take out the values corresponding to each degree of latitude, and obtain the difference, as indicated below: This having been done, take, with the dividers, 1° 22.5' from the longitude scale and lay it off on each perpendicular from the base line, and through the points thus obtained draw the parallel of 44°. In like manner, from the parallel of 44° lay off 1° 23.8', taken from the scale of longitude, and draw the parallel of 45°. Proceed similarly and get the parallels of 45° and 46°. Divide this last parallel into degrees and minutes, the same as the parallel of 43°, and draw the meridians of 82°, 83°, and 84° west longitude. The result, in reduced form will be as shown in the figure, representing a chart on Mercator's projection according to the limits required. 98. On this chart may now be laid down any required position that lies within the region embraced, and the course and distance between any two such places may be found as accurately as from a regular Hydrographic Office chart. To demonstrate this, let it be required to find the course and distance from Lake Huron Light Vessel to Point Clark, to Au Sable Pierhead, to Cape Hurd, to Spectacle Reef. The latitudes and longitudes of the places named are as follow: Lake Huron Light Vessel Lat. 43° 1' N, Long. 82° 24' Point Clark . Au Sable Pierhead Spectacle Reef . Lat. 44° 4.2′ N, Long. 81° 44.5' W Lat. 45° 46′ N, Long. 84° 8' W These positions are then laid down on the chart, according to the instructions given in the preceding articles, and connected by straight lines, as shown in the figure. The angle that each of these lines makes with one of the meridians will be the true course between the places, and the distance between each is found by measuring the length of each line by a unit taken from the latitude scale on or near the middle latitude of the two places. Thus, the course and distance from Lake Huron Light Vessel to Point Clark are N 24° E, 70 miles; from Point Clark to Au Sable Pierhead N 73° W, 71 miles; from Au Sable Pierhead to Cape Hurd N 54° E, 84 miles; from Cape Hurd to Spectacle Reef N 721 W, 107 miles. The correctness of this may be verified either by calculation or by the inspection of any Mercatorial chart of Lake Huron. From what has been shown, it is evident that, by the aid of a Table of Meridional Parts, the construction of charts on Mercator's projection is quite simple and can be mastered by any one possessing a knowledge of drawing and simple arithmetic. 99. Correction of Charts, - Great care should be taken to keep charts up to date. By omitting this precaution an accident is liable to occur sooner or later. In order to assist users of charts in keeping them up to date, corrections to be inserted are issued monthly by the Hydrographic Office under the title of "Notice to Mariners." Copies of these notices can be obtained by mariners, free of charge, by applying to the Hydrographic Office, Washington, D. C., to one of the Branch Offices, or to any of the agencies in seaboard or lake ports. Shipmasters are especially requested. to inform the Hydrographic Office immediately of any newly discovered danger to navigation, or of the establishment or change of any aid to navigation. LAKE NAVIGATION (PART 3) THE SEXTANT ANGULAR DISTANCE This distance 20° -20° b 1. The angular distance between any two objects a and b, Fig. 1, is the angle a ob subtended by lines drawn from the place of an observer o to each object; it is usually expressed in degrees, minutes, and seconds. must not be confounded with the actual linear distance between the objects represented by the dotted line ab. Since no relation exists between the two, the angular distance will remain the same at any point between the lines oa and ob, as shown in the figure, while the linear distance will vary between any two points on these lines having the same radii. Therefore, whenever the expression "angular distance" is used in connection with methods of determining the position of a ship while in sight of land, it should be understood as the angle at the observer's eye formed by the lines drawn from the observer to each of the observed objects. -20° FIG. 1 2. Instrument for Measuring Angular Distances. Among the instruments used by navigators for measuring the angular distance between any two objects, celestial or For notice of copyright, see page immediately following the title page terrestrial, the sextant is one of the most important, particularly in ocean navigation, where the measurement of altitudes of celestial bodies is performed exclusively by means of that instrument. BRIEF DESCRIPTION OF THE SEXTANT 3. The sextant consists of a metal frame CED, Fig. 2, in the form of a sector, the arc of which is about 60°; the arc ED, commonly known as the limb, is divided into half degrees, which are marked as whole degrees. Thus, the graduations on the limb are read from 0° to 120°. The arm BI B called the index arm, or index bar, is fitted with a vernier and rotates about the center C of the sextant; to this index bar is affixed a mirror B C called the index glass. To the arm CD of the instrument is affixed the horizon glass A; half of the back of this glass is usually silvered and the other half is transparent. To the arm CE is attached a telescope T, directed toward the horizon glass A. When the zero of the index bar I is at E, that is, at the zero of the graduated arc D E, the mirrors A and B C should be parallel. H D FIG. 2 E The index bar is fastened to the limb by means of a clamp screw. The instrument is provided also with a tangent screw by which a small motion is given to the index bar after it has been partially fastened by the clamp screw. In Fig. 3 is shown a modern sextant to which is affixed a magnifying glass and colored shades- the former for reading the graduations on the limb and vernier, the latter for preventing the glare of an observed body from affecting the eye of the observer. 4. The Index Error. - When the zero point of the index bar stands near but not on zero on the limb, and an observer looks through the telescope at a very distant object, for instance, a star or the sea horizon, he will see two images of the object. One of these images is seen direct by the rays of light that pass through the unsilvered portion of the horizon glass A; the other image is formed by the rays that are reflected from the index glass to the horizon glass and thence to the eye through the telescope T. If, now, the observer moves the index bar slightly, the image formed by the direct rays remains steady while the image formed by the reflected rays moves. By moving the index bar sufficiently, the observer can now make the two images coincide; FIG. 3 then, if the observed object is very distant, the zero mark on the index bar should coincide exactly with the zero mark on the graduated arc D E. But, if the two zero marks do not coincide, the difference, as read on the graduated arc, is the index error of the instrument. This error is either + or -, and has to be applied accordingly to the observed altitude, or angle measured. If the zero on the index bar, or vernier, is to the left of the zero on the arc, the index error is subtractive; if it is to the right, the error is additive. |