SECTION THIRD. Description and Use of Instruments. Besides the Chronometer already alluded to, the principal instruments of the navigator are the Compass, the Log, and the Sex tant. PROPOSITION I. To steer a determinate course. This is effected by aid of the Mariner's Compass, which consists, essentially, of a circular card, poised on a pivot and carrying a magnetic needle. The circumference of the card is divided into thirty-two equal parts, denominated points, and each point into quarters. The bearings, called rhumbs,are estimated from the north and south toward the east and west, as follows; Fig. 136a. N, N by E, NNE, NE by N, NE, NE by E, ENE, E by N, E: N, N by W, NNW, NW by N, NW, NW by W, NNW,W by N, W ; S, S by E, SSE, SE by S, SE, SE by E, ESE, E by S, E; S, S by W, SSW, SW by S, SW, SW by W, WSW, W by S, W. It is easy, therefore, to convert any rumb into degrees; thus, SE by E = S 5 points ES 90° ES 56° 15′ E. PROPOSITION II. To determine the Ship's Rate. are attached to the vertical radius of a wooden sector, having its arc so loaded with a strip of lead as to swim buried in the sea with its face perpendicular to the line of draft. The instrument is denominated the Log and Line. The log-line is divided into equal parts, called knots, of which 120 = a nautical mile; hence the number of knots run off from a light reel while a half minute glass is emptying, corresponds to the miles which the ship sails in an hour. PROPOSITION III. To determine the zenith distance of a heavenly body. H H #T I. The apparent altitude above the apparent horizon is observed with the sextant. This instrument, so useful to the surveyor and astronomer and indispensable to the navigator since it may be held in the hand without any fixed support, consists essentially of an arc embracing 60° and graduated as 120°, of an index, I, carrying upon the centre, O, a mirror, MON, of a second glass, PGQ, one half silvered, and of a telescope, T. Besides, there are screws for fastening and tilting the mirror, MN, for tilting and turning G, for tilting and elevating or depressing the telescope, T, and for fastening the index, I, and moving it over a small arc when once clamped. Now let the index, I, take up such a position that the moveable mirror, MN, shall be parallel to the fixed, PQ, and let a ray of light, HO, fall upon MN in a direction Fig. 137. Fig. 1372. to be reflected in OG and again from G through the telescope, T, to the eye. Since, by a principle in Optics, the incident and reflected rays make equal angles with the mirrors, we have and < HOM = GON | HOM=TGQ = GTM ; hence, the rays HO and HGT being parallel, the two images of the distant object from which they proceed, the one seen by reflection from G and the other through the clear part, will appear to coincide in the direction TGH. But a ray, SO, falling in any other direction, being reflected in OS, will not enter the telescope, and, in order to make it do so, we advance the index, I, till arriving at i, OS, coincides with OG. There results, The angle measured by bringing into coincidence the (631) images of two objects, one seen by reflection and the other directly, is double the arc passed over by the index. The reasons for the following adjustments will now be (632) obvious. First Adjustment. To make the index glass, O, perpendicular to the plane of the instrument. Bring the index to the middle of the graduated arc, and, looking into the mirror, observe whether the limb seen directly and by reflection appear broken or continuous. Second Adjustment. To make the horizon glass, G, perpendicular to the plane of the instrument. Having interposed the colored glasses, direct the telescope to the sun, or, better at night, to a star of the first magnitude, when, on moving the index backward and forward, the two images, in passing each other, should exactly coincide. Third Adjustment. To make the line of collimation, or the axis of the telescope, parallel to the plane of the instrument. Turn the eye-piece till the two wires stretched parallel to each other in the common focus of the lenses for the purpose of restricting the observer to the centre of the field of view, become parallel to the plane of the instrument; next, bring two objects, as the edges of the sun and moon, distant by 90° or more, into coincidence upon one of the wires; the images should continue to coincide when, by turning the instrument a little, they are made to appear on the sec ARTIFICIAL HORIZON. 307 ond wire. The above adjustments should be repeated one after the other till all are quite accurate. Fourth Adjustment. To determine the index error, or to make the zeros of the vernier and limb agree. The error will be determined by bringing the reflected and direct images of a star or planet into coincidence, or, by observing the readings when the images of the sun are brought into contact on opposite sides. Fifth Adjustment. To make the reflected and direct images equally bright. Turn the up and down piece which carries the telescope to and from the plane of the instrument, till the object is accomplished. For a description of the Reflecting Circle, see Francœur's "Géodésie." Now, for example, suppose it be required to find the ap- (633) parent altitude of the sun's lower limb above the apparent horizon. Turn the shades which are situated in front of the mirrors into the lines OG, HG, so as properly to soften both the reflected and direct rays; next, set the index at zero and direct the telescope to the sun; push the index a little till the lower image is out of sight, following the upper one; drop the screen in front of the horizon glass that the sky may appear, and continue the motion of the index till the sun's image touches the horizon; clamp, and balance the instrument gently about the line TGH, alternately producing and breaking contact, the better to see when the tangency becomes exact, and this will be accomplished by carefully turning the tangent screw, which impresses a small motion upon the index. A microscope may be employed for reading the angle, and one is sometimes attached to the index. S Scholium I. On shore an artificial horizon may be employed, consisting of a basin of mercury, from the surface of which the light of the celestial body is reflected. The measured distance, SMS, of the two images will be double the apparent altitude, SMH. H Sa (634 M Fig. 138. Scholium II. As a convenience in finding the time, we (635) may choose a point of observation, and determine, once for all, the hour angle of a terrestrial object, sufficiently remote and distinct, from which to measure the angular distance of the sun, whenever required. Scholium III. In obtaining the data for the longitude, (636) three arcs, measured at the same instant, are required; viz., the altitudes of the moon and a star or the sun and the lunar distance. The three measures may, however, be executed by a single observer, by taking at equal and short intervals of time, 1°, the altitude of the sun or star; 2°, the altitude of the moon; 3°, the lunar distance; 4°, a second altitude of the sun; 5°, a second altitude of the moon-from which the altitudes simultaneous with the lunar distance will be readily found. II. For the depression of the horizon. Let A be the position of the observer, elevated above the level of the sea by the altitude h, let T be the apparent horizon, O the earth's centre and r its radius, also let AOT e, and the depression TAH [= AOT] = d. We find H d h Fig. 139. 648000 12 IAL => (637) π observing that h is small compared with r, and, consequently, tand = d nearly, also that an arc of 1", π ; (= 180.60.60 60) is contained Now, from the aggregate of many observations made on shore, with an instrument adjusted by a spirit level, there results, Scholium. It will be observed that the value 24395000 (639) is greater than the true radius, which, according to Dr. Bowditch, may be taken at 20911790 feet. We infer, therefore, that a ray of light, passing tangent to the sea, is bent into a curve concave toward the earth's centre; since (637), if the true value of r be taken, |