5. To find the angular distance between two objects H and S, Fig. 2, the index bar is moved until the image of S, formed after two reflections, coincides with the image of H, formed by the direct rays. Then the angular distance between S and H is equal to twice the angle ECI. But, as previously stated, every half degree on the graduated arc ED is marked as a whole degree; hence, the reading of the

scale gives double the angle ECI, which is the required angular distance between S and H. The fineness of the reading, as made by means of the vernier, on a good instrument is 10".

6. How to Read Off the Sextant. - As previously stated, the limb of a sextant is divided into degrees; these are further subdivided into 20', 15', or 10', commencing from the right when the instrument is held before the observer.

If the space between each degree is divided into three parts, you can measure an angle up to 20'; if divided into four parts, you can measure an angle up to 15'; if divided into six parts, you can measure an angle up to 10' on the limb. Thus, the fineness of the graduations on the limb of the instrument, part of which is shown in Fig. 4, is 20'. Now, at the end of the index bar C, just below the graduations on the limb mn, is affixed the vernier plate a b, at the right-hand side of which is a spearshaped mark called the index. If this index points directly to a division on the limb, for instance, as

10

0

20

15

10 5

in the figure, to that

FIG. 5

of the second degree,

the reading will be at once obtained as 2°. But if, as is more likely, the index points between two divisions, as in Fig. 5, between 1° 20′ and 1° 40', the reading will be about 1° 30'.

This, however, is not sufficiently exact, and in order to obtain a more accurate reading the graduations on the vernier are used as follows: First read off on the limb the degrees and divisions nearest the index mark; then run the eye along the graduations on the vernier until you find one of its divisions that coincides exactly with one of the divisions on the limb. Read off the number of minutes and fraction of minutes thus indicated on the vernier, and add this to the number of degrees and minutes previously read off on the limb. The result is the exact angle measured. Thus, in Fig. 5, the division on the limb nearest the index mark indicates 1° 20'; then along the graduations on the vernier we find the mark indicating 11' to coincide with one of the graduations on the limb; adding this number of minutes to those previously obtained, the exact angle measured will be 1° 20' + 11' = 1° 31'.

7. When readings are made "off the arc," that is, when the index mark stands to the right of the zero mark, proceed as follows: Read off on the limb the number of degrees and minutes from the zero mark to the

division nearest the index mark (left side) and add to this the number of minutes, read toward the right, from the last mark on the vernier to the coincident division.

Thus, on the limb in Fig. 6, we have 1° 20′, and from the last, or 20, mark to Hence,

the coincident division on the vernier we have 6'. the measured angle is 1° 20′ + 6′ = 1° 26'.

8. When the first attempt is made to read off a sextant, the student will probably see several divisions on the limb and the vernier that appear to coincide; this, however, is only a delusion of the inexperienced eye. After some practice, he will soon be able to single out the division on the vernier that coincides exactly with the one on the limb.

9. When measuring the angular distance between any two objects on shore, the instrument should be held so that its plane passes through the two objects; the reflected image of one object is then brought into contact with the other object seen direct through the transparent portion of the horizon glass. The measured angle is then read off-as directed in Art. 6.

10. Measurement of Horizontal Angles. For obvious reasons, the student should master the method of measuring horizontal angles with the sextant. The instrument is then held in a horizontal position with its face either up or down, depending on which of the two selected objects. is best suited as the base. For instance, when measuring

angles at night, if y, Fig. 7 (a), represents a fixed light and x a flash light, it is evidently more convenient to see y by reflection and x direct; therefore, x is used as the base and y is brought into contact with it by moving forwards the index bar, the instrument being held face up. Again, if the conditions are reversed, that is, x, Fig. 7 (b), being a fixed

light and y a flash light, then y, for similar reasons, is used as the base and x is brought into contact with it, the instrument being held horizontally, face down. In case both lights are flash lights, the one having the longest or most frequent interval of display should be brought into contact with the other.

DETERMINING THE POSITION OF A SHIP WHEN IN SIGHT OF LAND

11. The position of a ship when in sight of land may be found by several methods, a few of which are given in the following articles:

12. By Means of a Single Bearing and Estimated Distance. This method consists of observing the bearing of some known object by the compass and then estimating the distance by the eye. The method is practicable when the distance is small, but since distances measured by the eye, as a rule, are overestimated, probably to the extent of

one-fifth or more of the whole, this method must not be relied on when the safety of the ship depends on an accurate knowledge of its position.

13. By Means of Cross-Bearings. This method has been described in Lake Navigation, Part 2.

14. By Means of the Isosceles Triangle, and "Four-Point" Bearing. A compass bearing is taken of a light, or other prominent known object, when it is 2, 3, or 4 points on the bow, and the time and log noted. When

the bearing has doubled, the log and time are again noted. (If a patent log is used, it is not necessary to note the time but simply the register of the log at both bearings.) The distance of the ship from the object is then equal to the distance run in the interval between the first and second bearings, or, the difference of readings of the patent log at the two bearings.

15. To find the ship's position on the chart, lay off from the object the second bearing properly corrected, and on this line, from the object, mark the distance run. The point thus obtained will be the position of the ship. To

exemplify this, let a, Fig. 8, represent a ship steering a course due north. At e is situated a known object; when this object bears N N E, or the angle bae is two points on the bow, note the indication of the patent log. Then, when