See typed list of tables in side this cover

1916, 1930, 1951, 1934, and 1956 editions of

(tables in back of book)

(1916)

fable So. litle

% Traverse table, degrees

Conversion of departure into differ-

531

621 634

755

772

817

5

5B

42 44

45

not in these editions - refer to 1958 edition, Table 4, pace 106)

Meridional parts

Distance of an object by tso bear ings, degrees

tables

(not in these editions - refer to 1988 edition, Table l?JLj^ise_140>

Logarittes of numbers

Logarithms of trigonometric func tions, degrees

Logarithmic and natural haversines

i

No. 9

American Practical Navigator

An Epitome of Navigation and Nautical Astronomy

ORIGINALLY BY

NATHANIEL BOWDITCH, LL. D.

PUBLISHED BY THE

UNITED STATES HYDROGRAPHIC OFFICE

UNDER THE AUTHORITY OF THE SECRETARY OF THE NAVY

WASHINGTON

GOVERNMENT PRINTING OFFICE 1916

y /

/

Mtton.

STATUTES OF AUTHOKIZATION.

There shall be a Hydrographic Office attached to the Bur.eau of Navigation in the Navy Department, for the improvement of the means for navigating safely the vessels of the Navy and of the mercantile marine, by providing, under the authority of the Secretary of the Navy, accurate and cheap nautical charts, sailing directions, navigators, and manuals of instructions for the use of all vessels of the United States, and for the benefit and use of navigators generally. (R. S. 431.)

The Secretary of the Navy is authorized to cause to be prepared, at the Hydro- graphic Office attached to the Bureau of Navigation in the Navy Department, maps, charts, and nautical books relating to and required in navigation, and to publish and furnish them to navigators at the cost of printing and paper, and to purchase the plates and copyrights of such existing maps, charts, navigators, sail ing directions, and instructions, as he may consider necessary, and when he may deem it expedient to do so, and under such regulations and instructions as he may prescribe. (R. S. 432.)

2

r

TEXT AND APPENDICES.

.300861

NOTE ON REPRINT OF 1916. — This reprint is the same as the 1914 edition, except that the examples worked out in the text have been brought up to date to accord with the form of the American Nautical Almanac as now published.

CONTENTS OF F^RT I.

Page. Abbreviations

Chapter I. Definitions relating to Navigation 9

II. Instruments and Accessories in Navigation 11

III. The Compass Error 36

IV. Piloting 56

V. The Sailings 72

VI. Dead Reckoning 84

VII. Definitions relating to Nautical Astronomy 87

VIII. Instruments employed in Nautical Astronomy 91

IX. Time and the Nautical Almanac 102

X. Correction of Observed Altitudes 115

XI. The Chronometer Error 121

XII. Latitude 126

XIII. Longitude 140

XIV. Azimuth 144

XV. The Sumner Line 150

XVI. The Practice of Navigation at Sea 169

XVII. Marine Surveying 189

XVIII. Winds 206

XIX. Cyclonic Storms 212

XX. Tides 225

XXI. Ocean Currents 232

XXII. Ice and its Movements in the North Atlantic Ocean 238

Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1916

which have reference to examples for that year given in this work 248

II. A collection of Forms for working Dead Reckoning and various Astronomical Sights,

with notes explaining their application under all circumstances 254

III. Explanation of certain Rules and Principles of Mathematics of use in the Solution

of Problems in Navigation 266

IV. Maritime Positions and Tidal Data ; 278

Index.. 358

ABBREVIATIONS USED IN THIS WORK.

Alt. (or ft) Altitude.

a. m Ante meridian.

Amp Amplitude.

App Apparent.

App. t Apparent time.

Ast Astronomical.

Ast. t Astronomical time.

Aug Augmentation.

Az. (orZ) Azimuth.

C Course.

C. C Chronometer correction.

C — W Chronometer minus watch.

Chro. t Chronometer time.

Co. L Co. latitude.

Col Column.

Corr Correction.

Cos Cosine.

Cosec Cosecant.

Cot Cotangent.

d (or Dec.) Declination.

D (or D.Lo) Difference longitude.

Dep Departure.

Dev Deviation.

Diff Difference.

Dist Distance.

DL Difference latitude.

D. R Dead reckoning.

E., Ely East, easterly.

Elap. t Elapsed time.

Eq. t Equation of time.

F Longitude factor.

/ Latitude factor.

G. (or Gr.) Greenwich.

G. A. T Greenwich apparent time.

G. M. T Greenwich mean time.

G. S. T Greenwich sidereal time.

ft Altitude.

H Meridian altitude.

H. A. (or t) Hour angle.

Hav Haversine.

H. D Hourly difference.

H. P. (or Hor. par.). .Horizontal parallax.

Hr-s Hour-s.

H. W High water.

I. C Index correction.

L. (or Lat.) Latitude.

L. A. T Local apparent time.

L. M. T Local mean time.

L. S. T Local sidereal time.

Lo. (or Long.) Longitude.

Log Logarithm.

Lun. Int Lunitidal interval.

L. W Low water.

A Longitude.

m Meridional difference.

Merid Meridian or noon.

Mag Magnetic.

M. D Minute's difference.

Mid Middle.

Mid. L Middle latitude.

M. T Meantime.

nat Natural.

N., Nly North, northerly.

N. A. (orNaut. Aim.) Nautical Almanac.

Np Neap .

Obs Observation.

p (or P. D.) Polar distance.

p. c Per compass.

JP. D. (or p) Polar distance.

P. L. (or Prop. Log.). Proportional logarithm.

p. m Post meridian.

p, & r Parallax and refraction.

rar Parallax.

R. A Right ascension.

R. A. M. S Right ascension mean sun.

Red Reduction.

Ref Refraction.

S., Sly South, southerly.

S. D Semidiameter.

Sec Secant.

Sid Sidereal.

Sin Sine.

Spg Spring.

t Hour angle.

T Time.

Tab Table.

Tan Tangent.

Tr. (or Trans. ) Transit.

Var Variation.

Vert Vertex or vertical.

W., Wly West, westerly.

W. T Watch time.

z Zenith distance.

Z Azimuth.

6 Auxiliary angle.

X Difference longitude in time.

SYMBOLS.

The Sun.

The Moon. * _ A Star or Planet. "Q (C Alt. upper limb. LQ ([_ Alt. lower limb. (J) |3 Azimuthal angle.

A a ..Alpha. £/? ..Beta. F Y ..Gamma. Ad.. Delta. E e . .Epsilon. Z C -.Zeta. Hr) ..Eta. 8 d ..Theta.

Iota.

Kappa.

Lambda. u.

GREEK LETTERS.

f.

I

K K A X M it

Degrees. Minutes of Arc. Seconds of Arc. Hours.

Minutes of Time. Seconds of Time.

N v Nu.

s e xi.

0 o Omicron.

n 7i Pi.

, P p Rho.

1 a (r)... Sigma. T T Tau.

T y Upsilon.

0 <j> Phi.

X x Chi.

¥</> Psi.

Q a> Omega .

CHAPTER I. DEFINITIONS KELATING TO NAVIGATION,

1. That science, generally termed Navigation, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree of accuracy, the position of his vessel at any tune, is properly divided into two branches : Navigation and Nautical Astronomy.

2. Navigation, in its limited sense, is that branch which treats of the determina tion of the position of the ship by reference to the earth, or to objects thereon. It comprises (a) Piloting, in which the position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning, in which the position at any moment is deduced from the direction and amount of a vessel's progress from a known point of departure.

3. Nautical Astronomy is that branch of the science which treats of the deter mination of the vessel's place by the aid of celestial objects — the sun, moon, planets, or stars.

4. Navigation and Nautical Astronomy have been respectively termed Geo- Navigation and Celo- Navigation, to indicate the processes upon which they depend.

5. As the method of piloting can not be employed excepting near land or in moderate depths of water, the navigator at sea

must fix his position either by dead reckoning or by observation of celestial objects; the latter method is more exact, but as it is not always available, the former must often be depended upon.

6. THE EARTH. — The Earth is an oblate spheroid, being a nearly spherical, body slightly flattened at the poles; its longer or equatorial axis measures about 7,927 statute miles, and its E shorter axis, around which it rotates, about 7,900 statute miles.

The Earth (assumed for purposes of illustra tion to be a sphere) is represented in figure 1.

The Axis of Rotation, usually spoken of simply as the Axis, is PP'.

The Poles are the points, P and P', in which the axis intersects the surface, and are designated, respectively, as the North Pole and the South Pole.

The Equator is the great circle EQMW, formed by the intersection with the earth's surface of a plane perpendicular to the axis ; the equator is equidistant from the poles, every point upon it being^90° from each pole.

Meridians are the great circles rQP', PMP', PM'P', formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane).

Parallels of Latitude are small circles NTn, N'n'T', formed by the intersection with the earth's surface of planes passed parallel to the equator.

The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. Latitude is reckoned North and South, from the equator as an origin, through 90° to the poles; thus, the latitude of the point T is MT, north, and of the point T', MT, north. The Difference of Latitude between any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction; tnus, the difference of latitude between T and T' is Tnf or T'n, north from T or south from T'.

The Longitude of a place on the surface of the earth is the arc of the equator inter cepted between its meridian and that of some place from which the longitude is

9

FIG. l.

10 ... fc.. DEFINITION RELATING TO NAVIGATION.

reckoned. Longitude is measured East or West through 180° from the meridian of a designated- place, such meridian being termed the Prime Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich, England. If, in the figure, the prime meridian be PGQP', then the longitude of the point T is QM, east, and of T', QM', east. The Difference of Longitude between any two places is the arc of the equator intercepted between their meridians, and is called East or West, according to direction ; thus, the difference of longitude between T and T' is MM', east from M or west from M'. The Departure is the linear distance, measured on a parallel of latitude, between two meridians; unlike the various quanti ties previously defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number of miles corresponding to the distance Tn in the latitude of T, or to n'T' in the latitude of T'.

The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equian gular Spiral. In the figure this line is represented by TYT'. The constant angle which this line makes with the meridians is called the Course; and the length of the line between any two places is called the Distance between those places;

The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. This unit is defined in the United States of America as being 6,080.27 feet in length and equal to one-sixtieth part of a degree of a great circle ot a sphere whose surface is equal in area to the area of the surface of the earth.

The nautical mile is not exactly the same in all countries, but, from the navi gator's standpoint, the various lengths adopted do not differ materially.

Since, upon the ocean, latitude has been capable of easier and more accurate determination than longitude, it might naturally be expected that there exists an intimate fixed relation between the nautical mile and the minute of latitude (or the length of that portion of a meridian which subtends at the earth's center the angular measure of one minute); but on account of the fact that the earth is not a perfect sphere, a fixed relation does not exist, and the arc of a meridian that subtends an angle of 1' at the center of the earth varies slightly in length from the Equator to the poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Its average length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France, Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23 feet.

For purposes of navigation the nautical mile is assumed to be equal to a minute of latitude in all parts of the world; and, hence, when a vessel changes her position to the north or south by 1 nautical mile, it may always be considered that the latitude has changed 1'. Owing to the fact that the meridians converge toward the poles, the difference of longitude produced by a change of position ol 1 mile to the east or west will vary with the latitude ; thus, a departure of 1 mile will equal a difference of longitude of 1' at the Equator, but of more than 1' at any higher latitude, being in fact equal to I'.l of longitude in latitude 30° and to 2' of longitude in latitude 60°.

In England the nautical mile, corresponding to the Admiralty knot, is regarded as having a length of 6,080 feet.

The statute mile of 5,280 feet, which is employed in land measurements, is commonly used in navigating river and lake vessels. This is notably the case on the Great Lakes of America, but with the recognition of the advantages to be gamed by the nractice of nautical astronomy in the navigation of these vessels, the use of the nautical mile is extending.

The Great Circle Track or Course between any two places is the route between those places along the circumference of the great circle which joins them. In the figure this line is represented by T/T . From the properties of a great circle (which is a circle upon the earth's surface formed by the intersection of a plane passed through its center) the distance between two points measured on a great circle track is shorter than the distance upon any other line which joins them. Except when the two points are on the same meridian or when both lie upon the equator, the great circle track will always differ from the rhumb line, and the great circle track wul intersect each intervening meridian at a different angle.

CHAPTER II.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION,

DIVIDERS OB COMPASSES.

7. This instrument consists of two legs movable about a joint, so that the points at the extremities of the legs may be set at any required distance from each other. It is used to take and transfer distances and to describe arcs and circles. When used for the former purpose it is termed dividers, and the extremities of both legs are metal points; when used for describing arcs or circles, it is called a compass, and one of the metal points is replaced by a pencil or pen.

PARALLEL RULERS.

8. Parallel rulers are used for drawing lines parallel to each other in any direc tion, and are particularly useful in transferring the rhumb-line on the chart to the nearest compass-rose to ascertain the course, or to lay off bearings and courses.

PROTRACTOR.

9. This is an instrument used for the measurement of angles upon paper; there is a wide variation in the material, size, and shape in which it may be made. (For a description of the Three Armed Protractor, see art. 428, Chap. XVII.)

THE CHIP LOG.

10. This instrument, for measuring the rate of sailing, consists of three parts; viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the ship ceases to partake of the motion 01 the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain interval, if the distance of the ship from this stationary object be measured, the approximate rate of sailing will be given. The log-chip is the float, the log-line is the measure of the distance, and the log-glass defines the interval of tune.

The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with lead on the circular edge sufficiently to make it float upright in the water. There is a hole in each corner of the log-chip, and the log-line is knotted in the one at the apex; at about 8 inches from the end there is seized a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its bight a wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as the line is checked this peg pulls out, thus allowing the log-chip to be hauled in with the least resistance.

The log-line is about 150 fathoms in length, one end made fast to the log-chip, the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms from the log-chip a permanent mark of red bunting about 6 inches long is placed to allow sufficient stray line for the log-chip to clear the vessel's eddy or wake. The rest of the fine is divided into lengths of 47 feet 3 inches called Jcnots, by pieces of fish-fine thrust through the strands, with one, two, three, etc., knots, according to the number from stray-fine mark; each knot is further subdivided into five equal lengths of two-tenths of a knot each, marked by pieces of white rag.

The length of a knot depends upon the number of seconds which the log-glass measures; the length of each knot must bear the same ratio to the nautical mile (-gV of a degree of a great circle of the earth, or 6,080 feet) that the time of the glass does to an hour.

11

12 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

In the United States Navy all log-lines are marked for log-glasses of 28 seconds, for which the proportion is :

3600 : 6080 = 28s : x,

x being the length of the knot. Hence,

z = 47ft.29, or47ft3in.

The speed of the ship is estimated in knots and tenths of a knot.

The log-glass is a sand glass of the same shape and construction as the old hour glass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a high rate of speed, the number of knots indi cated on a line marked for a 28-second glass being doubled to obtain the true rate of speed.

11. The log in all its parts should be frequently examined and adjusted; the

Eeg must be found to fit sufficiently tight to keep the log-chip upright; the log- ne shrinks and stretches and should often be verified; the log-glass should be compared with a watch. One end of the glass is stopped with a cork, by removing which the sand may be dried or its quantity corrected.

12. A ground log consists of an ordinary log-line, with a lead attached instead of a chip; in shoal water, where there are no well-defined objects available for fixing the position of the vessel and the course and speed are influenced by a tidal or other current, this log is sometimes used, its advantage being that the lead marks a sta tionary point to which motion may be referred, whereas the chip would drift with the stream. The speed, which is marked in the usual manner, is the speed over the ground, and the trend of the line gives the course actually made good by the vessel.

THE PATENT LOG.

13. This is a mechanical contrivance for registering the distance actually run by a vessel through the water. There are various types of patent logs, but for the most part they act upon the same principle, consisting of a registering device, a fly or rotator, and a log or towline; the rotator is a small spino3e with a number of blades extending radially in such manner as to form a spiral, and, when drawn through the water in the direction of its axis, rotates about that axis after the manner of a screw propeller; the rotator is towed from the vessel by means of a log or towline from 30 to 100 fathoms in length, made fast at its apex, the line being of special make, so that the turns of the rotator are transmitted through it to. the worm shaft of the register, to which the inboard end of the line is attached; the registering device is so constructed as to show upon a dial face the distance run, according to the number of turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that the rotator will be towed clear of the wake.

14. Though not a perfect instrument, the patent log affords a means of deter mining the vessel's speed through the water. It will usually be found that the indications of the log are in error by a constant percentage, and the amount of this error should be determined by careful experiment and applied to all readings.

Various causes may operate to produce inaccuracy of working in the patent log, such as the bending of the blades of the rotator by accidental blows, fouling of the rotator by seaweed or refuse from the ship, or mechanical wear of parts of the register. The length of the towline has much to do with the working of the log, and by varying the length the indications of the instrument may sometimes be adjusted when the percentage of error is small; it is particularly important that the line shall not be too short. The readings of the patent log can not be depended upon for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head or a following sea, when the effect depends upon the wave motion as well as upon the speed of the vessel.

15. Electrical registers for patent logs are in use, the distance recorded by the mechanical register being communicated electrically to some point of the vessel which is most convenient for the purposes of those charged with the navigation.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

13

17 fathoms from the lead, same as at 7 fathoms.

20 fathoms from the lead, with 2 knots.

25 fathoms from the lead, with 1 knot.

30 fathoms from the lead, with 3 knots.

35 fathoms from the lead, with 1 knot.

40 fathoms from the lead, with 4 knots.

And so on.

16. A number of instruments based upon different physical principles have been devised for recording the speed of a vessel through the water and have been used with varying degrees of success. Of these the hydraulic speed indicator, known as the Nicholson Ship Log, affords an instance.

17. The revolutions of the screw propeller afford in a steamer the most valuable means of determining a vessel's speed through the water. The number of revolu tions per knot must be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foulness of bottom.

THE LEAD.

18. This device, for ascertaining the depth of water, consists essentially of a suitably marked line, having a lead attached to one of its ends. It is an invaluable aid to the navigator in shallow water, particularly in thick or foggy weather, and is often of service when the vessel is out of sight of land.

Two leads are used for soundings — the Tiand-lead, weighing from 7 to 14 pounds, with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the line being 100 fathoms or upward in length.

Lines are generally marked as follows :

2 fathoms from the lead, with 2 strips of leather.

3 fathoms from the lead, with 3 strips of leather. 5 fathoms from the lead, with a white rag.

7 fathoms from the lead, with a red rag.

10 fathoms from the lead, with leather having a

hole in it.

13 fathoms from the lead, same as at 3 fathoms. 15 fathoms from the lead, same as at 5 fathoms.

Fathoms which correspond with the depths marked are called marks; the inter mediate fathoms are called deeps; the only fractions of a fathom used are a half and a quarter.

A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of the vessel by which it is to be used.

Lead lines should be measured frequently while wet and the correctness of the marking verified. The distance from the leadsman's hand to the water's edge should be ascertained in order that proper allowance may be made therefor in taking soundings at night.

19. The deep-sea lead may be armed by filling with tallow a hole hollowed out in its lower end, by which means a sample of the bottom is brought up.

THE SOUNDING MACHINE.

20. This machine possesses advantages over the deep-sea lead, for which it is a substitute, in that soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship. It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is controlled by a suitable brake. Crank handles are provided for reeling in the wire after the sounding has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end for the reception of the tallow for arming. Above the lead is a cylindrical case containing the depth-registering mechanism; various devices are in use for this purpose, all depending, however, upon the increasing pressure of the water with increasing depths.

21. In the Lord Kelvin machine a slender glass tube is used, sealed at one end and open at the other, and coated inside with a chemical substance which changes color upon contact with sea water; this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the contained air being compressed with a force dependent upon the depth. The limit of discoloration is marked by a clearly defined line, and the depth of the sounoling corresponding to this line is read off from a scale. Tubes that have been used in comparatively shallow water may be used again where the water is known to be deeper.

22. A tube whose inner surface is ground has been substituted for the chemical- coated lube, ground glass, when wet, showing clear. The advantage of these tubes

14

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

is that they may be used an indefinite number of times if thoroughly dried. To facilitate drying, a rubber cap is fitted to the upper end, which, when removed, admits of a circulation of the air through the tube.

23. As a substitute for the glass tubes a mechanical depth recorder contained in a suitable case has been used. In this device the pressure of the water acts upon a piston against the tension of a spring. A scale with an index pointer records the depth reached. The index pointer must be set at zero before each sounding.

24. Since the action of the sounding machine, when glass tubes are used, depends upon the compression of the air, the barometric pressure of the atmosphere must be taken into account when accurate results are required. The correction consists in increasing the indicated depth by a fractional amount according to the following table :

Bar. reading.	Increase.
29.75	One-fortieth.
30.00	One-thirtieth.
30.50	One- twentieth.
30.75	One-fifteenth.

THE MARINER'S COMPASS.

25. The Mariner's Compass is an instrument consisting either of a single magnet, or, more usually, of a group of magnets, which, being attached to a graduated circle pivoted at the center and allowed to swing freely in a horizontal plane, has a tendency, when not affected by disturbing magnetic features within the ship, to lie with its magnetic axis in the plane of the earth's magnetic meridian, thus affording a means of determining the azimuth, or horizontal angular distance from that meridian, of the ship's course and of all visible objects, terrestrial or celestial.

26. The circular card of the compass is divided on its periphery into 360°, frequently numbered from 0° at North and South to 90° at East and West; also into thirty-two divisions of 11J° each, called points, the latter being further divided into naif-points and quarter-points; still finer subdivisions, eighth-points, are some- tunes used, though not indicated on the card. A system of numbering the degrees from 0° to 360°, always increasing toward the right, is shown in figure 2. This system is in use in the United States Navy and by the mariners of some foreign nations, and its general adoption would carry with it certain undoubted advantages.

27. Boxing the Compass is the process of naming the points in their order, and is one of the first things to be learned by the young mariner. The four principal points are called cardinal points and are named North, South, East, and West; each differs in direction from the adjacent one by 90°, or 8 points. Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal points, named according to their position Northeast, Southeast, etc. Midway between each cardinal and inter-cardinal point, at an angular distance of 22£°, or 2 points, is a point whose name is made up of a combination of that of the cardinal with that of the inter-cardinal point: North-Northeast, East-Northeast, East-Southeast, etc. At an angular distance of 1 point, or 11J°, from each cardinal and inter-cardinal point (and therefore midway between it and the 22£°-division last described), is a point which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardinal point in the direction of which it lies : North by East, Northeast by North, Northeast by East, etc.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

15

In boxing by fractional points, it is evident that each division may be referred to either of the whole points to which it is adjacent; for instance, NE. by N. £ N. and NNE. £ E. would describe the same division. It is the custom in the United States Navy to box from North and South toward East and West, excepting that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point; as

No. 1742

JUNE 1908

FIG. 2.

N. i E., N. by E. £ E., NNE. $ E., NE. £ N., etc. Some mariners, however, make it a practice to box from each cardinal and inter-cardinal point toward a 22 J°-point (NNE., ENE., etc.); as N. * E., N. by E. J E., NE. by N. * N., NE. i N., etc.

The names of the whole points, together with fractional points (according to the nomenclature of the United States Navy), are given in the following table, which

16

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

shows also the degrees, minutes, and seconds from North or South to which each division corresponds:

	Points.	Angular measure.		Points.	Angular measure.
NORTH TO EAST. Nnrlh-		0 / //	EAST TO SOUTH. East.	8	90 00 00
N 1 E	1	2 48 45	E.-JS	8J	92 48 45
N | E		5 37 30	E. IS	8J	95 57 30
N £ E	1	8 26 15	E. f S	8|	98 26 15
N bv E	1	11 15 00	E. byS...	9	101 15 00
N hv E 4 E		14 03 45	ESE. f E . .	91	104 03 45
N byE }E	14	16 52 30	ESE.iE	91	106 52 30
N by E £ E	if	19 41 15	ESE. IE	9|	109 41 15
NNE	2	22 30 00	ESE	10	112 30 00
NNE £E	21	25 18 45	SE. byE. fE	101	115 18 45
NNE $ E	2*	28 07 30	SE. byE. |E	101	118 07 30
NNE f E	2i	30 56 15	SE. byE. IE...	id	320 56 15
NE by N	3	33 45 00	SE. by E	11	123 45 00
NE. f N	31	36 33 45	SE. |E	111	126 33 45
NE. 1 N	3f	39 22 30	SE.^E	111	129 22 30
NE 1 N	3J	42 11 15	SE. IE	llf	13^ 11 15
NE	4	45 00 00	SE	12	135 00 00
NE £ E	41	47 48 45	SE 1 S	121	137 48 45
NE A E	41	50 37 30	SE £ S	12i	140 37 30
NE f E	4J	53 26 15	SE | S	12£	143 26 15
NE byE	5	56 15 00	SE by S	13	146 15 00
NE by E 1 E	51	59 03 45	SSE £ E	131	149 03 45
NE byE. IE	5A	61 52 30	SSE. * E .	m	151 52 30
NE byE. IE	53	64 41 15	SSE. 1 E .	13f	154 41 15
ENE	6	67 30 00	SSE	14	157 30 00
ENE i E	61	70 18 45	S by E f E	141	160 18 45
ENE i E	6f	73 07 30	S by E ^ E	14!	163 07 30
ENE. IE..	S|	75 56 15	S by E IE	LUZ 14 1	165 56 15
E.byN	7	78 45 00	S byE	15	168 45 00
E £ N	71	81 33 45	S 4 E	151	171 33 45
E $N	71	84 2? 30	S i E	151	174 " 30
E JN	7i	87 11 15	S i E	15?	177 11 15
SOUTH TO WEST.			WEST TO NORTH. West	24	270 00 00
South	16	180 00 00	WIN	241	272 48 45
S.I W	161	182 48 45	W £N	241	275 37 30
S. * W	161	185 37 30	W f N	24J	278 96 15
S.fW	16J	188 26 15	W by N	25	281 15 00
S. byW	17	191 15 00	WNW £ W	251	284 03 45
S.byW.JW	171	194 03 45	WNW ^W	251	286 52 30
S. byW. *W	17*	196 52 30	WNW 1 W	25J	289 41 15
S.byW.fW..,	17|	199 41 15	WNW	26	292 30 00
ssw	18	202 30 00	NW by W f W	9fil	295 IS 4^
SSW. -JW	181	205 18 45	NW by W \ W	*'U4 261	298 07 30
ssw. ^w	18*	208 07 30	NW byW 1W	262	300 56 15
ssw. * w....	181	210 56 15	NW byW	27	303 45 00
SW. byS	19	213 45 00	NW £ W	271	306 33 45
SW.f S	191	216 33 45	NW £ W	27^	309 22 30
SW. *S	191	219 22 30	NW 1 W	27J	311 11 15
SW.-fcS	19|	222 11 15	NW	28	315 00 00
SW	20	225 00 00	NW 1 N	281	317 48 45
SW. 1W	201	227 48 45	NW 1 N	981	320 37 30
SW. *W	201	230 37 30	NW £ N	98f	393 26 15
SW. | W	201	233 26 15	NW by N	99	326 15 00
SW. byW...	21	2o6 15 00	NNW £ W	291	329 03 45
Sw.byW.iW..	211	2o9 03 45	NNW 1 W	291	331 52 30
SW. by W. £W	21*	241 52 30	NNW 1 W	29$	334 41 15
SW. by W. 2 W	21|	244 41 15	NNW	30	337 30 00
WSW	22	247 30 00	NV>v W 3. W	cmi	340 1^4^
WSW.iW....	22J	250 18 45	N by W 1 W	Qfii	343 07 30
WSW. *W	22i	253 07 30	N "by W 1 W	30f	345 5(j 15
WSW. £ W..	22|	255 56 15	N byW	31	348 45 00
W.bvS	23	258 45 00	N £ W	311	351 33 45
W.f S	231	261 33 45	N 4 W	311	354 " 30
W.-fcS	Oof 23*,	264 '22 30	N 1 W	Qli	357 n 15
W.-JS	23£	267 11 15	North	39	3fiO 00 00

INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 17

28. The compass card is mounted in a bowl which is carried in gimbals, thus enabling the card to retain a horizontal position while the ship is pitching and rolling. A vertical black line called the lubber's line is marked on the inner surface of the bowl, and the compass is so mounted that a line joining its pivot with the lubber's fine is parallel to the keel line of the vessel; thus the lubber's line always indicates the com pass direction of the ship's head.

29. According to the purpose which it is designed to fulfill, a compass is desig nated as a Standard, Steering, Check, or Boat Compass. On United States naval ves sels additional compasses are designated as follows: Maneuvering, battle, auxiliary battle, top, and conning-tower compasses.

30. There are two types of magnetic compass in use, the liquid or wet and the dry; in the former the bowl is filled with liquid, the card being thus partially buoyed with consequent increased ease of working on the pivot, and the liquid further serving to decrease the vibrations of the card when deflected by reason 01 the motion of the vessel or other cause. On account of its advantages the liquid compass is used in the United States Navy.

31. THE NAVY SERVICE T^-INCH LIQUID COMPASS. — This consists of a skeleton card 7i inches in diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets symmetrically placed.

The magnet system of the card consists of four cylindrical bundles of steel wires; these wires are laid side by side and magnetized as a bundle between the poles of a powerful electro-magnet. They are afterwards placed in a cylindrical case, sealed, and secured to the card. Steel wires made up into a bundle were adopted because they are more homogeneous, can be more perfectly tempered, and for the same weight give greater magnetic power than a solid steel bar.

Two of the magnets are placed parallel to the north and south diameter of the card, and on the chords of 15° (nearly) of a circle passing through their extremities. These magnets penetrate the air vessel, to which they are soldered, and are further secured to the bottom of the ring of the card. The other two magnets of the system are placed parallel to the longer magnets on the chords of 45° (nearly) of a circle passing through their extremities and are secured to the bottom of the ring of the card.

The card is of a curved annular type, the outer ring being convex on the upper and inner side, and is graduated to read to one-quarter point, a card circle being adjusted to its outer edge and divided to half degrees, with legible figures at each 3°, for use in reading bearings by an azimuth circle or in laving the course to degrees.

The card is provided with a concentric spheroidal air vessel, to buoy its own weight and that of the magnets, allowing a pressure of between 60 and 90 grains on the pivot at 60° F.; the weight of the card in air is 3,060 grains. The air vessel has within it a hollow cone, open at its lower end, and provided with the pivot bearing or cap, containing a sapphire, which rests upon the pivot and thus supports the card; the cap is provided with adjusting screws for accurately centering the card. The pivot is fastened to the center of the bottom of the bowl by a flanged plate and screws. Through this plate and the bottom of the bowl are two small holes which communicate with the expansion chamber and admit of a circulation of the liquid between it and the bowl. The pivot is of gun metal with an iridium cap.

The card is mounted in a bowl of cast bronze, the glass cover of which is closely packed with rubber, preventing the evaporation or leakage of the liquid, which entirely nils the bowl. This liquid is composed of 45 per cent pure alcohol and 55 per cent distilled water, and remains liquid below —10° F.

The lubber's line is a fine line drawn on an enameled plate on the inside of the bowl, the inner surface of the latter being covered with an insoluble white paint.

Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal, by means of which the bowl is kept constantly full without the show of bubbles or the development of undue pressure caused by the change in volume of the liquid due to changes of temperature.

The rim of the compass bowl is made rigid and its outer edge turned strictly to gauge to receive the azimuth circle.

32. THE DRY COMPASS. — The Lord Kelvin Compass, which may be regarded as the standard for the dry type, consists of a strong paper card with the central parts cut away and its outer edge stiffened by a thin aluminum ring. The

61828°—]

20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

standard compass being located, all peloruses may be oriented from it by any one of the following methods :

(a) By making the azimuth of a celestial body, taken by the pelorus, coincide with the simultaneous azimuth of the same body taken by the standard compass.

(b) By a similar process with distant objects; and the parallax may be entirely eliminated in an apparently near object, in view of the moderate distance that usually separates the two instruments on board ship.

(c) By reciprocal bearings between the correct instrument and the instrument to be established; it is evident that if the lubber lines of the two instruments are both in the direction of the keel line, the bearing of the sight vane of each from the other (one being reversed) should coincide.

(d) By computing the angle subtended at the pelorus by the fore-and-aft line through the pelorus and the line drawn through the pelorus to the jack staff, and setting the pelorus at this angle and sighting on the jack staff.

THE CHART.

37. A nautical chart is a miniature representation upon a plane surface, in accordance with a definite system of projection or development, 01 a portion of the navigable waters of the world. It generally includes the outline of the adjacent land, together with the surface forms and artificial features that are useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the land, by soundings that are fixed in position by accurate determinations. Except in charts of harbors or other localities so limited that the curvature of the earth is inappreciable on the scale of construction, a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude in relation to which the features to be depicted on the chart are located and drawn; and the mathematical relation between the meridians and parallels of the chart and those of the terrestrial sphere determines the method of measurement that is to be employed on the chart and the special uses to which it is adapted.

38. There are three principal systems of projection in use: (a) the Mercator, (b) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally used for purposes of navigation proper, while the polyconic and the gnomonic charts are employed for nautical purposes in a more restricted manner, as for plotting surveys or for facilitating great circle sailing.

39. THE MERCATOR PROJECTION. — The Mercator Projection, so called, may be said to result from the development, upon a plane surface, of a cylinder which is tangent to the earth at the equator, the various points of the earth's surface having been projected upon the cylinder in such manner that the loxodromic curve or rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of bearing with respect to the intersected meridians as does the ship's track.

In order to realize this condition, the line of tangency, which coincides with the earth's equator, being the circumference of a right section of the cylinder, will appear as a right ^line on the development; while the series of elements of the cylinder corresponding to the projected terrestrial meridians will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the chart, main taining the same relative positions and the same distance apart on that equator as the meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a system of right lines parallel to each other and to the equator, and will so^intersect the meridians as to form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable, increasing from the equator in such manner that the angles made by the rhumb line with the meridian on the chart may maintain the required equality with the corresponding angles on the spheroid. , 40. MERIDIONAL PARTS. — At the equator a degree of longitude is equal to a degree of latitude^ but in receding from the equator and approaching the pole, while the degrees of latitude remain always of the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the degrees of longitude become less and less.

Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of the same length, it becomes necessary, in order to preserve the propor-

INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 21

tion that exists at different parts of the earth's surface between degrees of latitude and degrees of longitude, that the former be increased from their natural lengths, and such increase must become greater and greater the higher the latitude.

The length of the meridian, as thus increased, between the equator and any given latitude, expressed in minutes at the equator as a unit, constitutes the number of Meridional Parts corresponding to that latitude. The Table of Meridional Parts or Increased Latitudes (Table 3), computed for every minute of latitude between 0° and 80°, affords facilities for constructing charts on "the Mercator projection and for solving problems in Mercator sailing.

41. To CONSTRUCT A MERCATOR CHARTS — If the chart for which a projection is to be made includes the equator, the values to be measured off are given directly by Table 3. If the equator does not come upon the chart, then the parallels of latitude to be laid down should be referred to a principal parallel, preferably the lowest parallel to be drawTi on the chart. The distance of any other parallel of latitude from the principal parallel is then the difference of the values for the two taken from Table 3.

The values so found may either be measured off, without previous numerical conversion, by means of a diagonal scale constructed on the chart, or they may be laid dowTi on the chart by means of any properly divided scale of yards, meters, feet, or miles, after having been reduced to the scale of proportions adopted for the chart.

If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes of arc on the equator, a diagonal scale may first be constructed, on which ten meridional parts, or ten minutes of arc on the equator, have a length of half an inch.

It may often be desirable to adapt the scale to a certain allotment of paper. In this case, the lowest and the highest parallels of latitude may first be drawn on the sheet on which the transfer is to be made. The distance oetween these parallels may then be measured, and the number of meridional parts between them ascertained. Dividing the distance by this number will then give the length of one meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multiplied. This quantity will represent the scale of the chart. If it occurs that the limits of longitude are a governing consideration, the case may be similarly treated.

EXAMPLE: Let a projection be required for a chart of 14° extent in longitude between the parallels of latitude 20° 30' and 30° 25', and let the space allowable on the paper between these parallels measure 10 inches.

Entering the column in Table 3 headed 20°, and running down to the line marked 30' in the side column, will be found 1248.9; then, entering the column 30°, and running dowTi to the line 25', will be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which 1' of arc of the equator is taken as the unit. On the intended projection, therefore,

10in

I7 of arc of longitude will measure .,. ' =0.0152 inch, which will be the scale of the

o5o.b

chart. For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have to be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale of one inch.

Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart. Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this perpendicular to be the parallel of latitude 20° 30'; this will be the southern inner neat line of the chart. From the intersection of the lines lay off on the parallel, on each side of the middle meridian, seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches; and through the points thus obtained draw lines parallel to the middle meridian, and these will be the eastern and western neat lines of the chart.

In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for 21° 00', which are 1280.8. Subtracting from this number the number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch, which is the distance on the chart between 20° 30' and 21° 00'. On the meridians

a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is made of the Position Plotting Sheets published by the Hydrographic Office.

20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

standard compass being located, all peloruses may be oriented from it by any one of the following methods :

(a) By making the azimuth of a celestial body, taken by the pelorus, coincide with the simultaneous azimuth of the same body taken by the standard compass.

(&) By a similar process with distant objects; and the parallax may be entirely eliminated in an apparently near object, in view of the moderate distance that usually separates the two instruments on board ship.^

(c) By reciprocal bearings between the correct instrument and the instrument to be established; it is evident that if the lubber lines of the two instruments are both in the direction of the keel line, the bearing of the sight vane of each from the other (one being reversed) should coincide.

(d) By computing the angle subtended at the pelorus by the fore-and-aft line through the pelorus and the line drawn through the pelorus to the jack staff, and setting the pelorus at this angle and sighting on the jack staff.

THE CHART.

37. A nautical chart is a miniature representation upon a plane surface, in accordance with a definite system of projection or development, of a portion of the navigable waters of the world. It generally includes the outline of the adjacent land, together with the surface forms and artificial features that are useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the land, by soundings that are fixed in position by accurate determinations. Except in charts of harbors or other localities so limited that the curvature of the earth is inappreciable on the scale of construction, a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude in relation to which the features to be depicted on the chart are located and drawn; and the mathematical relation between the meridians and parallels of the chart and those of the terrestrial sphere determines the method of measurement that is to be employed on the chart and the special uses to which it is adapted.

38. There are three principal systems of projection in use: (a) the Mercator, (&) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally used for purposes of navigation proper, while the polyconic and the gnomonic charts are employed for nautical purposes in a more restricted manner, as for plotting surveys or for facilitating great circle sailing.

39. THE MERCATOR PROJECTION. — The Mercator Projection, so called, may be said to result from the development, upon a plane surface, of a cylinder which is tangent to the earth at the equator, the various points of the earth's surface having been projected upon the cylinder in such manner that the loxodromic curve or rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of bearing with respect to the intersected meridians as does the ship's track.

In order to realize this condition, the line of tangency, which coincides with the earth's equator, being the circumference of a right section of the cylinder, will appear as a right line on the development; while the series of elements of the cylinder corresponding to the projected terrestrial meridians will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the chart, main taining the same relative positions and the same distance apart on that equator as the meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a system of right lines parallel to each other and to the equator, and will so^intersect the meridians as to form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable, increasing from the equator in such manner that the angles made by the rhumb line with the meridian on the chart may maintain the required equality with the corresponding angles on the spheroid. , 40. MERIDIONAL PARTS. — At the equator a degree of longitude is equal to a degree of latitude^ but in receding from the equator and approaching the pole, while the degrees of latitude remain always of the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the degrees of longitude become less and less.

Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of the same length, it becomes necessary, in order to preserve the propor-

INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 21

tion that exists at different parts of the earth's surface between degrees of latitude and degrees of longitude, that the former be increased from their natural lengths, and such increase must become greater and greater the higher the latitude.

The length of the meridian, as thus increased, between the equator and any given latitude, expressed in minutes at the equator as a unit, constitutes the number of Meridional Parts corresponding to that latitude. The Table of Meridional Parts or Increased Latitudes (Table 3), computed for every minute of latitude between 0° and 80°, affords facilities for constructing charts on the Mercator projection and for solving problems in Mercator sailing.

41. To CONSTRUCT A MERCATOR CHART.® — If the chart for which a projection is to be made includes the equator, the values to be measured off are given directly by Table 3. If the equator does not come upon the chart, then the parallels of latitude to be laid down should be referred to a principal parallel, preferably the lowest

Earallel to be drawn on the chart. The distance of any other parallel of latitude *om the principal parallel is then the difference of the values for the two taken from Table 3.

The values so found may either be measured off, without previous numerical conversion, by means of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any properly divided scale of yards, meters, feet, or miles, after having been reduced to the scale of proportions adopted for the chart.

If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes of arc on the equator, a diagonal scale may first be constructed, on which ten meridional parts, or ten minutes of arc on the equator, have a length of half an inch.

It may often be desirable to adapt the scale to a certain allotment of paper. In this case, the lowest and the highest parallels of latitude may first be drawn on the sheet on which the transfer is to be made. The distance between these parallels may then be measured, and the number of meridional parts between them ascertained. Dividing the distance by this number will then give the length of one meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multiplied. This quantity will represent the scale of the chart. If it occurs that the limit.fi of longitude are a governing consideration, the case may be similarly treated.

EXAMPLE: Let a projection be required for a chart of 14° extent in longitude between the parallels of latitude 20° 30' and 30° 25', and let the space allowable on the paper between these parallels measure 10 inches.

Entering the column in Table 3 headed 20°, and running down to the line marked 30' in the side column, will be found 1248.9; then, entering the column 30°, and running down to the line 25', will be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which I' of arc of the equator is taken as the unit. On the intended projection, therefore,

10in

1' of arc of longitude will measure -_„ ' =0.0152 inch, which will be the scale of the

DOO.D

chart. For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have to be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale of one inch.

Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart. Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this perpendicular to be the parallel of latitude 20° 30'; this will be the southern inner neat line of the chart. From the intersection of the lines lay off on the parallel, on each side of the middle meridian, seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches; and through the points thus obtained draw lines parallel to the middle meridian, and these will be the eastern and western neat lines of the chart.

In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for 21° 00', which are 1280.8. Subtracting from this number the number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch, which is the distance on the chart between 20° 30' and 21° 00'. On the meridians

a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is made of the Position Plotting Sheets published by the Hydrographic Office.

22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

lay off distances equal to 0.478 inch, and through the three points thus obtained draw a straight line, which will be the parallel of 21° 00'.

Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the distances will be respectively:

Oin.015X (1344.9- 1248.9) = 1.440 inches. Oin.015 X (1409.5 - 1248.9) = 2.409 inches. Oin. 105 X (1474.5 -1248.9) =3.384 inches, etc.

Thus will be shown the parallels of latitude 22° 00', 23° 0<X, 24° 00', etc. FinaUy, lay down in the same way the parallel of latitude 30° 25', which will be the northern inner neat line of the chart.

A degree of longitude will measure on this chart Oin.015X60 = Oin.9. Lay off, therefore, on the lowest parallel of latitude drawn on the chart, on a middle one, and on the highest parallel, measuring from the middle meridian toward each side, the distances of Oin.9, lin.8, 2in.7, 3in.6, etc., in order to determine the points where meridians answering to full degrees cross the parallels drawn on the chart. Through the points thus found draw the meridians. Draw then the outer neat lines of the chart at a convenient distance outside of the inner neat lines, and extend to them the meridians and parallels. Between the inner and outer neat lines of the chart sub divide the degrees of latitude and longitude as minutely as the scale of the chart will permit, the subdivisions of the degrees of longitude being found by dividing the degrees into equal parts, and the subdivisions of the degrees of latitude being accu rately found in the same manner as the full degrees of latitude previously described, though it will generally be found sufficiently exact to make even subdivisions of the degrees, as in the case of the longitude.

The subdivisions between the two eastern as well as those between the two western neat lines will serve for measuring or estimating terrestrial distances. Dis tances between points bearing North and South of each other may be ascertained by referring them to the subdivisions between the same parallels. Distances repre sented by fines at an angle to the meridians (loxodromic lines) may be measured by taking between the dividers a small number of the subdivisions near the middle latitude of the line to be measured, and stepping them off on that line. If, for instance, the terrestrial length of a line running at an angle to the meridians between the parallels of latitude of 24° 00' and 29° 00' be required, the distance shown on the neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may be taken between the dividers and stepped off on that line.

42. Coast lines and other positions are plotted on the chart by their latitude and longitude. A chart may be transferred from any other projection to that of Mercator by drawing a system of corresponding parallels of latitude and meridians over both charts so close to each other as to form minute squares, and then the lines and characters contained in each square of the map to be transferred may be copied by the eye in the corresponding squares of the Mercator projection.

Since the unit of measure, the mile or minute of latitude, has a different value in every latitude, there is an appearance of distortion in a Mercator chart that covers any large extent of surface; for instance, an island near the pole will be represented as being much larger than one of the same size near the equator, due to the different scale used to preserve the character of the projection.

43. THE POLYCONIC PROJECTION. — This projection is based upon the develop ment of the earth's surface on a series of cones, a different one for each parallel of latitude, each one having the parallel as its base, and its vertex in the point where a tangent to the earth at that latitude intersects the earth's axis. The degrees of latitude and longitude on this chart are projected in their true length, and the general distortion of the figure is less than in any other method of projection, the relative magnitudes being closely preserved.

A straight line on the polyconic chart represents a near approach to a great circle, making a slightly different angle with each successive meridian as the meridians converge toward the pole and are theoretically curved lines; but it is only on charts of large extent that this curvature is apparent; the parallels are also curved, this fact being apparent to the eye upon all excepting the largest scale charts.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

23

This method of projection is especially adapted to the plotting of surveys; it is also employed to some extent in the charts of the United States Coast and Geodetic Survey.

44. GXOMONIC PROJECTION. — This is based upon a system in which the plane of projection is tangent to the earth at some given point; the eye of the spectator is situated at the center of the sphere, where, being at once in the plane of every great circle, it will see all such circles projected as straight lines where the visual rays passing through them intersect tie plane of projection. In a gnomonic chart, tne straight line between any two points represents the arc of a great circle, and is there fore the shortest line between those points.

Excepting in the polar regions, for which latitudes the Mercator projection can not be constructed, the gnomonic charts are not used for general navigating purposes. Their greatest application is to afford a ready means of finding the course and distance at any time in great circle sailing, the method of doing which will be explained in Chapter V.

45. MERIDIANS ADOPTED IN THE CONSTRUCTION OF CHARTS. — The nautical charts published by the United States are based upon the meridian of Greenwich, and this meridian is also the origin of longitudes in use on the nautical charts pub lished by the Governments of Argentina, Austria, Belgium, Brazil, Chile, Denmark, France, Germany, Great Britain, Holland (for all charts published at Batavia and for some published at The Hague), Italy, Japan, Norway, Kussia, and Sweden.

In addition to the meridian of Greenwich, the meridian of Pulkowa Observatory, at St. Petersburg, in longitude 30° 19' 40" east of Greenwich, is sometimes referred to in the Kussian charts. At one time the Royal Observatory at Naples, in longitude 14° 15' 26" east of Greenwich, was referred to in the Italian charts, and the observatory at Christiania, in longitude 10° 43' 23" east of Greenwich, was referred to in the Norwegian charts.

The French charts are based both upon the meridian of Greenwich and of the Observatory at Paris, which has been determined to be in longitude 2° 20' 14.6" east of Greenwich. The longitudes of a few Dutch charts published at The Hague are reckoned from the meridian of the west tower of the cathedral at Amsterdam, which is hi longitude 4° 53' 01.5" east of Greenwich. Portuguese charts refer to the meridian of the observatory of Lisbon Castle, which is 9° 07' 54.86" west of Greenwich, and to the meridian of Greenwich. In Spain the meridian of San Fernando Observatory, at Cadiz, which is in longitude 6° 12' 20" west of Greenwich, and also the meridian of Greenwich, are used.

46. QUALITY OF BOTTOM. — The following table shows the qualities of the bottom, as expressed on charts of various nations:

United States.	English.	French.	Italian.	Spanish.	German.
Clay C.	Clay cl.	Argile A.	Argila arg.	Arcillo or Barro.arc.	Lehm L.
Coral Co.	Coral crl	Corail Cor	Corallo crl	Coral cl	KoT"allen Kor.
Gravel G	Gravel g	Gravier Gr	Rena or Ghia'a gh	Cases' jo Co	Ivies k
Mud. M	Mud m	Vase V	Fango f	Fango or Luno F	RnhlamTn Schl.
Rocky rky.	Rock rk.	Roche... R.	Roccia r.	PiedraorRoca P.orr.	Felsig Fls.
Sand S	Sand s	Sable S	Sfibbiaor Vena s	\rpna -V	Sand Sd.
Shells Sh	Shells • sh	Coquille Coq			Muscheln M
Stone St	Stones st	Pierre P	Pietre p	Piedra P	Stein St.
Weed Wd	Weed wd	Kerb II		Alga V	Gras Grs
Fine fne	Fine f	Fin fir.	Fino	Fina f	Fein f.
Coarse crs.	Coarse c	Gros g	Grosso	Gruesa ™	Grob . gb.
Stiff stf.	Stiff stf.	Dure.. d.	Tenace.	Tena?	Schlick sk.
Soft sft.	Soft sff	Voile ni	Molle	Blando bclo	Welch Wch.
Black.. bk	Black blk		Nero		Schwarz sch\v.
Red rd.	Red. rd	Rou^e r	Rosse	Rojo r	Roth r.
Yellow... yl	Yellow v	Jaune j	Giallo	\marillo am	Gelb.... g.
Gray . . ev

24

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

47. MEASURES OF DEPTH. — The following table shows the units of measure employed in expressing the soundings in the more modern nautical charts of foreign nations together with their equivalents in the units of measure used in the charts published by the United States :

Nationality of chart.	Unit of soundings.	Equivalent in United States units.	Nationality of chart.	Unit of soundings.	Equivalent in United States units.
Feet. 3.281 3.281 6.223 3. 281 3.281 6.176 5.905 3.281 3.281 3.281 3.281	Fathoms.	Feet.	Fathoms.
Argentine... Austrian Belgian	Metro	0.547 0.547 1.037 0.547 0.547 1.029 0.984 0.547 0.547 0.547 0.547	Japanese Norwegian	Fathom	6.000 3.281 6.176 3.281 6.000 3.281 5.492 3.281 5.844 6.000	1.000 0.547 1.029 0.547 1.000 0.547 0.914 0.547 0.974 1.000
Metro	Metre
or faden	Portuguese. . Russian	or favn
Metre Metro	Metro .
Chilean Danish. Dutch	Sajene
favn vadem	Spanish	Metro
Swedish. . .	or braza
French	or metre	Metre
Metre	British	or famn Fathom..
German .	do..
Italian 1	Metro

THE BAROMETER.

48. The barometer is an instrument for measuring the pres sure of the atmosphere, and is of great service to the mariner in affording a knowledge of existing meteorological conditions and of the probable changes therein. There are two classes of barometer — mercurial and aneroid.

49. THE MERCURIAL BAROMETER. — This instrument, in vented by Torricelli in 1643, indicates the pressure of the atmos phere by the height of a column of mercury.

If a glass tube of uniform internal diameter somewhat more than 30 inches in length and closed at one end be com pletely^ filled with pure mercury, and then placed, open end down, in a cup of mercury (the open end having been tempo rarily sealed to retain the liquid during the process of inverting), it will be found that the mercury in the tube will fall until the top of the column is about 30 inches above the level of that which is in the cup, leaving in the upper part of the tube a vacuum. Since the weight of the column of mercury thus left standing in the tube is equal to the pressure by which it is held WISP! HI *n Pos^on — namely, that of the atmospheric air — it follows that the height of the column is subject to variation upon variation of that pressure; hence the mercury falls as the pressure of the atmosphere decreases and rises as that pressure increases. The mean pressure of the atmosphere is equal to nearly 15 pounds to the square inch; the mean height of the barometer is about 30 inches.

50. In the practical construction of the barometer the glass tube which contains the mercury is encased in a brass tube, the latter terminating at the top in a ring to be used for suspension, and at the bottom in a flange, to which the several parts form ing the cistern are attached. The upper part of the brass tube is partially cut away to expose the mercurial column for observation; abreast this opening is fitted a scale for measur ing the height, and along the scale travels a vernier for exact reading; the motion of the vernier is controlled by a rack and pinion, the latter having a milled head accessible to the observer,

FIG. 3. by which the adjustment is made. In the middle of the brass FIG. 4.

tube is fixed a thermometer, the bulb of which is covered from the outside but open toward the mercury, and which, being nearly in contact with the glass tube, indicates the temperature of the mercury and not that of the external

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

25

air; the central position of the column is selected in order that the mean temperature may be obtained — a matter of importance, as the temperature of the mercurial column must be taken into account in every accurate application of its reading.

51. In the arrangement of further details mercurial barometers are divided into two classes, according as they are to be used, as Standards (fig. 4) on shore, or as Sea Barometers (fig. 3) on shipboard.

In the Standard Barometer the scale and vernier are so graduated as to enable an observer to read the height of the mercurial column to the nearest 0.002 inch, while in the Sea Barometer the reading can not be made closer than 0.01 inch.

The instruments also differ in the method of obtaining the true height of the mercurial column at varying levels of _ the liquid in the cistern. It is evident that as the mercury in the tube rises, upon increase of atmospheric pressure, the mercury in the cistern must fall; and, conversely, when the mercurial column falls the amount of fluid in the cistern will thereby be increased and a rise of level will occur. As the height of the mercurial column is required above the existing level in the cistern, some means must be adopted to obtain the true height under varying conditions. In the Standard Barometer the mercury of the cistern is contained in a leather bag, against the bottom of which presses the point of a vertical screw, the milled head of the screw projecting from the bottom of the instrument and thus placing it under control of the observer. By this means the surface of the mercury in the cistern (which is visible through a glass casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero of the scale, and which is indicated by an ivory pointer in plain view.

In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point, but compensation for the variable level is made in the scale gradu ations ; a division representing an inch on the scale is a certain fraction short of the true inch, proper allowance being thus made for the rise in level which occurs with a fall of the column, and for the reverse condition.

Further modification is made in the Sea Barometer to adapt it to the special use for which intended. The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column known as "pumping," which arises from the motion of the ship ; and just below this point is a trap to arrest anv small bubbles of air from finding their way upward. The instrument aboard ship is suspended in a revolving center ring, in gimbals, supported on a horizontal brass arm which is screwed to the bulkhead; a vertical position is thus maintained by the tube at all times.

52. The vernier is an attachment for facilitating the exact reading of the scale of the barometer, and is also applied to many other instruments of precision, as, for example, the sextant and theodolite. It consists of a metal scale similar

in general construction to that of the instrument to which it is fitted, and arranged to move alongside of and in contact with the main scale.

The general principle of the vernier requires that its scale shall have a total length exactly equal to some whole number of divisions of the scale of the instrument and tnat this length shall be subdivided into a number of parts equal to 1 more or 1 less than the number of divisions of the instrument scale which are covered; thus, if a space of 9 divisions of the main scale be designated as the length of the vernier, the vernier scale would be divided into either 8 or 10 parts.

Suppose that a barometer scale be divided into tenths of an inch and that ^ a length of 9 divisions of such a scale be divided into 10 parts for a vernier (fig. 5) ; and suppose that the divisions of the vernier be numbered consecutively from zero at the origin to 10 at the upper extremity^. If, now, by means of the movable rack and pinion, the.bottom or zero division of the vernier be brought level with the top of the mercurial column, and that division falls into exact coincidence with a division of the main scale, then the height of the column will correspond with the scale reading indicated. In such a case the top of the vernier will also exactly coincide with a scale division, but none of the intermediate divisions will be evenly abreast FIG. 5. of such a division; the division marked "I" will fall short of a scale division by one-tenth of 1 division of the scale, or by 0.01 inch ; that marked "2" by two-tenths of a division, or 0.02 inch; and so on. If the vernier, instead of having

26

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

the zero coincide with a scale division, has the division " 1 " in such coincidence, it follows that the mercurial column stands at 0.01 inch above that scale division which is next below the zero; for the division "2," at 0.02 inch; and similarly for the others. In the case portrayed in figure 5, the reading of the^column is 29.81 inches, the scale division next below the zero being 29.80 inches, while the fact that the first division is abreast a mark of the scale shows that 0.01 inch must be added to this to obtain the exact reading.

Had an example been chosen in which 8 vernier divisions covered 9 scale divisions — that is, where the number of vernier divisions was 1 ^less than the number of scale divisions covered — the principle would still have applied. But, instead of the length of 1 division of the vernier falling short of a division of the scale by one- tenth the length of the latter, it would have fallen beyond by one-eighth. To read in such a case it would therefore be necessary to number the vernier divisions from up downward and to regard the subdivisions as -fo instead of 0.01 inch.

It is a general rule that the smallest measure to which a vernier reads is equal to the length of 1 division of the scale divided by the number of divisions of the vernier; hence, by varying either the scale or the vernier, we may arrive at any subdivision that may be desired.

53. The Sea Barometer is arranged as described for the instrument assumed in the illustration; the scale divisions are tenths of an inch, and the vernier has 10 divisions, whence it reads to 0.01 inch. It is not necessary to seek a closer reading, as complete accuracy is not attainable in observing the height of a barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capable of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts; hence the column may be read to 0.002 inch.

54. To adjust the vernier for reading the height of the mercurial column the eye should be brought exactly on a level with the top of the column; that is, the line of sight should be at right angles to the scale. When properly set, the front and rear edges of the vernier and the uppermost point of the mercury should all be in the line of sight. A piece of white paper, held at the back of the tube so as to reflect the light, assists in accurately setting the vernier by day, while a small bull's-eye lamp held behind the instrument enables the observer to get a correct reading at niojht. When observing the barometer it should hang freely, not being inclined by holding or even by touch, because any inclination wm cause the column to rise in the tube.

55. Other things being equal, the mercury will stand higher in the tube when it is warm than when it is cold, owing to expansion. For the purposes of comparison, all barometric observations are reduced to a standard which assumes 32° F. as the temperature of the mercurial column, and 62° F. as that of the metal scale; it is therefore important to make this reduction, as well as that for instrumental error (art. 57), in order to be enabled to compare the true barometric pressure with the normal that may be expected for any locality. The following table gives the value of this correction for each 2° F., the plus sign showing that the correction is to be added to the reading of the ship's barometer and the minus sign that it is to be subtracted:

Tempera ture.	Correction.	Tempera ture.	Correction.	Tempera ture.	Correction.	Tempera ture.	Correction.
0	Inch.	0	Inch..	o	Inch.	0	Inch.
20	+0.02	40	-0.03	60	-0.09	80	-0. 14
22	+0.02	42	-0.04	62	-0.09	82	-0. 14
24	+0.01	44	-0.04	64	-0.09	84	-0.15
26	+0.01	46	-0.05	66	-0. 10	86	-0. 15
28	0. 00	48	-0. 05	68	-0. 10	88	-0. 16
30	0.00	50	-0.06	70	-0. 11	90	-0.16
32	-0. 01	52	-0.06	72	-0. 12	92	-0.17
34	-0. 02	54	-0. 07	74	-0. 12	94	-0. 17
36	-0.02	56	-0. 07	76	-0. 13	96	-0. 18
38	-0.03	58	-0.08	78	-0.13	98	-0. 18

INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 27

As an example, let the observed reading of the mercurial barometer be 29.95 inches, and the temperature as given by the attached thermometer 74°; then we have:

//

Observed height of the mercury 29. 95

Correction for temperature (74°) — 0. 12

Height of the mercury at standard temperature 29. 83

56. THE ANEROID BAROMETER. — This is an instrument in which the pressure of the air is measured by means of the elasticity of a plate of metal. It consists of a cylindrical brass box, the metal in the sides being very thin; the contained air having been partially, though not completely, exhausted, the box is hermetically sealed. When the pressure of the atmosphere increases the inclosed air is compressed, the capacity of the box is diminished, and the two flat ends approach each other; when the pressure of the atmosphere decreases, the ends recede from one another in conse quence of the expansion of the inclosed air. By means of a combination of levers, this motion of the ends of the box is communicated to an index pointer which travels over a graduated dial plate, the mechanical arrangement being such that the motion of the ends of the box is magnified many times, a very minute movement of the box making a considerable difference in the indication of the pointer. The graduations of the aneroid scale are obtained by comparison with the correct readings of a standard mercurial barometer under normal and reduced atmospheric pressure.

The thermometer attached to the aneroid barometer is merely for convenience in indicating the temperature of the air, but as regards the instrument itself no cor rection for temperature can be applied with certainty. Aneroids, as now manufac tured, are almost perfectly compensated for temperature by the use of different metals having unequal coefficients of expansion; they ought, therefore, to show the same pressure at all temperatures.

The aneroid barometer, from its small size and the ease with which it may be trans ported, can often be usefully employed under circumstances where a mercurial barometer would not be available. It also has an advantage over the mercurial instrument in its greater sensitiveness, and the fact that it gives earlier indications of change of pressure. It can, however, be relied upon only when frequently com pared with a standard mercurial barometer; moreover, considerable care is required in its handling; while slight shocks will not ordinarily affect it, a severe jar or knock may change its indications by a large amount.

When in use the aneroid barometer may be suspended vertically or placed flat, but changing from one position to another ordinarily makes a sensible change in the readings; the instrument should always, therefore, be kept in the same position, and the errors determined by comparisons made while occupying its customary place.

57. COMPARISON OF BAROMETERS. — To determine the reliability of the ship's barometer, whether mercurial or aneroid, comparisons should from time to time be made with a standard barometer. Nearly all instruments read either too high or too low by a small amount. These errors arise, in a mercurial barometer, from the improper placing of the scale, lack of uniformity of caliber of the glass tube, or similar causes ; in an aneroid, which is less accurate and in which there is even more necessity for frequent comparisons, errors may be due to derangement of any of the various mechanical features upon which its working depends. The errors of the barometer should be determined for various heights, as they are seldom the same at all parts of the scale.

In the principal ports of the world standard barometers are observed at specified times each day, and the readings, reduced to zero and to sea level, are published. It is therefore only necessary to read the barometer on shipboard at those times and, if a mercurial instrument is used, to note the attached thermometer and apply the correction for temperature (art. 55). It is evident that a comparison of the heights by reduced standard and by the ship's barometer will give the correction to be applied to the latter, including the instrumental error, the reduction to sea level, and the personal error of the observer. In the United States, standard barometer readings are made by the Weather Bureau.

Aneroid Barometers may be adjusted for instrumental error by moving the index hand, but this is usually done only in the case of errors of considerable magnitude.

28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

58. DETERMINATION OF HEIGHTS BY BAROMETER. — The barometer may be used to determine the difference in heights between any two stations by means of the difference in atmospheric pressure between them. An approximate rule is to allow 0.0011 inch for each difference in level of 1 foot, or, more roughly, 0.01 inch for every 9 feet.

A very exact method is afforded by Babinet's formula. If B0 and B represent the barometric pressure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively, and t0 and t the corresponding temperatures of the air; then,

Diff . in height = C X if the temperatures be taken by a Fahrenheit thermometer,

C (in feet) =52, 494 (l + if a centigrade thermometer is used,

C (in meters) = 16,000^1

THE THERMOMETER.

59. The TJiermometer is an instrument for indicating temperature. In its construction advantage is taken of the fact that bodies are expanded by heat and contracted by cold. In its most usual form the thermometer consists of a bulb filled with mercury, connected with a tube of very fine cross-sectional area, the liquid column rising or falling in the tube according to the volume of the mercury due to the actual degree of heat, and the height of the mercury indicating upon a scale the temperature; the mercury contained in the tube moves in a vacuum produced by the expulsion of the air through boiling the mercury and then closing the top of the tube by means of the blowpipe.

There are three classes of thermometer, distinguished according to the method of graduating the scale as follows: the Fahrenheit, in which the freezing point of water is placed at 32° and its boiling point (under normal atmospheric pressure) at 212°; the Centigrade, in which the freezing point is at 0° and the boiling point at 100°; and the Reaumur, in which these points are at 0° and 80°, respectively. The Fahrenheit thermometer is generally used in the United States and England. Tables will be found in this work for the interconversion of the various scale readings (Table 31).

60. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it affords him in judging meteorological conditions from the tem perature of the air and the amount of moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea water, of the ship's position and the probable current that is being encountered.

61. The thermometers employed in determining the temperature of the air (wet and dry bulb) and of the water at the surface, should be mercurial, and of some standard make, with the graduation etched upon the glass stem; they should be compared with accurate standards, and not accepted ii their readings vary more than 1° from the true at any point of the scale.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

29

62. The dry-bulb thermometer gives the temperature of the free air. The wet-bulb thermometer, an exactly similar instrument, the bulb of \vhich is surrounded by an envelope of moistened cloth, gives what is known as the temperature of evapora tion, which is always somewhat less than the temperature of the free air. From the difference of these two temperatures the observer may determine the proximity of the air to saturation; that is, how near the air is to that point at which it will be obliged to precipitate some of its moisture (water vapor) in the form of liquid. With the envelope of the wet bulb removed, the two thermometers should read precisely the same; otherwise they are practically useless.

The two thermometers, the wet and the dry bulb, should be hung within a few inches of each other, and the surroundings should be as far as possible identical. In practice the two thermometers0 are gener ally inclosed within a small lattice case, such as that shown in figure 6 ; the case should be placed in a position on deck remote from any source of artificial heat, sheltered from the direct rays of the sun, and from the rain and spray, but freely exposed to the circulation of the air; the door should be kept closed except during the process of reading. The cloth envelope of the wet bulb should be a single thickness of fine muslin, tightly stretched over the bulb, and tied with a fine thread. The wick which serves to carry the water from the cistern to the bulb should consist of a few threads of lamp cotton, and should be of sufficient length to admit of two or three inches being coiled in the cistern. The muslin envelope of the wet bulb should be at all times thoroughly moist, but not dripping.

When the temperature of the air falls to 32° F. the water in the wick freezes, the capillary action is at an end, the bulb in consequence soon becomes quite dry, and the thermometer no longer shows the tem perature of evaporation. At such times the bulb should be thoroughly wetted with ice- cold water shortly before the time of observation, using for this purpose a camel's hair brush or feather; by this process the temperature of the wet bulb is temporarily raised above that of the dry, but only for a brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of the ice thus formed precisely as from the surface of the wrater, the thermometer will act in the same way as if it nad a damp bulb. The wet-bulb thermometer can not properly read higher than the dry, and if the reading of the wet bulb should be the higher, it may always be attributed to imperfections in the instruments.

o Called a psychrometer.

FIG. G.

30

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

63. Knowing the temperature of the wet and dry bulbs, the relative humidity of the atmosphere at the time of observation may be found from the following table :

Tempera ture of the	Difference between dry-bulb and wet-bulb readings.
					i		10°
mometer.	1°
0	PC r ct.	Per ct.	Per ct.	Per ct.	Per ct.	Per ct. Per ct.	Per ct. \ Per ct.	Per ct.
24	87	75	62	50	38	26
26	88	76	65	53	42	30	'
28	89	78	67	56	45	34	24
30	90	79	68	58	48	38	28
32	90	80	70	61	51	41	32	23
34	90	81	72	63	53	44	35	27
36	91	82	73	64	55	47	38	30	22
38	92	83	75	66	57	50	42	34	26
40	92	84	76	68	59	52	44	37	30	22
42	92	84	77	69	61	54	47	40	33	26
44	92	85	78	70	63	56	49	43	36	29
46	93	85	79	72	65	58	51	45	38	32
48	93	80	79	73	66	60	53	47	41	35
50	93	87	80	74	67	61	55	49	43	37
52	94	87	81	75	69	63	57	51	46	40
54	94	88	82	76	70	64	59	53	48	42
56	94	88	82	77	71	65	60	55	50	44
58	94	89	83	78	72	67	61	56	51	46
60	94	89	84	78	73	68	63	58	53	48
62	95	89	84	79	74	69	64	59	54	50
64	95	90	85	79	74	70	65	60	56	51
66	95	90	85	80	75	71	66	61	57	53
68	95	90	85	81	76	71	67	63	58	54
70	95	90	86	81	77	72	68	64	60	55
72	95	91	86	82	77	73	69	65	61	57
74	95	91	86	82	78	74	70	66	62	58
76	95	91	87	82	78	74	70	66	63	59
78	96	91	87	83	79	75	71	67	63	60
80	96	92	87	83	79	75	72	68	64	61
82	96	92	88	84	80	76	72	69	65	62
84	96	92	88	84	80	77	73	69	66	63
86	96	92	88	84	81	77	73	70	67	63
88	96	92	88	85	81	77	74	71	67	64
90	96	92	88	85	81	78	74	71	68	65

The table may be readily understood. For example, if the temperature of the air (dry bulb) be 60°, and the temperature of evaporation (wet bulb) be 56°, the difference being 4°, look in the column headed " Temperature of the air7' for 60°, and for the figures on the same line in column headed 4°; here 78 wiU be found, which means that the air is 78 per cent saturated with water vapor; that is, that the amount of water vapor present in the atmosphere is 78 per cent of the total amount that it could carry at the given temperature (60°). This total amount, or saturation, is thus represented by 100, and if there occurred any increase of the quantity ^of vapor beyond this point, the excess would be precipitated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per cent, or even higher in the doldrums; over the land in dry winter weather it may fall as low as 40 per cent.

64. The sea water of which the temperature is to be taken should be drawn from a depth of 3 feet below the surface, the bucket used being weighted in order to sink it. The bulb of the thermometer should remain immersed in the water at least three minutes before reading, and the reading should be made with the bulb immersed.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 31

THE LOG BOOK.

65. The Log Book is a record of the ship's cruise, and, as such, an important accessory in the navigation. It should afford all the data from which the position of the snip is established by the method of dead reckoning; it should also comprise a record of meteorological observations, which should be made not only for the purpose of foretelling the weather during the voyage, but also for contribution to the general fund of knowledge of marine meteorology.

66. A convenient form for recording the data, which is employed for the log books of United States naval vessels, is shown on page 32 ; beside the tabulated matter thus arranged, to which one page of the book is devoted, a narrative of the miscella neous events of the day, written and signed by the proper officers, appears upon the opposite page.

32

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

I 1 <| •4 Q 3 1 •s >• i g q -( 5 1		_«		Drills and exercises.
Clouds.	'01 o^ 0 areos '^unotny	::::::::::::
•raoij		Afternoon First division Second division Third division Fourth division ...... Fifth division Sixth division . Seventh division
SIoqm s 'JO SULIOJ
*;•'	sioqra^s jo a^B^g
Temperature.	,?2gS
•qinq •qinq		ejt
.
Barometer.	'pauiBWB		,o fl i§ ^ fl "-1 1||l||l fe 02 E-i fe P=H CQ 02
•satgor
Wind.	•aoioj
	;
•sstjd -THOO PJB -pireis A"q
	: : : : : : •
•ssedmoo paaaa^s sasjnoo "ja^unoo 8ui3 -ua jo SorpBa'jj		illl PI 1^1 &?SoSxfloHPl.2 f£j ^> Q P3 W O PH W O P •ssuduioo '1^03 'ITO lanj
|
E -led	as.	: : : ;	: ! • •' fl a ; ^ J J -dp(5 "rto^o^q g a>	S fLatitude ^Longitude igazine temperatures:	1:1 5<	i j
,noH	^'rHC^CO^iOOt- 0 rH g
	•aoovr	^

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

33

67. For the most part, the nature of the information called for, with the method of recording it, will be apparent. A brief explanation is here given of such points as seem to require it.

68. THE WIND. — In recording the force of the wind the scale devised by the late Admiral Sir F. Beaufort is employed. According to this scale the wind varies from 0, a calm, to 12, a hurricane, the greatest velocity it ever attains. In the lower grades of the scale the force of the wind is estimated from the speed imparted to a man-of-war of the early part of the nineteenth century sailing full and by; in the higher grades, from the amount of sail which the same vessel could carry when close-hauled. The scale, with the estimated velocity of the wind in both statute and nautical miles per hour, is as follows :

Force of -wind.	Conditions.	•Velocity.	Mean pressure in pounds per square foot.
Statute miles per Nautical miles per hour. ' hour.
0 — Calm	Full-rigged ship, all sails set, no headway. . Just sufficient to give steerage wav	0 to 3 8 13 18 23 28 34 40 48 56 65 75 90 and over.	0 to ' 2.G 6.9 11.3 15.6 20.0 24.3 29.5 34.7 41.6 48.6 56.4 65.1 78. 1 and over.	O.C3 0.23 0.62 1.2 1.9 2.9 4.2 5.9 S.4 11.5 15.5 20.6 29.6
1 Light air
2 Light breeze	Speed of 1 or 2 knots, " full and by "
3 — Gentle breeze	Speed of 3 or 4 knots, "full and by"...
4. — Moderate breeze . . . 5 Fresh breeze	Speed of 5 or 6 knots, "full and by "
All plain sail "full and by "..
6 —Strong breeze 7. — Moderate gale 8.— Fresh gale	T opgallant sails over single-reefed topsails. . Double-reefed topsails
Treble-reefed topsails (or reefed upper topsails and courses). Close-reefed topsails and courses (or lower topsails and courses). Close-reefed main topsail and reefed fore sail (or lower main topsail and reefed foresail). Storm staysails
9. — Strong gale
10 — Whole gale
11. — Storm
12. — Hurricane	Under bare poles

69. When steaming or sailing with any considerable speed, the apparent direc tion and force of the wind, as determined from a vane flag, or pennant aboard ship, may differ materially from the true direction and force, the reason being that the air appears to come from a direction and with a force dependent, not only upon the wind itself, but also upon the motion of the vessel. For instance, suppose that the wind has a velocity of 20 knots an hour (force 4), and take the case 01 two vessels, eachsteaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The former vessel will be moving with the same velocity as the ah" and in the same direction; the velocity of the wind relatively to the ship will thus be zero; on the vessel an apparent calm will prevail and the pennant will hang up and down. The latter vessel will be moving with the same velocity as the air, but in the opposite direction; the relative velocity of the two will thus be the sum of the two velocities, or 40 knots an hour, and on the second vessel the wind will apparently have the velocity corresponding very nearly with a fresh gale. Again, it might be shown that in the case of a vessel steaming west at the rate of 20 knots, with the wind blowing from north with the velocity of 20 knots an hour, the velocity with which the air strikes the ship as a result of the combined motion will be 23 knots an hour, and the direction from which it comes will be IN W. If, therefore, the effect of the speed of the ship is neglected the wind will be recorded as ]STW., force 6, when in reality it is north, force 4.

In order to make a proper allowance for this error and arrive at the true direction and force of the wind, Table 32 may be entered with the ship's speed and the apparent direction and force of the wind as arguments, and the true direction and force will be found.

61828°— 16 3

34 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

70. WEATHER. — To designate the weather a series of symbols devised by the late Admiral Beaufort is employed. The system employed in the United States Navy is as follows :

&.— Clear blue sky. p.— Passing showers of rain.

c.— Clouds. 5.— Squally weather.

d. — Drizzling, or light rain. r. — Rainy weather, or continuous rain.

/. — Fog, or foggy weather. s. — Snow, snowy weather, or snow falling.

f. — Gloomy, or dark, stormy-looking weather. t. — Thunder.

. — Hail. u. — Ugly appearances, or threatening weather.

1. — Lightning. v. — Variable weather.

m— Misty weather. w— Wet, or heavy dew.

o. — Overcast. 2. — Hazy weather.

To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain.

71. CLOUDS. — The following are the principal forms of clouds, named in the order of the altitude above the earth at which they usually occur, beginning with the most elevated. The symbols by which each is designated follows its name:

1. CIRRUS (Ci.). — Detached clouds, delicate and fibrous looking, taking the form of feathers, generally of a white color, sometimes arranged in belts which cross a portion of the sky in great circles, and, by an effect of perspective, converging toward one or two opposite points of the horizon.

2. CIRRO-STRATUS (Ci.-S.). — A thin, whitish sheet, sometimes completely cover ing the sky and only giving it a whitish appearance, or at others presenting, more or less distinctly, a formation like a tangled web. This sheet often produces halos around the sun and moon.

3. CIRRO-CUMULUS (Ci.-Cu.). — Small globular masses or white flakes, having no shadows, or only very slight shadows, arranged in groups and often in lines.

4. ALTO-CUMULUS (A.-Cu.). — Rather large globular masses, white or grayish, partially shaded, arranged in groups or lines, and often so closely packed that their edges appear confused. The detached masses are generally larger and more compact at the center of the group; at the margin they form into finer flakes. They often spread themselves out in lines in one or two directions.

5. ALTO-STRATUS (A.-S.). — A thick sheet of a gray or bluish color, showing a brilliant patch in the neighborhood of the sun or moon, and which, without causing halos, may give rise to coronse. This form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great.

6. STRATO-CUMULUS (S.-Cu.). — Large globular masses or rolls of dark cloud, frequently covering the whole sky, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato-Cumulus is not, as a rule, very thick, and patches of blue sky are often visible through the intervening spaces. All sorts of transitions between this form and the Alto-Cumulus are noticeable. It may be distinguished from Nimbus by its globular or rolled appearance and also because it does not bring rain.

7. NIMBUS (N.). — Rain clouds; a thick layer of dark clouds, without shape and with ragged edges, from which continued rain or snow generally falls. Through the openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates into shreds or if small loose clouds are visible floating at a low level underneath a large nimbus, they may be described as Fracto-Nimbus (Fr.-N.), the "scud" of sailors.

8. CUMULUS (Cu.).— Wool-pack clouds; thick clouds of which the upper surface is dome-shaped and exhibits protuberances, while the base is horizontal. When these clouds are opposite the sun the surfaces usually presented to the observer have a greater brilliance than the margins of the protuberances. When the light falls aslant, they give deep shadows; when, on the contrary, the clouds are on the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear superior and inferior limits. It is often broken up by strong winds, and the detached portions undergo continual changes. These may be distinguished by the name of Fracto-Cumulus (Fr.-Ou,.). '

INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 35

9. CUMULO-NIMBUS (Cu.-N.). — The thunder-cloud or shower-cloud; heavy masses of clouds rising in the form of mountains, turrets, or anvils, generally having a sheet or screen of fibrous appearance above, and a mass of clouds similar to Nimbus underneath. From the base there usually fall local showers of rain or of snow (occasionally hail or soft hail).

10. STRATUS (£.). — A horizontal sheet of lifted fog; when this sheet is broken up into irregular shreds by the wind or by the summits of mountains, it may be distinguished by the name of Fracto-Stratus (Fr.-S.).

72. In the scale for the amount of clouds 0 represents a sky which is cloudless and 10 a sky which is completely overcast.

73. STATE OF SEA. — The state of the sea is expressed by the following system of symbols :

B. — Broken or irregular sea. M. — Moderate sea or swell.

C. — Chopping, short, or cross sea. R. — Rough sea.

G. — Ground swell. S. — Smooth sea.

H. — Heavy sea. T. — Tide-rips. L. — Long rolling sea.

NOTE. — There are various publications issued by the Hydrographic Office dealing with special features of navigation, which should be regularly consulted. Among the most important of these are:

Pilot charts of the various oceans furnish information regarding the drift of derelicts, ice, and float ing obstructions, the tracks of storms, average conditions of wind and weather, ocean currents, magnetic variation, etc.

Hydrographic Bulletin, weekly, gives more detailed facts than the Pilot Charts regarding ice, wrecks, and derelicts; also items on port facilities, use of oil to calm the sea, and miscellaneous items of use and interest to mariners.

Daily Memorandum, published at the main office at Washington, also makes public these items through the Branch Hydrographic Offices.

Notice to Mariners, weekly, gives changes in aids to navigation (lights, buoyage, harbor constructions), dangers to navigation (rocks, shoals, banks, bars), important new soundings, and, in general, all such facts as affect mariners' charts, manuals, and pilots or sailing directions.

CHAPTER III. THE COMPASS EEEOE,

CAUSES OF THE ERROR.

74. The properties of magnets are such that when two magnets are near enough together to exert a mutual influence, those poles which possess like magnetism repel each other, and those which possess unlike magnetism attract each other.

The earth is a magnetized body, and acts like a great spherical magnet with poles of unlike magnetism situated within the Arctic and Antarctic circles close to longitudes 97° west and 155° east of Greenwich, respectively. In common with magnets, the earth is surrounded by a region in which magnetic influence is exercised upon the compass, giving the magnetic needle a definite direction in each locality and causing the end which we name the north pole of the compass to be directed in general toward the region of the magnetic pole in the geographical north and the south end toward the region of the magnetic pole in the geographical south.

The north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end which has opposite polarity to the earth's north magnetic pole, or, otherwise stated, which possesses like magnetism with the earth's south magnetic pole.

75. By reason of the fact that the magnetic pole in each hemisphere differs in geographical position by a large and unequal amount from the geographical pole, we are made aware that the earth is not magnetized symmetrically with reference to the geographical poles. Hence the directive influence of the earth's magnetism will not in general cause the compass needle to point in the direction of the true meridian, but each compass point will differ from the corresponding true point by an amount varying according to the geographical locality. The angle representing this difference is the Variation of ike Compass , sometimes also called the Magnetic Declination. It is the angle between the plane of the true meridian and a vertical plane passing through a freely suspended magnetic needle influenced solely by the earth's magnetism.

The variation not only changes as one travels from place to place on the earth, being different in different localities, but in every locality, besides the minor periodic movements of the needle known as the diurnal, monthly, and annual variations, which are not of material concern to the mariner, there is a progressive change which extends through centuries of time and amounts to large alterations in the pointing of the compass. ^ In taking account of the effect produced by the variation of the compass, the navigator must therefore be sure that the variation used is correct not only for the place, but also for the time under consideration.

Occasionally the magnetic needle is subject to spasmodic fluctuations of the earth's ^ magnetism lasting from a brief period to several days. These are called magnetic ^ storms, and are due to sudden changes in the electric currents which cir culate within the earth and in the region surrounding the earth. They come appar ently at random, and^ may occur nearly simultaneously over the whole world or be restricted to a certain region. The range of their effect upon the compass does not often exceed the half of a degree in the lower latitudes, and hence the navigator need only be concerned with them in the higher latitudes where he may look to the aurora as an indication of their occurrence.

76. Besides the error thus produced in the indications of the compass, a further one, due to Local Attraction, .may arise from extraneous influences due to natural magnetic attraction in the vicinity of the vessel. Instances of this are quite common

36

THE COMPASS ERROR.

37

when a ship is in port, as she may be in close proximity to vessels, docks, machinery, or other masses of iron or steel. It is also encountered in the shallow waters of the sea in localities where the mineral substances in the earth itself possess magnetic qualities — as, for example, at certain places in Lake Superior and at others off the coast of Australia. When due to the last-named cause, it may be a source of great danger to the mariner, but, fortunately, the number of localities subject to local attraction is limited. ^ The amount of this error can seldom be determined except by survey; if known, it might properly be included with the variation and treated as a part" thereof.

77. In addition to the variation, the compass ordinarily has a still further error in its indications, which arises from the effect exerted upon it by masses of magnetic metal within the shij) itself. This is known as the Deviation of the Compass. For reasons that will be explained later, it differs in amount for each heading of the ship, and, further, the character of the deviations undergoes modification as a vessel proceeds from one geographical locality to another.

APPLYING THE COMPASS ERROR.

78. From what has been explained, it may be seen that there are three methods by which bearings or courses may be expressed: (a) true, when they refer to the angular distance from the earth's geographical meridian; (b) magnetic, when they refer to the angular distance from the earth's magnetic meridian, and must be cor rected for variation to be converted into true; and (c) by compass, when they refer to the angular distance from the north indicated by the compass on a given heading of the ship), and must be corrected for the deviation on that heading for conversion to magnetic, and for both deviation and variation for conversion to true bearings or courses. The process of applying the errors under all circumstances is one of which the navigator must make himself a thorough master; the various problems of con version are constantly arising; no course can be set nor bearing plotted without involving the application of this problem, and a mistake in its solution may produce serious consequences. The student is therefore urged to give it his most careful attention.

79. When the effect of a compass error, whether arising from variation or from deviation, is to draw the north end of the compass needle to the right, or eastward, the error is named east, or is marked + ; when its effect is to draw the north end of the needle to the left or westward, it is named west, or marked — .

Figures 7 and 8 represent, respectively, examples of easterly and westerly errors. In^botn cases consider that the circles represent the observer's horizon, N and S being the correct north and south points in each case. If N' and S' represent the corresponding points indicated by a compass whose needle is deflected by a compass error, then in the first case, the north end of the needle being drawn to the right or east, the error will be easterly or positive, and in the second case, the north end of the needle being drawn to the left or west, the compass error will be westerly or negative.

38 THE COMPASS ERROR.

Considering figure 7, if we assume the easterly error to amount to one point, it will be seen that if a direction of N. by W. is indicated by the compass, the correct direction should be north, or one point farther to the right. If the compass indicates north, the correct bearing is N. by E.; that is, still one point to the right. If we follow around the whole card, the same relation will be found in every case, the corrected bearing being always one point, to the right of the compass bearing. Conversely, if we regard figure 8, assuming the same amount of westerly error, a compass bearing of N. by E. is the equivalent of a correct bearing of north, which is one point to the left; and this rule is general throughout the circle, the corrected direction being always to the left of that shown by the compass.

80. Having once satisfied himself that the general rule holds, the navigator may save the necessity of reasoning out in each case the direction in which the error must be applied, and need only charge his mind with some single formula which will cover all cases. Such a one is the following:

When the CORRECT direction is to the RIGHT, the error is EAST.

The words correct-right-east, in such a case, would be the key to all of his solutions. With easterly error, if he had a compass course to change to a corrected one, he would know that to obtain the result the error must be applied to the right; and, if it were desired to change a correct course to one indicated by compass, the error would be applied to the left. If a correct bearing is to be compared with a compass bearing to find the compass error, when the correct bearing is to the right, the error is easterly; and when the correct bearing is to the left, the error is westerly.

81. It must be remembered that the word east is equivalent to right in dealing with the compass error, and west to left, even though they involve an apparent departure from the usual rules. If a vessel steers NE. by compass with one point easterly error, her corrected course is NE. by E.; but if she steers SE., the corrected course is not SE. by E., but SE. by S. Another caution may be necessary to avoid confusion; the navigator should always regard himself as facing the point under consideration when he applies an error; one point westerly error on South will bring a corrected direction to S. by E.; but if we applied one point to the left of South while looking at the compass card in the usual way — north end up — S. by W. would be the point arrived at, and a mistake of two points would be the result.

82. In the foregoing explanation reference has been made to i 'correct " directions and "compass errors'' without specifying "magnetic" and "true" or "variation" and "deviation." This has been done in order to make the statements apply to all cases and to enable the student to grasp the subject in its general bearing without confusion of details.

Actually, as has already been pointed out, directions given may be true, magnetic, or by compass. By applying variation to a magnetic bearing we correct it and make it true, by applying a deviation to a compass bearing we correct it to magnetic, and by applying to it the combined deviation and variation we correct it to true. Which ever of these operations is undertaken, and whichever of the errors is considered, the process of correction remains the same; the correct direction is always to the right, when the error is east, by the amount of that error.

Careful study of the following examples will aid in making the subject clear:

EXAMPLES: A bearing taken by a compass free from deviation is 76°; variation, 5° W.; required the true bearing. 71°.

A bearing taken by a similar compass is NW. by W. J W.; variation, J pt. W.; required the true bearing. NW. by W. f W.

A vessel steers 153° by compass; deviation on that heading, 3° W.; variation in the locality, 12° E.; required the true course. 162°.

A vessel steers S. by W. JW.: deviation, \ pt. W.; variation, 1 pt, E.: required the true course. SSW. J W.

It is desired to steer the magnetic course 322°; deviation, 4° E.; required the course by compass. 318°.

The true course between two points is found to be W. } N.; variation, 1J pt. E.; no deviation; required the compass course. W. f S.

True course to be made, 55°; deviation, 7° E.; variation, 14° W.; required the course by compass. 62°.

THE COMPASS ERROR. 39

A vessel passing a range whose direction is known to be 200°, magnetic, observes the bearing by compass to be 178°; required the deviation. 22° E.

The sun's observed bearing by compass is 91°; it is found by calculation to be 84° (true); variation, 8° W.; required the deviation. 1° E.

FINDING THE COMPASS ERROR.

83. The variation of the compass for any given locality is found from the charts. A nautical chart always contains information from which the navigator is enabled to ascertain the variation for any place within the region embraced and for any year. Beside the information thus to be acquired from local charts, special charts are published showing the variation at all points on the earth's surface.

84. The deviation of the compass, varying as it does for every ship, for every heading, and for every geographical locality, must be determined by the navigator, for which purpose various methods are available.

Whatever method is used, the ship must be swung in azimuth and an observa tion made on each of the headings upon which the deviation is required to be known. If a new iron or steel ship is being swung for the first time, observations should be made on each of the twenty-four 15° rhumbs into which the compass card is divided. At later swings, especially after correctors have been applied, or in the case of wooden ships, twelve 15° rhumbs wiU suffice — or, indeed, only six. In case it is not prac ticable to make observations on exact 15° rhumbs, they should be made as near thereto as practicable and plotted on the Napier diagram (to be explained hereafter), whence the deviations on exact 15° rhumbs may be found.

85. In swinging ship for deviations the vessel should be on an even keel and all movable masses of iron in the vicinity of the compass secured as for sea, and the com pass accurately centered in the binnacle. The vessel, upon being placed on any head ing, should be steadied there for three or four minutes before the observation is made, in order that the compass card may come to rest and the magnetic conditions assume a settled state. To assure the greatest accuracy the ship should first be swung to starboard, then to port, and the mean of the two deviations on each course taken. Ships may be swung under their own steam, or with the assistance of a tug, or at ancnor, where the action of the tide tends to turn them in azimuth (though in this case it is difficult to get them steadied for the requisite time on each heading), or at anchor, by means of springs and hawsers.

86. The deviation of all compasses on the ship may be obtained from the same swing, it being required to make observations with me standard only. To accomplish this it is necessary to record the ship's head by all compasses at the time of steadying on each even rhumb of the standard; applying the deviation, as ascertained, to the heading by standard, gives' the magnetic heads, with which the direction of the ship's head by each other compass may be compared, and the deviation thus obtained. Then a complete table of deviations may be constructed as explained in article 94.

87. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal bearings, by bearings of the sun, by ranges, and by a distant object"

88. RECIPROCAL BEARINGS. — One observer is stationed on shore with a spare compass placed in a position free from disturbing magnetic influences; a second observer is at the standard compass on board ship. At the instant when ready for observation a signal is made, and each notes the bearing of the other. The bearing by the shore compass, reversed, is the magnetic bearing of the shore station from the ship, and the difference between this and the bearing by the ship's standard compass represents the deviation of the latter.

In determining the deviations of compasses placed 011 the fore-and-aft amidship line, when the distribution of magnetic metal to starboard and port is symmetrical, the shore compass may be replaced by a dumb compass, or pelorus, or by a theodolite in which, for convenience, the zero of the horizontal graduated circle may be termed north; the reading of the shore instrument will, of course, not represent magnetic directions, but by assuming that they do we obtain a series of fictitious deviations, the mean value of which is the error common to all. Upon deducting this error from each of the fictitious deviations, we obtain the correct values.

40 THE COMPASS ERROR.

If ship and shore observers are provided with watches which have been com pared with one another, the times may be noted at^ each observation, and thus afford a means of locating errors due to misunderstanding of signals.

89. BEARINGS OF THE SUN. — In this method it is required that on each heading a bearing of the sun be observed by compass and the time noted at the same moment by a chronometer or watch. By means which will be explained in Chapter XIV, the true bearing of the sun may be ascertained from the known data, and this, compared with the compass bearing, gives the total compass error; deducting from the compass error the variation, there remains the deviation. The variation used may be that given by the chart, or, in the case of a compass affected only by symmetrically placed iron or steel, may be considered equal to the mean of all the total errors. Other celestial bodies may be observed for this purpose in the same manner as the sun.

This method is important as being the most convenient one available for deter mining the compass error at sea. When adjusting compasses much time will be saved by this simple modification of a detail:

Instead of tabulating magnetic azimuths for given stated times in advance, draw on cross-section paper a curve whose ordinates are minutes of local apparent time and whose abscissae are degrees of magnetic azimuth, that is, true azimuth corrected for variation. Then for any given instant (the navigator's watch being set to local apparent time) the magnetic azimuth may be read directly from the curve. The difference between the magnetic azimuth of the sun and its compass bearing is, of course, the deviation of the compass on that particular heading.

90. RANGES. — In many localities there are to be found natural or artificial range marks which are clearly distinguishable, and which when in line lie on a known magnetic bearing. By steaming about on different headings and noting the compass bearing of the ranges each time of crossing the line that they mark, a series of devia tions may be obtained, the deviation of each heading being equal to the difference between the compass and the magnetic bearing.

91. DISTANT OBJECT. — A conspicuous object is selected which must be at a con siderable distance from the ship and upon which there should be some clearly defined point for taking bearings. The direction of this object by compass is observed on successive headings. Its true or magnetic bearing is then found and compared with the compass bearings, whence the deviation is obtained.

The true or the magnetic bearing may be taken from the chart. The magnetic bearing may also be found by setting up a compass ashore, free from foreign magnetic disturbance, in range with the object and the ship, and observing the bearing of the object; or the magnetic bearing may be assumed to be the mean of the compass bearings.

In choosing an object for use in this method care must be taken that it is at such a distance that its bearing from the ship does not practically differ as the vessel swings in azimuth. If the ship is swung at anchor, the distance should be not less than 6 miles. If swung under way, the object must be so far that the parallax (the tangent of which may be considered equal to half the diameter of swinging divided by the distance) shall not exceed about 30'.

92. In all of the methods described it will be found convenient to arrange the results in tabular form. In one column record the ship's head by standard compass, and abreast it in successive columns the observations from which the deviation is determined on that heading, and finally write the deviation itself. When tha result of the swing has been worked up, another table is constructed showing simply the headings and the corresponding deviations. This is known as the Deviation Table of the^compass. If compensation is to be attempted, this table is the basis of the operation; if not, the deviation tables of the standard and steering compass should be posted in such place as to be accessible to all persons concerned with the naviga tion of the ship.

THE COMPASS ERROR.

41

93. Let it be assumed that a deviation table has been found ancl that the values

are as follows:

Deviation table.

Ship's head by standard compass		Deviation.	Ship's head by standard compass.		Deviation.
North	0	-15 29	South	0 180	+ 17 5°
Bra	15 30 45	-14 53 -13 16 — 11 19	SW	195 210 225	+23 47 +27 07 +95 35
Ea^t	60 75 90	- 9 59 - 9 42 - 9 06	West	240 255 270	+21 57 +15 54 + 9 56
SE	105 120 135	- 9 01 - 7 51 - 5 54	xw	285 300 .315	+ 1 56 - 4 09 -10 20
	150 165	- 2 16 + 8 29		330 345	-13 37 -16 01

We have from the table the amount of deviation on each compass heading; therefore, knowing the ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the magnetic neading. But if we are given the magnetic direction in which it is desired to steer and have to find the corresponding compass course, the problem is not so simple, for we are not given deviations on magnetic heads, and where the errors are large it may not be assumed that they are the same as on the corresponding compass headings. For example, with the deviation table just given, suppose it is required to determine the compass heading corresponding to 165°, magnetic.

The deviation corresponding to 165°, per compass, is + 84-°. If we apply this to 165°, magnetic, we have 156£° as the compass course. But, consulting the table, it may be seen that the deviation corresponding to 156^°, per compass, is + 2J°, and therefore if we steer that course the magnetic direction will be 159°, and not 165°, as desired.

A way of arriving at the correct result is to make a series of trials until a course is arrived at which fulfills the conditions. Thus, in the example given:

First trial. Mag. course desired ...................... 165°

Try dev. on 165° ....................... 8i° E.

Trial comp. course Dev. o

E.

Mag. course made good .................. 159°

Since this assumption carries the course 6° too far to the left, assume next a deviation on a course 3^° farther to the right than the one used here.

Second trial.

.Mag. course desired 165°

Trvdev. on 160°... 5° E.

Trial comp. course 160C

Dev. on 160° 5C

Mag. course made good 165°

This happens to be exactly the compass course required. But it often occurs that further trials may be necessary.

94. THE NAPIER DIAGRAM. — A much more expeditious method for the solution of this problem is afforded by the Napier Diagram, and as that diagram also facilitates a number of other operations connected with compass work it should be clearly understood by the navigator. This admits of a graphic representation of the table of deviations of the compass by means of a curve; besides furnishing a ready means of converting compass into magnetic courses and the reverse, one of its chief merits is that if the deviation has been determined on a certain number of head ings it enables one to obtain the most probable value of the deviation on any other course that the ship may head. The last-named feature renders it useful in making a table of deviations of compasses other than the standard when their errors are found as described in article 86.

95. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and straightened into a vertical line; for convenience, it is usually divided into two sections, representing, respectively, the eastern and western semi circles. The vertical line is of a convenient length and divided into twenty-four equal parts corresponding to the 15° rhumbs of the compass, beginning at the top

42

THE COMPASS ERROR.

with North and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked.

To obtain a complete curve, a sufficient number of observations should be taken while the ship swings through an entire circle. Generally, observations on every alternate 15° rhumb are enough to establish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on every 15° rhumb.

Compass courses on dotted tines.

Magnetic courses on solid linos.

FROM 0° NORTH TO 180° SOUTH

DEVIATION DEVIATION

WEST NORTH EAST

FROM 180° SOUTH TO 360° NORTH

DEVIATION DEVIATION

WEST SOOTH EAST

of Total Deviation

of Semicircular Component

of Quadrjjm-tal Component

FIG. 9.

The curve shown in the full line on figure 9 corresponds to the table of deviations given in article 93.

From a given^ compass course to find the corresponding magnetic course, through the point of the vertical fine representing the given compass course draw a line parallel to the dotted lines until the curve is intersected, and from the point of intersection draw another line parallel to the plain lines; the point on the scale where this last

THE COMPASS ERROR.

43

line cuts the vertical line is the magnetic course sought. The correctness of this solution will be apparent when we consider that the 60° triangles are equilateral, and therefore the distance measured along the vertical side will equal the distance meas ured along the inclined sides — that is, the deviation; and the direction will be correct, for the construction is such that magnetic directions will be to the right of compass directions when the deviation is easterly and to the left if westerly.

From a given magnetic course to find the corresponding compass course, the process is the same, excepting that the first line drawn should follow, or be parallel to, the plain lines, and the second, or return line, should be parallel to the dotted; and a proof similar to that previously employed will show the correctness of the result. As an example, the problem given in article 93 may be solved by the diagram, and the result will be found to accord with the solution previously given.

The vertical line is intersected at each 15° rhumb by two lines inclined to it at an angle of 60°, that line which is inclined upward to the right being drawn plain and the other dotted.

To plot a curve on the Napier diagram, if the deviation has been observed with the ship's head on given compass courses (as is usually the case with the standard compass), measure off on the vertical scale the number of degrees corresponding to the deviation and lay it down — to the right if easterly and to the left if westerly— on the dotted line passing through the point representing the ship's head; or, if the observation was not made on an even 15° rhumb, then lay it down on a line drawn parallel to the dotted ones through that division of the vertical line which represents the compass heading; if the deviation has been observed with the ship on given magnetic courses (as when deviations by steering compass are obtained by noting the ship's head during a swing on even 15° rhumbs of the standard), proceed in the same way, excepting that the deviation must be laid down on a plain line or a line parallel thereto. Mark each point thus obtained with a dot or small circle, and draw a free curve passing, as nearly as possible, through all the points.

THE THEORY OF DEVIATION."

96. FEATURES OF THE EARTH'S MAGNETISM. — It has already been stated that the earth acts like a great spherical magnet, with a pole in each hemisphere which is not coincident with the geographical pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical equator.

A magnetic needle freely suspended at a point on the earth's surface, and undisturbed by any other than the earth's magnetic influence, will lie in the plane of the magnetic meridian and at an angle with the horizon depending upon the geographical position.

The magnetic elements of the earth which must be considered are shown in figure 10. The earth's total force is represented in direction and intensity by the line AB. Since compass needles are mechanical! v arranged to move only in a horizontal plane, it Tbecomes necessary, when investigating the effect of the earth's magnetism upon them, to resolve the total force into two components which in the figure are represented by AC and AD. These are known, respectively, as the horizontal and vertical components of the earth's total force, and are usually designated as H and Z. The angle CAB, which the line of direction makes with the plane of the horizon, is called the magnetic inclination or dip, and denoted by 0.

It is clear that the horizontal component will reduce to zero at the magnetic poles, where the needle points directly downward, and that it will reach a maximum

a As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the compensation of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical Astronomy, it may be considered preferable to omit the remainder of this chapter at first and return to it later.

FIG. 10.

44 THE COMPASS ERROR.

at the magnetic equator, where the free needle hangs in a horizontal direction. The reverse is true of the vertical component and of the angle of dip.

Values representing these different terms may be found from special charts.

97. INDUCTION; HARD AND SOFT IRON.— -When a piece of unmagnetized iron or steel is brought within the influence of a magnet, certain magnetic properties are immediately imparted to the former, which itself becomes magnetic and continues to remain so as long as it is within the sphere of influence of the permanent magnet; the magnetism that it acquires under these circumstances is saia to be induced, and the properties of induction are such that that end or region which is nearest the pole of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into proximity again, but with its opposite pole nearer, magnetism will again be induced, but this time its polarity will be reversed. A further property is that if a piece of iron or steel, while temporarily possessed of magnetic qualities through induction, be subjected to blows, twisting, or mechanical violence of any sort, the magnetism is thus made to acquire a permanent nature.

The softer the metal, from a physical point of view, the more quickly and thor oughly will induced magnetism be dissipated when the source of influence is with drawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted to it in any way. Hence, in regarding the different features which affect deviation, it is usual to denominate as hard iron that which possesses retained magnetism of a stable nature, and as soft iron that which rapidly acquires and parts with its mag netic qualities under the varying influences to which it is subjected.

98. MAGNETIC PROPERTIES ACQUIRED BY AN IRON OR STEEL VESSEL IN BUILDING. — The inductive action of the earth's magnetism affects all iron or steel within its influence, and the amount and permanency of the magnetism so induced depends upon thd position of the metal with reference to tha earth's total force, upon its character, and upon the degree of hammering, bending, and twisting that it undergoes.

An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an angle thereto it would acquire magnetic properties dependent for their amount upon its inclination to the line of total force; when held at right angles to the line there would be no effect, as each extremity would be equally near the proles of the earth and all influence would be neutralized. If, while such a bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain magnetism of a permanent character is impressed upon it, which is never entirely lost unless the bar is subjected to causes equal and opposite to those that produced the first effect.

A sheet of iron is affected by induction in a similar way, the magnetism induced by the earth diffusing itself over the entire plate and separating itself into regions of opposite polarity divided by a neutral area at right angles to the earth's line of total force. If the plate is hammered or bent, this magnetism takes up a permanent character.

^ If the magnetic mass has a third dimension, and assumes the form of a ship, a similar condition prevails. The whole takes up a magnetic character; there is a magnetic axis in the direction of the line of total force, with poles at its extremities and a zone of no magnetism perpendicular to it. The distribution of magnetism will depend upon the horizontal and vertical components of the earth's force in the locality and upon the direction of the keel in building; its permanency will depend upon the amount of mechanical violence to which the metal has been subjected by the riveting and other incidents of construction, and upon the nature of the metal employed.

99. CAUSES THAT PRODUCE DEVIATION. — There are three influences that operate to produce deviation; namely, (a) subpermanent magnetism; (b) transient magnetism induced in vertical soft iron, and (c) transient magnetism induced in hori zontal soft iron. Their effect will be explained.

Subpermanent magnetism is the name given to that magnetic force which origi nates in the ship while building, through the process explained in the preceding article; after the vessel is launched and has an opportunity to swing in azimuth, the magnetism thus induced will suffer material diminution until, after the lapse of

THE COMPASS ERROR. 45

a certain time, it will settle down to a condition that continues practically unchanged; the magnetism that remains is denominated subpermanent. The vessel will then approximate to a permanent magnet, in which the north polarity will lie in that region which was north in building and the south polarity (that which exerts an attracting influence on the north pole of the compass needle) in the region which was south in building.

Transient magnetism induced in vertical soft iron is that developed in the soft iron of a vessel through the inductive action of the vertical component only of the earth's total force, and is transient in nature. Its value or force in any given mass varies with and depends upon the value of the vertical component at the place, and is proportional to the sine of the dip, being a maximum at the magnetic pole and zero at the magnetic equator.

Transient magnetism induced in horizontal soft iron is that developed in the soft iron of a vessel through the inductive action of the horizontal component only of the earth's total force, and is transient in nature. Its value or force in any given mass varies with and depends upon the value of the horizontal component at the place, and is proportional to the cosine of the dip, being a maximum at the magnetic equator and reducing to zero at the magnetic pole.

The needle of a compass in any position on board ship will therefore be acted upon by the earth's total force, together with the three forces just described. The poles of these forces do not usually lie in the horizontal plane of the compass needle, but as this needle is constrained to act in a horizontal plane, its movements will be affected solely by the horizontal components of these forces, and its direction will be determined by the resultant of those components.

The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but the resultant of the three remaining forces, wnen without this plane, deflects the needle, and the amount of such deflection constitutes the deviation.

100. CLASSES OF DEVIATION. — Investigation has developed the fact that the deviation produced as described is made up of three parts, which are known respec tively as Semicircular, quadrantal, and constant deviation, the latter being the least important. A clear understanding of the nature of each of these classes is essential for a comprehension of the methods of compensation.

101. Semicircular Deviation is that due to the combined influence, exerted in a horizontal plane, of the subpermanent magnetism of a ship and of the magnetism induced in soft iron by the vertical component of the earth's force. If we regard the effect of these two forces as concentrated in a single resultant pole exerting an attracting influence upon the north end of the compass needle, it may be seen that there will be some heading of the ship whereon that pole will lie due north of the needle and therefore produce no deviation; now consider that, from this position, the ship's head swings in azimuth to the right; throughout all of the semicircle first described an easterly deviation will be produced, and, after completing 180°, the pole will be in a position diameterically opposite to that from which it started, and will again exert no influence that tends to produce deviation. Continuing the swing, throughout the next semicircle the direction of the deviation produced will be always to the westward, until the circle is completed and the ship returns to her original neutral position. From the fact that this disturbing cause acts in the two semicircles with equal and opposite effect it is given the name of semicircular deviation.

In figure 9 a curve is depicted winch shows the deviations of a semicircular nature separated from those due to other disturbing causes, and from this the reason for the name will be apparent.

102. Returning to the two distinct sources from which the semicircular deviation arises, it may be seen that the force due to subpermanent magnetism remains constant regardless of the geographical position of the vessel; but since the horizontal force of the earth, which tends to hold the needle in the magnetic meridian, varies with the magnetic latitude, the deviation due to subpermanent magnetism varies inversely as

the horizontal force, or as Y>; this may be readily understood if it is considered that

the stronger the tendency to cling to the direction of the magnetic meridian the less will be the deflection due to a given disturbing force. On the other hand, that part

46

THE COMPASS ERROR.

of the semicircular force due to magnetism induced in vertical soft iron varies as the earth's vertical force, which is proportional to the sine of the dip; its effect in producing deviation, as in the preceding case, varies inversely as the earth's horizontal force — that is, inversely as the cosine of the dip ; hence the ratio representing the change of

sin

deviation arising from this cause on change of latitude is - — ^, or tan 6.

C/OS (7

If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude, it will be necessary to separate the two factors of the deviation and to remember that the portion produced by subpermanent magnetism varies as

TJ, and that due to vertical induction as tan 6. But for any consideration of the

effect of this class of deviation in one latitude only, the two parts may be joined together an'd regarded as having a single resultant.

103. Assuming that all the forces tending to produce semicircular deviation are concentrated in a single pole exerting an influence on the north pole of the compass, it will be seen that this can be resolved into a horizontal and a vertical component, just as the earth's magnetic force is illustrated in figure 10. It is now

evident, therefore, that the horizontal component of this single magnet may be resolved into two components — one fore-and-aft, and one athwartship; in this case, the semi- £> circular forces will be represented by two magnets, one fore- / and-aft and the other athwartship, and compensation may / be made by two separate magnets lying respectively in the directions stated, but with their north or repelling poles in the position occupied by the south or attracting poles of the ship's force.

Figure 11 represents the conditions that have been described. Let O be the center of the compass, XX7 and YY', respectively, the fore-and-aft and athwartship lines of the ship, and OS the direction in which the attracting pole of the disturbing force is exerted. Now, if OP be laid off on the line OS, representing the amount of the disturbing force according to some convenient scale, then O& and Oc, respec tively, represent, on the same scale, the resolved directions of that force in the keel line and in the transverse line of the ship. Each of these resolved forces will exert a maximum effect when acting at right angles to the needle, the athwart ship one when the ship heads north or south by compass, and the longitudinal one when the heading is east or west. On any other heading than those named the deviation pro duced by each force will be a fraction of its maximum whose magnitude will depend upon the azimuth of the ship's head. The maximum devia tion produced, therefore, forms in each case a basis for reckoning all of the various effects of the disturbing force, and is called a coefficient.

The coefficient of semicircular deviation produced by the force in the fore-and-aft line is called B, and is reckoned as positive when it attracts a north pole toward the bow , negative when toward the stern; that produced by the athwartship force is C, and is reckoned as positive to starboard and negative to port. These coefficients are expressed in degrees. a

104. The coefficient B is approximately equal to the deviation on East; or to the deviation on West with reversed sign; or to the mean of these two. Thus in the ship having the table of deviations previously given (art. 93), B is equal to -9° 06', or to -9° 56;, or to £ (-9° 06'-9° 56') = -9° 31'.

^The coefficient C is approximately equal to the deviation on North; or to the deviation on South with reversed sign; or to the mean of these two. In the example C is equal to -15° 29', or to -17° 52', or to i (-15° 29' -17° 52')= -16° 40'.

o It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between the approximate coefficients, B and C, here described, as alsa A, D, and E, to be mentioned later, and the exact coefficients denoted by the corresponding capital letters of the German alphabet, which latter are in reality the forces producing those deviations expressed in terms of the "mean force to north" (An), as unit. In the practical discussion of the subject here given, the question of the dif ference need not be entered into further.

FIG. 11.

THE COMPASS ERROR.

47

105. The value of the subpermanent magnetism remaining practically constant under all conditions, it will not alter when the ship changes her latitude; but that due to induction in vertical soft iron undergoes a change when, by change of geo graphical position, the vertical component of the earth's force assumes a different value, and in such case the correction by means of one or a pair of permanent magnets will not remain effective. If, however, by series of observations in two magnetic latitudes, the values of the coefficients can be determined under the differing cir cumstances, it is possible, by solving equations, to determine what effect each force has in producing the semicircular deviation; having done which, the subpermanent magnetism can be corrected by permanent magnets after the method previously described, and the vertical induction in soft iron can be corrected by a piece of vertical soft iron placed in such a position near the compass as to produce an equal but opposite force to the ship's vertical soft iron. This last corrector is called a Flinders par.

Having thus opposed to each of the component forces a corrector of magnetic character identical with its own, a change of latitude will make no difference in the effectiveness of the compensation, for in every case the modified conditions will produce identical results in the disturbing and in the correcting force.

106. Quadrantal Deviation is that which arises from horizontal induction in the soft iron of the vessel through the action of the horizontal component of the earth's total force. Let us consider, in figure 12, the effect of any piece of soft iron which is symmetrical with respect to the compass — that

is, which lies wholly within a plane passing through the center of the needle in either a fore-and-aft or an athwartship direction. It may be seen (a) that such iron produces no deviation on the cardinal points (for on north and south headings the fore- and-aft iron, though strongly magnetized, has no tendency to draw the needle from a north-and-south line, while the athwartship iron, being at right angles to the meridian, receives no magnetic induction, and therefore exerts no force; and on east and west headings similar conditions prevail, the athwart ship and the fore-and-aft iron having simply ex changed positions) ; and (&) the direction of the deviation produced is opposite in successive quad rants. The action of unsyinmetrical soft iron is

FIG. 12.

not quite so readily apparent, but investigation shows that part of its effect is to produce a deviation which becomes zero at the inter-cardinal points and is of oppo site name in successive quadrants. From the fact that deviations of this class change sign every 90° throughout the circle, they gain the name of quadrantal devi ations. One of the curves laid down in the Napier diagram (fig. 9) is that of quad- rantal deviations, whence the nature of this disturbance of the needle may be observed.

107. All deviations produced by soft iron may be considered as fractions of the maximum deviation due to that disturbing influence; and consequently the maximum is regarded as a coefficient, as in the case of semicircular deviations.' The coefficient due to symmetrical soft iron is designated as D, and is considered positive when it produces easterly deviations in the quadrant between North and East; the coefficient of deviations arising from unsymmetrical soft iron is called E, and is reckoned as positive when it produces easterly deviations in the quadrant between ^NW. and NE.; this latter attains importance only when there is some marked inequality in the distribution of metal to starboard and to port, as in the case of a compass placed off the amidship line.

108. D is approximately equal to the mean of the deviations on NE. and SW.; or to the mean of those on SE. and NW., with sign reversed; or to the mean of those means. In the table of deviations given in article 93, D is equal to ^ ( — 11° 19/ + 25° 35') =+ 7° 08', or to £ ( + 5° 54' + 10° 20') = +8° 07'; or to J (7°08/ + 8°07/) = + 7°37'. By reason of the nature of the arrangement of iron in a ship, D is almost invariably positive.

48 THE COMPASS ERBOK.

E is approximately equal to the mean of the deviations on North and South; or to the mean of those on East and West with sign reversed; or to the mean of those means. In the example, E is equal to ^ (-15° 29/ + 17° 52')= +1° 11'; or to i ( + 9006'-9056')=-0°25'; or to J ( + 1° ll'-0° 25') = +0° 23'.

109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic latitude ; being due to induction in horizontal soft iron, the magnetic force exerted to produce it is proportional to the horizontal component of the earth's magnetism; but the directive force of the needle likewise depends upon that same component ; consequently, as the disturbing force exerted upon the needle increases, so does the power that holds it in the magnetic ^meridian," with the result that on any given heading the deflection due to soft iron is always the same.

110. Quadrantal deviation is corrected by placing masses of soft iron (usually two hollow spheres in the athwartship line, at equal distances on each side of the compass) , with the center of mass in the horizontal plane of the needle. The distance is made such that the force exerted exactly counteracts that of the ship's iron. As the correcting effect of this iron will, like the directive force and the quadrantal disturbing force, vary directly with the earth's horizontal component, the compen sation once properly made will be effective in all latitudes; provided that the compass needles are short and, consequently, exercise little or no induction on the quadrantal correctors.

With compasses such as the United States Navy standard 7 J-inch liquid compass, the needles of which are long and powerful, it will usually be found that the position of the spheres must be changed with change of latitude. This may be accounted for by the magnetism induced in the spheres by the compass needles at the same time and in the same manner as the earth's force. In this case the quadrantal correcting force is the resultant of the constant force due to the induction of the needles in the spheres and the variable force (the earth's horizontal force, H, varying with change in magnetic latitude) due to the induction of the earth in the spheres. This resultant of these two forces is a variable force, and, after a given quadrantal deviation is corrected in one latitude by this force, the balance will be changed upon going into another latitude and the correction will fail to hold good.

In practice, the quadrantal deviation due to unsymmetrical iron is seldom corrected; the correction may be accomplished, however, by placing the soft iron masses on a line which makes an angle to the athwartship line through the center of the card.

111. Constant Deviation is due to induction in horizontal soft iron unsym- metrically placed about the compass. It has already been explained that one effect of such iron is to produce a quadrantal deviation, represented by one coefficient E ; another effect is the constant deviation, so called because it is uniform in amount and direction on every heading of the ship. If plotted on a Napier diagram, it would appear as a straight line parallel with the initial line of the diagram.

112. Like other classes of deviation, the effect of the disturbing force is repre sented by a coefficient ; this coefficient is designated as A, and is considered plus for easterly and minus for westerly errors. It is approximately equal to the mean of the deviations on any number of equidistant headings. In the case previously given, it might be found from the four headings, North, East, South, and West, and would then be equal to J (-15° 29'-9° 06' + 17° 52' + 9° 50')= +0° 48';' or from all of the 24 headings, when it would equal —0° 01'.

For the same reason as in the case of E, the value of A is usually so small that it may be neglected; it only attains a material size when the compass is placed off the midship line, or for some similar cause.

113. Like quadrantal deviation, since its force varies with the earth's horizontal force, the constant deviation will remain uniform in amount in all latitudes. (See art. 110.)

No attempt is made to compensate for this class of error.

114. COEFFICIENTS. — The chief value of coefficients is in mathematical analyses of the deviations and their causes. It may, however, be a convenience to the practical navigator to find their approximate values by the methods that have been given, in order that he may gain an idea of the various sources of the error, with a view to ameliorating the conditions, when necessary, by moving the binnacle or altering the

THE COMPASS ERROR. 49

surrounding iron. The following relation exists between the coefficients and the deviation:

sin z'+C cos z' + T> sin 2^+E cos 2zr,

where d is the deviation, and z' the ship's heading by compass, measured from compass North.

115. MEAN DIRECTIVE FORCE. — The effect of the disturbing forces is not confined to causing deviations ; it is only those components acting at right angles to the needle which operate to produce deflection; the effect of those acting in the direction of the needle is exerted either in increasing or diminishing the directive force of the compass, according as the resolved component is northerly or southerly.

It occurs, with the usual arrangement of iron in a vessel, that the mean effect of this action throughout a complete swing of the ship upon all headings is to reduce the directive force — that is, while it varies with the heading, the average value upon all azimuths is minus or southerly. The result of such a condition is unfavorable from the fact that the compass is thus made more " sluggish," is easily disturbed and does not return quickly to rest, and a given deflecting force produces a greater deviation when the directive force is reduced. The usual methods of compensation largely correct this fault, but do not entirely do so ; it is therefore the case that the mean combined horizontal force of earth and ship to north is generally less than the horizontal force of the earth alone; but it is only in extreme cases that this deficiency is serious.

116. HEELING ERROR. — This is an additional cause of deviation that arises when the vessel heels to one side or the other. Heretofore only those forces have been considered which act when the vessel is on an even keel; but if there is an incli nation from the vertical certain new forces arise, and others previously inoperative become effective. These forces are (a) the vertical component of the subpermanent magnetism acquired in building; (b) the vertical component of the induced magnetism in vertical soft iron, and (c) the magnetism induced by the vertical component of the earth's total force in iron which, on an even keel, was horizontal. The first two of these disturbing causes are always present, but, when the ship is upright, have no tendency to produce deviation, simply exerting a downward pull on one of the poles of the needle; the last is a new force that arises when the vessel heels.

The maximum disturbance due to heel occurs when the ship heads North or South. When heading East or West there will be no deviation produced, although the directive force of the needle will be increased or diminished. The error will increase with the amount of inclination from the vertical.

117. For the same reason as was explained in connection with semicircular deviations, that part of the heeling error due to subpermanent magnetism will vary,

on change of latitude, as YJ> while that due to vertical induction will vary as tan 0.

In south magnetic latitude the effect of vertical induction will be opposite in direction to what it is in north latitude.

118. The heeling error is corrected by a permanent magnet placed in a vertical position directly under the center of the compass. Such a magnet has no effect upon the compass when the ship is upright ; but since its force acts in an opposite direction to the force of the ship which causes heeling error, is equal to the latter in amount, and is exerted under the same conditions, it affords an effective compensation. For similar reasons to those affecting the compensation of B and C, the correction by means of a permanent magnet is not general and must be rectified upon change of latitude.

PRACTICAL COMPENSATION.

119. In the course of explanation of the different classes of deviation occasion has been taken to state generally the various methods of compensating the errors that are produced. The practical methods of applying the correctors wiu next be given.

120. ORDER OF CORRECTION. — The following is the order of steps to be followed in each case. It is assumed that the vessel is on an even keel, that the compass is properly centered in the binnacle, that all surrounding masses of iron or steel are in their normal positions, all correctors removed, and that the binnacle is one in which

61828°— 16 - 4

50 THE COMPASS EBROB.

the semicircular deviation is corrected by two sets of permanent magnets at right angles to each other.

In order to ascertain if the compass is properly centered in the binnacle, the heeling corrector may be temporarily placed in its tube and drawn from its lowest to its nighest position; if no deflection is shown by the needle the compass is prop erly centered; if not it should be adjusted by the screws provided for the purpose.

1 . Place quadrantal correctors by estimate.

2. Correct semicircular deviation.

3. Correct quadrantal deviation. _

4. Swin^ ship for residual deviations.

The heeling corrector may be placed at any time after the semicircular and quadrantal errors are corrected. A Flinders bar can be put in place only after observations in two latitudes.

121. The ship is first placed on some magnetic cardinal point. If North or South, the only force (theoretically speaking) which tends to produce deflection of the needle will be the athwartship component of the semicircular force, whose effect is represented by the coefficient C. It East or West, the only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is represented by the coefficient B. This will be apparent from a consideration of the direction of the forces producing deviation, and is also shown by the equation connecting the terms (where A and E are zero) :

•d = B sin zf + C cos z' + D sin 2z'.

If the ship is headed North or South, z' being equal to 0° or 180°, the equation becomes d = ± C. If on East or West, z' being 9(T or 270°, we have d = ± B.

This statement is exact if we regard only the forces that have been considered in the problem, but experience has demonstrated that the various correctors when in place create certain additional forces by their mutual action, and in order to correct the disturbances thus accidentally produced, as well as those due to regular causes, it is necessary that the magnetic conditions during correction shall approximate as closely as possible to those that exist when the compensation is completed; therefore the quadrantal correctors should first be placed on their arms at the positions which it is estimated that they will occupy later when exactly located. An error in the estimate will have but slight effect under ordinary conditions. It should be under stood that the placing of these correctors has no corrective effect while the ship is on a cardinal point. Its object is to create at once the magnetic field with which we shall have to deal when compensation is perfected.

This having been done, proceed to correct the semicircular deviation. If the ship heads North or South, the force producing deflection is, as has been stated, the athwartship component of the semicircular force, which is to be corrected by perma nent magnets placed athwartships ; therefore enter in the binnacle one or more such magnets, and so adjust their height that the heading of the ship by compass shall agree with the magnetic heading. When this is done all the deviation on that azimuth will be corrected.

Similarly, if the ship heads East or West, the force producing deviation is the fore-and-aft component of the semicircular force, and this is to be corrected by entering fore-and-aft permanent magnets in the binnacle and adjusting the height so that the deviation on that heading disappears.

With the deviation on two adjacent cardinal points corrected, the semicircular force has been completely compensated. Next correct the quadrantal deviation. Head the ship NE., SE., SW., or NW. The coefficients B and C having been reduced to zero by compensation, and 2zf ', on the azimuths named, being equal to 90° or 270°, the equation becomes d = ± D. The soft-iron correctors are moved in or out from the positions in which they were placed by estimate until the deviation on the heading (all of which is due to quadrantal force) disappears. The quadrantal disturbing force is then compensated.

122. DETERMINATION OF MAGNETIC HEADINGS. — To determine when a ship is heading on any given magnetic course, and thus to know when the deviation has been corrected and the correctors are in proper position, four methods are available:

THE COMPASS ERROR. 51

(a) Swing the ship and obtain by the best available method the deviations on a sufficient number of compass courses to construct a curve on the Napier diagram for one quadrant, and thus find the compass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal point, as North, NE., and East, magnetic.0 Then put the ship successively on these courses, noting the corresponding headings by some other compass, and when it is desired to head on the various magnetic azimuths during the process of correction the ship may be steadied upon them by the auxiliary compass. Variations of this method will suggest themselves and circumstances may render their adoption convenient. The compass courses corresponding to the magnetic directions may be obtained from observations made with the auxiliary compass itself, or while making observations with another compass the headings by the auxiliary may be noted and a curve for the latter constructed, as explained in article 95, and the required headings thus deduced.

(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance the true bearing of the sun at frequent intervals during the period which is to be devoted to the compensation of the compasses; apply to these the variation and obtain the magnetic bearings ; record the times and bearings in a convenient tabular form, or, better still, plot a curve of magnetic azimuths of the sun on cross section paper, the coordinates being local apparent time and magnetic bearings of the sun, as described in article 89. Set the watch accurately for the local apparent time; then when it is required to steer any given magnetic course, set that point of the pelorus for the ship's head and set the sight vanes for the magnetic bearing of the sun corresponding to the time by watch. Maneuver the ship with the helm until the sun comes on the sight vanes, when the azimuth of the ship's head will be that which is required. The sight vanes must be altered at intervals to accord with the curve or table of times and bearings.

(c) Construct a curve or table showing times and corresponding magnetic bearings of the sun, and also set the watch, as explained for the previous method. Then place the sight vanes of the azimuth circle of the compass at the proper angular distance to the right or left of the required azimuth of the ship's head ; leave them so set and maneuver the ship with the helm until the image of the sun comes on with the vanes. The course will then be the required one. As an example, suppose that the curve or table shows that the magnetic azimuth of the sun at the time given by the watch is N. 87° E., and let it be required to head magnetic North; when placed upon this heading, therefore, the sun must bear 87° to the right or east of the direction of the ship's head; when steady on any course, turn the sight vane to the required bearing relative to the keel. It on N. 11° W., for example, turn the circle to N. 76° E.; leave the vane undisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjustment may be made accordingly.

(d) When ranges are available, they may be utilized for determining magnetic headings.

123. SUMMARY OF ORDINARY CORRECTIONS. — To summarize, the following is the process of correcting a compass for a single latitude, where magnets at right angles are employed for compensating the semicircular deviation and where the dis turbances due to unsymmetrical soft iron are small enough to be neglected.

First. All correctors being clear of the compass, place the quadrantal correctors in the position which it is estimated that they will occupy when adjustment is com plete. The navigator's experience will serve in making the estimate, or if there seems no other means of arriving at the probable position they may be placed at the middle points of their supports.

Second. Steady the ship on magnetic north, east, south, or west, and hold on that heading by such method as seems best. By means of permanent magnets alter the indications of the compass until the heading coincides with the magnetic course. If heading north, magnets must be entered north ends to starboard to correct easterly deviation and to port to correct westerly, and the reverse if heading south. If heading east, enter north ends forward for easterly and aft for westerly deviations, and the reverse if heading west. (Binnacles differ so widely in the methods of carry ing magnets that details on this point are omitted. It may be said, however, that

o This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a complete swing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions.

52 THE COMPASS ERROR.

the magnetic intensity of the correctors may be varied by altering either their number or their distance from the compass; generally speaking, several magnets at a dis tance are to be preferred to a small number close to the compass.)

Third. Steady the ship on an adjacent magnetic cardinal point and correct the compass heading by permanent magnets to accord therewith in the same manner as described for the first heading.

Fourth. Steady the ship on an intercardinal point (magnetic) and move the quadrantal correctors away from or toward the compass, keeping them at equal distances therefrom, until the compass and magnetic headings coincide.

Fifth. If time permits, it is very important that the ship should next be steadied on opposite cardinal and semicardinal points and one-half 01 the remaining deviation corrected by changing the position or number of the correctors.

The compensation being complete, the navigator should proceed immediately to swing ship and make a table of the residual deviations. Though the remain ing errors will be small, it is seldom that they will be reduced to zero, and it must never be assumed that the compass may be relied upon without taking the devi ation into account. Observations on eight equidistant points will ordinarily suffice for this purpose.

124. COMPENSATION OF THE COMPASS WHILE CRUISING. — Every effort should be made to keep at least the standard and steering compasses compensated, as it is always easier to keep- the compasses compensated than to keep a deviation table correct, at hand, and in use.

RECTANGULAR METHOD.

By the following method the compasses may be kept practically compensated and, after the data are once obtained, it requires very little time or trouble.

After the first compensation is completed, or while it is being done, head the ship north or south and move the athwartship magnets up exactly 1 inch, noting by the bearing of the sun or of a distant .object, the amount and direction of the effect on the compass. Then repeat the observation, lowering the magnets 1 inch, and noting the effect. Then head the ship east or west and take the same obser vations with the fore-and-aft magnets. Then head on an intercardinal point and record the effect of moving spheres first in and then out an inch from the correct position.

The record would then take this form:

Date Latitude Longitude

H e

On North, raising B magnets (6 bundles) 1 inch (from 9.85 to 8.85) causes 12° 30' Easterly deviation,

therefore a movement of ^ inch causes 1° 15' Ely. Lowering B magnets (6 bundles) 1 inch (from 9.85 to 10.85) causes 10° 15' Westerly deviation,

therefore a movement of -^ inch causes 1° 2/ Wly. On East, raising G magnet (2 bundles) 1 inch (from 10.45 to 9.45) causes 8° 15' Westerly deviation,

therefore a movement of ^ inch causes 0° 50' Wly. Lowering C magnet (2 bundles) 1 inch (from 10.45 to 11.45) causes 6° 30' Easterly deviation,

therefore a movement of ^ inch causes 0° 39' Ely. On Northeast, moving spheres in 1 inch (from 10.6 to 9.6) causes 4° 15' Westerly deviation, therefore a

movement of ^ inch causes 0° 25' Wly.

Moving spheres out 1 inch (from 10.6 to 11.6) causes 3° 207 Easterly deviation, therefore a move ment of ^j- inch causes 0° 20' Ely.

If now it is^found at any time that there is, say, 1° 45' Easterly on East, it is evident that raising the C magnets -f$ inch will correct it, and careful observations on two adjacent cardinal points and an inter-cardinal point are enough to recompensate. This may ordinarily be done at no expense of time and with little trouble. More confidence may be felt in the result if observations for deviations are afterwards obtained on the four cardinal points and the mean of the results on opposite courses taken for the true value; this must be done if the variation is uncertain. A new set of data observations should be taken after a large change of magnetic latitude, but it will usually be found that the changes are slight.

Theoretically the quadrantal deviation, once corrected, should remain at zero. It will usually be found, however, that the position of the spheres must be changed

THE COMPASS ERROR. 53

with change of latitude. A convenient way of dealing with this is to construct a curve showing the positions of the spheres for varying values of H. A similar curve showing the position of the heeling magnet is also convenient.

Whenever the position of any corrector is changed, a note showing new position, date, latitude, longitude, H and 6 should be made on one of the blank leaves of the compass record. A complete record of this kind will be found of the utmost value in keeping track of the compasses.

125. CORRECTING THE HEELING ERROR. — The heeling error may be corrected by a method involving computation, together with certain observations on shore. A more practical method, however, is usually followed, though its results may be less precise. The heeling corrector is placed in its vertical tube, N. end uppermost in north latitudes, as this is almost invariably the required direction; the ship being on a course near North or South and rolling, observe the vibrations of the card, which, if the error is material, will be in excess of those due to the ship's real motion in azimuth; slowly raise or lower the corrector until the abnormal vibrations disappear, when the correction will be made for that latitude; but it must be readjusted upon any considerable change of geographical position.

In making this observation care must be taken to distinguish the vessel's ' 'yawing" in a seaway from the apparent motion due to heeling error; for this reason it may be well to have an assistant to watch the ship's head and keep the adjuster informed of the real change in azimuth, by which means the latter may better judge the effect of the heeling error.

In the case of a sailing vessel, or one which for any reason maintains a nearly steady heel for a continuous period, the amount of the heeling error may be exactly ascertained by observing the azimuth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly rolling.

126. FLINDERS BAR. — The simplest method that presents itself for the placing of the Flinders bar is one which is available only for a vessel crossing the magnetic ec-uator. Magnetic charts of the world show the geographical positions at which the dip becomes zero — that is, where a freely suspended needle is exactly horizontal and where there exists no vertical component of the earth's total magnetic force. In such localities it is evident that the factor of the semicircular deviation due to vertical induction disappears and that the whole of the existing semicircular deviation arises from subpermanent magnetism. If, then, w^hen on the magnetic equator the compass be carefully compensated, the effect of the subpermanent magnetism will be exactly opposed by that of the semicircular correcting magnets. Later, as the ship departs from the magnetic equator, the semicircular deviation will gradually acquire a material value, which will be known to be due entirely to vertical induction, and if the Flinders bar be so placed as to correct it, the compensation of the compass will be general for all latitudes.

In following this method it may usually be assumed that the soft iron of the vessel is symmetrical with respect to the fore-and-aft line and that the Flinders bar may be placed directly forward of the compass or directly abaft it, disregarding the effect of components to "starboard or port. It is therefore merely necessary to observe whether a vertical soft iron rod must be placed forward or abaft the compass to reduce the deviation, and, having ascertained this fact, to find by experiment the exact distance at which it completely corrects the deviation.

The Flinders bar frequently consists of a bundle of soft iron rods contained in a case, which is secured in a vertical position near the compass, its upper end level with the plane of the needles; in this method, the distance remaining fixed, the intensity of the force that it exerts is varied by increasing or decreasing the number of rods ; this arrangement is more convenient and satisfactory than the employment of a single rod at a variable distance.

The United States Navy Flinders bar, Type II, is made of carefully annealed pure soft iron, 2 inches in diameter, total length 24 inches, consisting of pieces 12 inches, 6 inches, 3 inches, 1 J inches, and £ inch (2 of these) long. Hardwood blocks of the same dimensions are used to support the proper length of Flinders bar at the top of a fixed brass tube, which is secured ordinarily at the forward end of the bin nacle in the fore-and-aft line.

54 THE COMPASS ERROR.

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, vibra tion 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 pro cedure 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 C)

is made up of a subpermanent factor varying as jj and of a vertical induction factor

varying as tan 0. If we indicate by the subscripts s and v, respectively, the parts due to each force, we may write the equations of the coefficients:

; and

tr-v tan d.

Now if we distinguish by the subscripts 1 and 2 the values in the first and in the second position of observation, respectively, of those quantities that vary with the magnetic latitude, we have :

B. X TT- + BV X tan #!, **t

and

C2 = C8 X TT- + Cv X t an 02 . -ti2

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 B8 and Bv, and the second pair for C8 and Cv; and having found the values of these various coefficients, we may correct the effects of Bs and C3 by permanent magnets in the usual way and correct the remainder — that due to Bv and Cv — 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 Bv and Cv ; but since, as before stated, horizontal soft iron may usually be regarded as sym metrical, Cv 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, except ing 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 magnetic latitude of compensation will undergo considerable change as that latitude

THE COMPASS EKKOB. 55

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.

)he athwartship magnets or alter their number until the deviation disappears; thon 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 navi gator's part. As the ship's iron is partly "hard" and partly "soft," the subper- manent 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 follow ing 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. 6V/- necticut'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 mag netism being "cooked out."

(e) On the U. S. S. Oregon, a grounded searchlight circuit caused a change of 9°. (/) 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.

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

CHAPTER IV. PILOTING,

130. Piloting, in the sense given the word by modern and popular usage, is the ; rt of conducting a vessel in channels and harbors and along coasts, where landmarks ,;nd aids to navigation are available for fixing the position, and where the depth of v/ater 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 t xperience and nicest j udgment. An error in position on the high seas may be rec tified 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

xpects 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

rder. 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 v/ith 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.

f the compass rose indicates Redirections, this will be the true course; and must be orrected for variation and deviation (by applying each in the opposite direction o its name) to obtain the compass course; ii it is a magnetic rose, the course need •e 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 ' lethods: ^(a) cross bearings of two known objects; (b) the bearing and distance of a ' nown object; (c) the bearing of a known object and the angle between two known

bjects; (d) two bearings of a known object separated by an interval of time, with

h.e^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 ; (#) 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 i'rom 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 56

PILOTING. 57

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.

The plotting of a position from two bearings is greatly facilitated by the use of a plotter devised by Lieut. K. 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. A 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 (7J 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 re quired. 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 FIG. 13.

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 011 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.

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

tune; work out the sight and obtain the Sumner line (as explained in Chapter XV), and the inter section of this with the direction line from the

object will give the observer's position in the same X)

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 bear ing and distance. Follow the preceding method in FlG. 14> the manner of taking, correcting, and plotting the

bearing; then, on this line, lay off the distance from the object, which will give t point occupied by the observer. In figure 14, if A represents the object and AO :ing and distance, the position sought will be at O.

earn

60

PILOTING.

EXAMPLE: A vessel on a course 128° takes the first bearing of an object at 154°, and the second at 182°, running in the interval 0.8 mile. Required the distance at which she will pass abeam.

Difference between course and first bearing, 26° Difference between course and second bearing, 54°. Multiplier from second column, Table 5B, 0.76. 0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.

145. As has been said, there are certain special cases ot this problem where it is exceptionally easy of application; these arise when the multiplier is equal to unity and the distance run is therefore equal to the distance from the object. When the angular distance on the bow at the second bearing is twice as great as it was at the first bearing, the distance of the object from the ship at second bearing is equal to the run, the multiplier being 1.0. For if, in figure 18, when the ship is in the first position, O, the object A bears a° on the bow, and at the second position, P, 2a°, we have in the triangle APO, observing that APO = 180° - 2o?, and POA = a :

PAO = 180°- (POA+APO),

a.

0

FIG. 18.

Or, since the angles at O and A are equal to each other, the sides OP and AP are equal or the distance at second bearing is equal to the run. This is known as doubling the angle on the low.

146. A case where this holds good is familiar to every navigator as the ~bow and 'beam bearing, where the first bearing is taken when the object is broad on the bow (four points or 45° from ahead) and the second when it is abeam (eight points or 90° from ahead); in that case the distance at second bearing and the distance abeam are identical and equal to the run between bearings.

147. When the first bearing is 26J° from ahead, and the second 45°, the distance at which the object will be passed abeam will equal the run between bearings. This is true of any two such bearings whose^ natural cotangents ^ differ by unity, and the following table is a collection of solutions of this relation in which the pairs of bearings are such that, when observed in succession from ahead upon the same fixed object, the distance run between the bearings will be equal to the distance of the fixed object when it bears abeam, provided that a steady course has been steered, unaffected by current or drift.

The marked pairs will probably be found the most convenient ones to use, as they involve whole degrees only.

Bearings from ahead.

First.	Second.	First.	Second.	First.	Second.
20	29|	28	48£	37	71f
21	811	*29	51	38	74*
*22	34	30	53f	39	76}
23	36£	31