liable to hide the land marks on the chart between which the angles are taken.
The advantages of the three-armed, both as to speed and accuracy, for plotting a ship's position by sextant angles, are well known to navigators, and no doubt this most excellent instrument would be in general use, were it not that as generally made it is rather expensive, and many of the charts used are constructed on too small a scale to permit its use.
2. As shown on Sheets I and II, the instrument consists of a circular plate of xylonite, or celluloid, 16 or 18 inches in diameter, graduated in degrees and one-quarter degrees from the line AC right and left from 0° to 180.° One side of the plate is roughened to resemble ground glass in order that lines may be drawn upon it with a lead pencil. At the center a small hole C, 1/8 inch in diameter, is drilled. A small pin on the index arm EC ships into this hole and by means of this index arm EC and the vernier V, graduated to minutes, angles may be laid off as accurately as with an ordinary station pointer. The index arm has a beveled edge and may be extended beyond the edge of the protractor as far as convenient or be fitted with an extension piece. A, B, C, and D are small brass clips with buttons, shown full size at J. These clips are slipped over the edge of the protractor for convenience in handling.
3. To Use the Protractor.—Though this protractor is used just as the ordinary station pointer or a transparent protractor made on tracing cloth or paper, there are several practical points deserving attention.
4. Referring to Sheet I, the case here shown is taken from actual practice.
Example.—While passing between Pta. del Este and Lobos Island, these angles were taken: right angle, right tangent Lobos Island to Pta. del Este Light House, and Maldonado Cathedral in range 110°; left angle, same range to peak marked 0.45.° Plot position. Turn the protractor as shown on Sheet I, rough side up, and zero of the scale towards you. Ship the index arm EF, lay off the angle ACH = 110°, draw the line CH; lay off ACE = 45°, draw CE. The line AC should be permanently drawn on the plate. Unship the radial arm CF, and holding the protractor by the clips B and D, revolve it about the diameter BD so that the zero will be away from you, bringing the roughened side next to the chart. By doing this the parallax due to the thickness of the plate, is eliminated, and the rough surface in no way interferes with the transparency of the plate. If a sheet of ground glass 1/8 inch thick be laid on a chart with the rough side up, the lines on the chart will be indistinct, but if the rough side be placed next to the chart, they may be clearly seen. As the angle ACH was taken when the tower and the light house were in range, it was not necessary to take the angle ACE, which is plotted to illustrate the case when one or more of the points fall outside the protractor. To plot the position with the angle ACO, use the index bar as an extension arm by shipping it and making its edge coincide with the line CE. The pencil lines may be easily erased with a damp cloth or a rubber eraser, when they become too thick. As each pair is used they should be scratched over with a pencil. For the ordinary purposes of navigation it will not be necessary to have an index bar with a vernier. The straight edge shown at KL will answer, the 1/4° divisions being sufficiently large to lay off 7 1/2 minutes with accuracy. The bar KL has a pin P to fit the hole C, and a small hole, h, through P for a pricker, to mark the position. The pin, P, should project above the bar KL in order that two other light extension arms may be placed over it when all three points lie outside the protractor; see QR- p-pin secured to arm c; a and b ends of other arms, curved to ship over upper end of p. The upper end of the pin p is also threaded for the thumb nut S which may be used for clamping the arms and holding them in position while plotting. The pricker, t, extends through the hole in the pin, p, for making the position when it is necessary to use the extension arms, which will rarely happen.
6. The writer uses a protractor made of ground glass 1/8 inch thick, and 16 inches square, with a hole 1/8 inch drilled in the center, no more suitable material being obtainable. The corners were cut off making a regular octagon, and a circular paper protractor 16 inches in diameter was glued by its outer edges to the ground side of the glass and the central part cut out. The arc is graduated to degrees and quarters, i minutes of arc being about equal to 1/32 inch, so that angles may be accurately laid off to 1/8°. Three brass clips or handles similar to J are used for lifting, and except for the inconvenience in handling, which necessarily requires great care, this has proved a very efficient instrument, with which positions may be plotted with far greater ease and accuracy than by compass bearings. The pencil marks may be readily erased with a damp cloth.
7. There are other uses to which this instrument may be put which will suggest themselves to the navigator. For instance it may be used with advantage instead of parallel rules to lay off courses. Thus referring to Sheet I, place the center of the protractor over the position of the ship at C; bring the zero line ACG parallel to a meridian marked on the chart. This is readily done as the chords joining the extremities of equal arcs laid off from ACG are all parallel to ACG. CU is the meridian through C. Revolve the protector through an angle equal to the compass error, to the right if easterly, to the left, if westerly, and the compass course corresponding to the direction CW is read from the protractor, N. 80° E., the assumed error in this case being 9° west.
To aid in laying off courses when the distances are great, a cord Y, attached to a metal button, X, with a small stud, to fit in the hole C, may be used.
8. A more convenient and accurate instrument is shown on Sheet III. This consists of a circular plate of xylonite or other transparent substance, about 1/16" or 1/8" thick, smooth on both sides, and secured to a metal ring, which may be graduated, or the ring may be plain and the graduations made on the transparent plate. The arms A and B rotate about the hollow center C, through which the point of a pencil is inserted to mark the position of the ship. These arms are fitted with verniers, M and N, clamp screws, E and F, and extension pieces, G, H, as long as desired, held in place by the screws J and L. The verniers read to minutes, and the divisions are sufficiently large to permit the verniers being set without the aid of a magnifying glass. The xylonite plate is smooth on both sides, as the arms, A and B, make it unnecessary to mark the lines on the plate.
Two forms of vernier are shown. The one fitted to the arm A is so arranged that when both arms are fitted with this pattern, the index edges of the arms may be made to coincide on the line CD. CD is marked permanently on the plate, and has an extension piece held in place by the thumb screw K. The vernier shown at A permits very small right and left angles being used, but that shown at B is stronger.
The details of the vernier, clamps, &c., may be similar to those used on the ordinary three armed protractor or sextant, but it is thought that tangent screws are unnecessary, on account of the size of the divisions of the arc and vernier.
A section of the ring is shown at U. If made of aluminum bronze, the ring may be made wider and thicker without increase of weight, and the arms A and B may be made to stand edge-wise to the plate, which would be an advantage, serving to correct the parallax in plotting due the thickness of the plate and at the same time, appearing only as lines when viewed from above, they will not obscure objects on the chart.
If, however, the instrument is intended to be used in surveying, the arms and their extension pieces should be made heavier, so as not to be sprung when very long extension pieces are used, which is often necessary when working on a large scale chart. Each extension piece should be made in two parts.