It should be noted, however, that it is extremely difficult to get soft iron rods of a satisfactory quality, for, after being placed, they seldom fail to take up more or less subpermanent magnetism. This magnetism, due to shock of gunfire, vibration while cruising or on speed trials, etc., is subject to greater and more erratic changes than that of the harder portion of the hull, and its proximity to the compass intensifies the effect of the variations in its magnetic properties.

127. When it is not possible to correct the compass at the magnetic equator there is no ready practical method by which the Flinders bar may be placed; the operation will then depend entirely upon computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work the details of procedure will not be gone into; the general principles involved are indicated, and students seeking more must consult the various works that treat the subject fully. It has been explained that each coefficient of semicircular deviation (B and Č) is made up of a subpermanent factor varying as and of a vertical induction factor varying as tan 0. If we indicate by the subscripts, and, respectively, the parts due to each force, we may write the equations of the coefficients:

1 H

+Byx tan 0; and

Now if we distinguish by the subscripts, and, the values in the first and in the second position of observation, respectively, of those quantities that vary with the magnetic latitude, we have:

The values of the coefficients in both latitudes are found from the observations made for deviations; the values of the horizontal force and of the dip at each place are known from magnetic charts; hence we may solve the first pair of equations for B, and By, and the second pair for C, and C,; and having found the values of these various coefficients, we may correct the effects of B, and C, by permanent magnets in the usual way and correct the remainder-that due to B, and C,-by the Flinders bar.

Strictly, the Flinders bar should be so placed that its repelling pole is at an angular distance from ahead equal to the "starboard angle" of the attracting pole of the vertical induced force, this angle depending upon the coefficients B, and C,; but since, as before stated, horizontal soft iron may usually be regarded as symmetrical, C, is assumed as zero and the bar placed in the midship line.

128. TO CORRECT ADJUSTMENT ON CHANGE OF LATITUDE.-The compensation of quadrantal deviation, once properly made, remains effective in all latitudes, excepting as noted in article 110; but unless a Flinders bar is used a correction of the semicircular deviation made in one latitude will not remain accurate when the vessel has materially changed her position on the earth's surface. With this in mind the navigator must make frequent observations of the compass error during a passage and must expect that the table of residual deviations obtained in the

is departed from. The new deviations may become so large that it will be found convenient to readjust the semicircular correcting magnets. This process is very simple.

When correctors at right angles are used, provide for steadying the ship, by an auxiliary compass or by the pelorus, upon two adjacent magnetic cardinal points (art. 122). Put the ship on heading North or South (magnetic), and raise or lower the athwartship magnets or alter their number until the deviation disappears; then steady on East or West (magnetic) and similarly adjust the fore-and-aft magnets, Swing ship for a new table of residual deviations."

129. It must be borne in mind that the compensation of the compass is not an exact science and that the only safeguard is unceasing watchfulness on the navigator's part. As the ship's iron is partly "hard" and partly "soft," the subpermanent magnetism may change appreciably from day to day, especially in a new ship as the magnetism absorbed in building "shakes out." After a ship has been in service for one or two years, the magnetic conditions may be said to be "settled." They undergo changes, however, to a greater or less extent, on account of the following influences or conditions:

(a) Continuous steaming on one general course for several days, especially in rough weather, or lying alongside a dock on one heading for a long period.

(b) Shock of gunfire, even on a ship that has been in commission for more than a year, has been known to introduce an 8° error, which disappeared in the course of a few days.

(c) Extensive alterations or repairs in the vicinity of the compass. The use of scaling hammers on a military top caused a 3° change in one of the U. S. S. Connecticut's compasses.

(d) Steaming with boilers (especially under forced draft) whose funnel is near the compass has been known to cause a change of more than 10°, the retained magnetism being "cooked out."

(e) On the U. S. S. Oregon, a grounded searchlight circuit caused a change of 9°. (f) Ships have reported changes of as much as 7° when struck by lightning or after passing through very severe thunderstorms.

The binnacle fittings must be carefully inspected from time to time, to see that the correctors have not changed position. At least once a year the quadrantal correctors should be examined for polarity. This can be done by moving them, one at a time, as close to the compass as practicable and then revolving them slowly about the vertical axis; if the compass is deflected, the magnetism should be removed by bringing the sphere to a low red heat and then letting it cool slowly.

There is no excuse for large deviations in a standard or steering compass, and they should not be allowed to exist.

CHAPTER IV.
PILOTING.

130. Piloting, in the sense given the word by modern and popular usage, is the art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to navigation are available for fixing the position, and where the depth of water and dangers to navigation are such as to require a constant watch to be kept upon the vessel's course and frequent changes to be made therein.

Piloting is the most important part of navigation and the part requiring the most experience and nicest judgment. An error in position on the high seas may be rectified by later observation, but an error in position while piloting usually results in disaster. Therefore the navigator should make every effort to be proficient in this important branch, bearing in mind that a modern vessel is usually safe on the high seas and in danger when approaching the land and making the harbor.

131. Requisites.-The navigator should have ready on approaching the land the charts of the coast and the largest scale detail charts of the locality at which he expects to make his landfall, the sailing directions, and the light and buoy list, all corrected for the latest information from the Notices to Mariners and other sources. The usual instruments employed in navigation should be at hand and in good working order. The most important instrument-the sounding machine should be in place and in order at least a day before the land is to be made. The importance of the sounding machine can not be exaggerated. The latest deviation table for the standard compass must be at hand.

132. LAYING THE COURSE.-Mark a point upon the chart at the ship's position; then mark another point for which it is desired to steer; join the two by a line drawn with the parallel ruler, and, maintaining the direction of the line, move the ruler until its edge passes through the center of the compass rose and note the direction. If the compass rose indicates true directions, this will be the true course; and must be corrected for variation and deviation (by applying each in the opposite direction to its name) to obtain the compass course; if it is a magnetic rose, the course need be corrected for deviation only.

Before putting the ship on any course a careful look should be taken along the line over which it leads to be assured that it clears all dangers.

133. METHODS OF FIXING POSITION.-A navigator in sight of objects whose positions are shown upon the chart may locate his vessel by any one of the following methods: (a) cross bearings of two known objects; (b) the bearing and distance of a known object; (c) the bearing of a known object and the angle between two known objects; (d) two bearings of a known object separated by an interval of time, with the run during that interval; (e) sextant angles between three known objects. Besides the foregoing there are two methods by which, without obtaining the precise osition, the navigator may assure himself that he is clear of any particular danger. These are: (f) the danger angle; (g) the danger bearing.

The choice of the method will be governed by circumstances, depending upon which is best adapted to prevailing conditions.

134. CROSS BEARINGS OF TWO KNOWN OBJECTS.-Choose two objects whose position on the chart can be unmistakably identified and whose respective bearings from the ship differ, as nearly as possible by 90°; observe the bearing of each, either by compass or pelorus, taking one as quickly as possible after the other; see that the ship is on an even keel at the time the observation is made, and, if using the pelorus, be sure also that she heads exactly on the course for which the pelorus is set. Correct the bearings so that they will be either true or magnetic, according as they are to be plotted by the true or magnetic compass rose of the chart-that is, if observed by compass, apply deviation and variation to obtain the true bearing, or deviation

only to obtain the magnetic; if observed by pelorus, that instrument should be set for the true or magnetic heading, according as one or the other sort of reading is required, and no further correction will be necessary. Draw on the chart, by means of the parallel rulers, lines which shall pass through the respective objects in the direction that each was observed to bear. As the ship's position on the chart is known to be at some point of each of these lines, it must be at their intersection, the only point that fulfills both conditions.

In figure 13, if A and B are the objects and OA and OB the lines passing through them in the observed directions, the ship's position will be at O, their intersection.

A

A

C

The plotting of a position from two bearings is greatly facilitated by the use of a plotter devised by Lieut. R. A. Koch, United States Navy, as reference to the compass rose on the chart, the use of parallel rulers, and the drawing of lines on the chart are obviated. brief description of this plotter and its uses is as follows: All materials except bolt and washers are transparent. A square (7 by 7 inches) ruled with two series of lines at right angles about one-half inch apart, and a disk (7 inches in diameter) marked in degrees are placed on a central hollow bolt of brass and are capable of being clamped together with any degree of friction required. Three arms are placed so as to revolve around the same hollow bolt and can be clamped together in any position. In order to plot a position from compass bearings of two objects, and lay off a new course, the zero mark of the disk should be revolved to the East or West of the true North and South line of the square by an amount equal to the compass error in degrees. Two of the arms are then set by the degrees on the disk to the two observed compass bearings. The plotter is then manipulated on the chart until the two arms intersect the objects observed and the vertical lines on the square are parallel to the meridians of the chart. Mark the point of intersection of the arms by inserting a pencil in the hollow central bolt. An arm may then be swung to intersect any object on the chart and the compass course to that object read from the disk. This plotter can also be used to obtain the error of the compass from bearings of three objects by compass.

FIG. 13.

B

135. If it be possible to avoid it, objects should not be selected for cross bearings which subtend an angle at the ship of less than 30° or more than 150°, as, when the lines of bearing approach parallelism, a small error in an observed bearing gives a large error in the result. For a similar reason objects near the ship should be taken in preference to those at a distance.

136. When a third object is available a bearing of that may be taken and plotted. If this line intersects at the same point as the other two (as the bearing OC of the object C in the figure), the navigator may have a reasonable assurance that his "fix" is correct; if it does not, it indicates an error somewhere, and it may have arisen from inaccurate observation, incorrect determination or application of the deviation, or a fault in the chart.

137. What may be considered as a form of this method can be used when only one known object is in sight by taking, at the same instant as the bearing, an altitude of the sun or other heavenly body and noting the time; work out the sight and obtain the Sumner line (as explained in Chapter XV), and the intersection of this with the direction line from the object will give the observer's position in the same way as from two terrestrial bearings.

138. BEARING AND DISTANCE OF A KNOWN OBJECT.-When only one object is available, the ship's position may be found by observing its bearing and distance. Follow the preceding method in the manner of taking, correcting, and plotting the

FIG. 14.

bearing; then, on this line, lay off the distance from the object, which will give the point occupied by the observer. In figure 14, if A represents the object and AO the

The stadimeter is an instrument, similar to a sextant, employed in the United States Navy, reading directly the distance of the object observed when set for the height of the object.

Range-finding instruments are used in the United States Navy for readily finding the distance of an observed object, and these instruments do not require knowledge of the height of the object. These instruments are accurate for navigational purposes up to ten thousand yards.

139. It is not ordinarily easy to find directly the distance of an object at sea. The most accurate method is when its height is known and it subtends a fair-sized angle from the ship, in which case the angle may be measured by a sextant" and the distance computed or taken from a table. Table 33 of this work gives distances up. to 5 miles, corresponding to various heights and angles. Captain Lecky's "Danger Angle and Offshore Distance Tables" carries the computation much further. The use of this method at great distances must not be too closely relied upon, as small errors, such as those due to refraction, may throw out the results to a material extent, but it affords an excellent approximation; and, as this method of fixing position is employed only when no other is available, the best possible approximation has to suffice.

In measuring vertical angles, strictness requires that the observation should be so made that the angle at the foot of the object should equal 90° and that the triangle be a right triangle, as OMN, figure 15, where the line OM is truly horizontal, and not as in the triangle O'MN, where the condition is not fulfilled. This error is inappreciable, however, save at very close distances, when it may be sufficiently corrected by getting down as low as possible on board the vessel, so that the eye is near the water line. One condition exists, however, where the error is material-that shown in

figure 16, where the visible shore line is at M', a considerable distance from M, the point vertically below the summit. In this case there is nothing to mark M in the observer's eye, and it is essential that all angles be measured from a point close down to the water line.

If a choice of objects can be made, the best results will be obtained by observing that one which subtends the greatest angle, as small errors will then have the least effect.

140. There is another method, known as Buckner's method, for determining the distance of an object, which is available under certain circumstances. This consists in observing, from a position aloft, the angle between the object and the line of the sea horizon beyond. By reference to Table 34 will be found the distance in yards corresponding to different angles for various heights of the observer from 20 to 120 feet. The method is not accurate beyond moderate distances (the table being limited to 5,000 yards) and is obviously only available for finding the distance of an isolated object, such as an islet, vessel, or target, over which the horizon may In employing this method the higher the position occupied by the observer the more precise will be the results.

be seen.

141. In observing small angles, such as those that occur in the methods just described, it is sometimes convenient to measure them on and off the limb of the sextant. First look at the bottom of the object and reflect the top down into coincidence; then look through the transparent part of the horizon glass at the top and bring the bottom up by its reflected ray. The mean of the two readings will be the true angle, the index correction having been eliminated by the operation.

142. When the methods of finding distance by a vertical or a horizon angle are not available, it must be obtained by such means as exist. Estimate the distance by the appearance; take a sounding, and note where the depth falls upon the line