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No. 9 ^IcQ 2.

25

American Practical Navigator

An Epitome of Navigation and Nautical Astronomy

By NATHANIEL BOWDITCH, LL. D., Etc.

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ORDERS RELATING TO REVISION.

BuRKAU OF ^Navigation, Wavy Departnwrif. January i, 1881. In accoi'dance with the purpose contemplated in the pui'chase of the copyright of the New American Practical Navigator, a thorough and complete revision has been made by Commander P. H. Cooper, U. S. Navy, acting under th(> direction of the Bureau. The revision Consists principally in the substitution of the more concise and convenient methods of the present day for the obsolete methods of the past, and a complete reari-angement under proper chapters and paragraphs for read}- reference, keeping in view, however, the character of the work as a Practical Navigator.

The revision having been completed, it was submitted to Capt. Ralph Chandler, U. S. Navy, for a final review, and having received a satisfactory report from that officer it has been accepted bj^ the Bureau and will hereafter bo substituted for the former editions of the work.

William D. Whiting,

Chief of Bureau.

Bureau of Equipment, Navy JJe_partmetit, March 18, 190o. A revision of Bowditch's American Practical Navigator having become neces- sary, the work has been cooipletcd by Lieut. G. W. Logan, U. S. Navy, under the supervision of the Hydrographer to the Bureau of Equipment. The revision was approved by a Board consisting of Capt. Colby M. Chester, U. S. Navy, Commander C. J. Badger, U. S. Navy, and Lieut. Commander C. C. Rogers, U. S. Navy. It is directed that this revised edition be substituted for all former editions.

R. B. Bradford,

Chief of Bureau. 2

VK5BB

YEDDING OF PROMINENT COUPLE THIS | '31 ^^^rnoon at First Presbyterian Chf^rcb, ''^^

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ii't'.?

PREFACE.

The copyright of the New American Practical Navigator, by the late Dr. Bowditch, became the property of the United States Government under the provision of an act of Congress to establish a Hydrographic Office in the Navy Department, approved June 21, 1866.

Under the direction of the Bureau of Navigation, at that time charged with such publications, the work was revised in 1880 by Commander P. H. Cooper, U. S. Navy, certain chapters being contributed by Lieuts. Richard Wainwright and Charles H. Judd, U. S. Navy, and the whole being reviewed by Capt. Ralph Chandler, U. S. Navj'. The object of this revision was to improve the general arrangement, and to introduce the more convenient and precise methods of navigation that had come into practice since the book was originally written.

The progress that has been made in the science of navigation since 1880 has rendered necessary a second extensive revision, to take cognizance of the changes of methods and instruments that have accompanied the general introduction of high-speed vessels built of iron and steel. This work has been carried out, under the direction of the Bureau of Equipment, by Lieut. G. W. Logan, U. S. Navy, who was aided in the collection of data and preparation for publication by Lieut. T. A. Kearnej, U. S. Navj; the chapters on Winds and Cyclonic Storms were contributed by Mr. James Page, nautical expert, Hydrographic Office.

There has been an extensive rewriting of the text, with the object of amplifying those matters that are of the greatest importance in the modern practice of navigation, and of omitting or condensing those of lesser importance; and the revision of the tables has proceeded along similar lines. This has involved, among other things, a much wider treatment of the subject of the compass; an extension of the traverse table for degi'ees to distances up to 600 miles; an improved table for reducing circum- meridian altitudes; the combination of the tables of maritime positions and tidal data; the omission of certain special methods for finding position by two observations; the addition of a series of annotated forms for the working of all sights, atid the intro- duction of a number of new tables of use to the navigator.

The explanation of the method of lunar distances, with its accompanying tables, has been I'etained, in order to be available for use when required; but since this obser- vation is so rarely employed in modern navigation, everything pertaining thereto has been incorporated in an appendix, that it may be distinct from matter of every-day use to the navigator.

For convenience in use the work has been divided into two parts, of which the first comprises the text and its appendices, and the second the tables.

W. H. H. SOUTHERLAND,

Commander, U. S. Navy, HydrograpJwr, Hydrographic Office,

Bureau of Equipment, Navy Department, ' •

Washington, D. C, March 19, 1903.

M767913

X O T E

Part I of this edition is a reprint of the revised edition of 1903 with typo- graphical errors corrected. Part II was revised and enhirfjed August 10, 1911 (see p. 503).

Jonx J. Knapp,

Captain, U. S. Navy, H;/ilrograph^r. Hydrographic Office.

Bi REAi- OF Navigation, Xavv Department,

Washin^on, D. C, January 15, 1912.

P J^ R T I

TEXT AND APPENDICES.

"Th» oe««Ln !■ th« •lemeut which nrtffht eontaln such conditions. The ) oiigrinatlon of the oooan flta It to sus- tain life better tljan any other en- vironment, and the fundamental char- acteristics of the ocean also encourasfp •volution of active life. Can we not therefore assume that the ocean Is the Attest of known substances for the creation of the origin of life?

"The orlsrln of lite itself depends upon stability. Onr present existence depends upon stability of climate and other elements of onr environments. Where conditions are most stable there you will find most active and progressive life. There Is one sub- stance that posspsses more stability than anythlnp else we know of and that Is the ocean.

"In the ocean we see every degree of development from the highest to the lowest forms of life. It we are to be- lieve In the theory of evolution mny we not fro a step further and conclude that Inorganic life under certain con- ditions, such«aa those contained In the ocean, will develop organic lite?"

OOISTTEN'TS OF P^RT I.

Page.

Orders relating to revision 2

Preface S

Abbreviations 9

Chapter I. Definitions relating to Navigation M

II. Instruments and Accessories in Navigation 13

III. The Compass Krror ?9

IV. Piloting 42

V. The Sailings 50

VI. Dead Reckoning 60

VII. Definitions relating to Nautical Astronomy 63

VIII. Instruments employed in Nautical Astronomy 66

IX. Time and the Nautical Almanac 74

X. Correction of Observed Altitudes 82

XI. The Chronometer Error 87

XII. Latitude 94

XIII. Longitude 103

XIV. Azimuth 109

XV. The Sumner Line 114

XVI. The Practice of Navigation at Sea 124

XVII . Marine Surveying 131

XVIII. Winds 142

XIX. Cyclonic Storms 147

XX. Tides 153

XXL Ocean Currents 158

Appendi.x I. Extracts from the American Ephemeris and Nautical Almanac for the year 1879,

which have reference to examples for that year given in this work 163

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

Sights, with not«s explaining their application under all circumstances 171

III. Explanation of certain Rules and Principles of Mathematics of u.se in the Solu-

tion of Problems in Navigation 178

IV. Maritime Positions and Tidal Data 190

V. Lunar Distances 288

Index 333

7

ABBREVIATIONS USED IN THIS WORK.

Alt. (or A) Altitude.

A. M Ante meridian.

Amp Amplitude.

App ..Apparent.

App. t Apparent time.

Ast Astronomical.

Ast. t Astronomical time.

Aug Augmentation.

Az. (orZj Azimuth.

C Course.

C C Chronometer correction.

C— W Chronometer mmif.? watch.

Chro. t Chronometer time.

Co. L Co. latitude.

Col Column.

Corr Correction.

Coe Cosine.

Cosec Cosecant.

Cot Cotangent.

d (or Dec. ) Declination.

D (or DLo) Difference lorigitude.

Dep Departure.

Dev Deviation.

Diff Difference.

Dist Distance.

DL Difference latitude.

D. R Dead reckoning.

E. , Ely Ea.st, easterly.

Elap. t Elai)8ed time.

I'xj. eq. alt Equation equal altitude"

Kq. t Etjuation of time.

G. (or Gr. ) Greenwich.

G. A. T Greenwich apparent Jie.

G. M. T Greenwich mean time.

G. S. T. Greenwich sidereal time.

h Altitude.

H Meridian altitude.

H. A. (or() Hour angle.

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 IM. ) 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.

m Meridional difference.

Merid Meridian or noon.

Mag Magnetic.

M. D Minute's difference.

Mid Middle.

Mid. L Middle latitude.

M. T Mean time.

N. , Nly North, northerly.

N. A. ("or Naut. Aim. ). Nautical Almanac.

Np Neap.

Obs Observation.

p ( or P. D. ) Polar distance.

p. c Per compass.

P. D. (orp) Polar distance.

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

P. M Post meridian.

p. <fc r Parallax and refraction.

Par Parallax .

R. A Right ascension.

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

Red Reduction.

Ref Refraction.

S., Sly South, southerly.

S. D Semi-diameter.

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.

			STMBOIvS.
o	The Sun.		° Degrees.
c	The Moon.		' Minutes of Arc.
*	A Star or Planet.	" Seconds of Arc.
r-x	Alt. upjx-r	limb.	' Hours.
(•)<(	Alt. lower limb.	" Minutes of Time
00	Azimuthal	angle.	• Seconds of Time
			GREEK LETTERS.
Aa.	.Alpha.		Ny....	.Nu.
BIS.	.Beta.		Bi ....	.Xi.
I'y.	.Gamma.		Oo....	-Omicron.
4S.	.Delta.		nx....	-Pi.
Ee .	.Epsilon.		Pp. ...	.Rho.
z?.	.Zeta.		. 2<J(5)-	.Sigma.
Hv.	.Eta.		Tt ....	.Tau.
Bf) .	.Theta.		rv....	.Upsilon.
1 1 ..	.Iota.		$ <p	.Phi.
Kk.	. Kappa.		V;r....	.Chi.
AX.	.I.ambda.		y v....	.Psi.
Mft.	.Mu.		n at ...	.Omega.

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npi

A

Uhi'INITlOU.S

KKLAllM,

ATIOif.

11

CHAPTER I.

DEFINITIONS EELATING TO NAVIGATION.

1. That science, generally termed Kavigcttion, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the inariner to determine, with a sufficient degree of accuracy, the position of his vessel at any time, is properly divided into two branches: yarix/ution and Navllcat Astronomy.

2. Navigation, in its limited sense, is that branch which treats of the determination 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 ssa, and (h) 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. Xauticat Adronotni/ is that branch of the science wliii-h treats of the determination 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-Namga'ion and Celo- Niirigaiion, to indicate the processes upon which they depend.

5. As the method of piloting can not be employefl excepting near land or in moderate depths of water, the navigator at sea must fix his position either hji dead reckoning or by obeervalion {of celestial obiects); 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 Ixxiy slightly flsttened at the poles; its longer or equatorial axis measures about 7,927 statute miles, antl its shorter axis, around which it rotates, about 7,900 statute miles.

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

The A.ris of Rotation, usuallv spoken of simplv 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 E'juator is tlie great circle pjQMW, formed by the intgrsection with the earth's surface of a plane perpendicular to the axis; the equator is equidistant from the poles, every ])oint upon it teing 90° from each pole.

Meridians are the great circles PQP', PMP', PM'P', formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through \t» poles an<i therefore perpendicular to its plane) .

Parallels of Latitude are small circles NT», N'»'T', lormeil by the intersection with the earth's surface of planes passed parallel to the etjuator.

The Ixititude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. I>atitude 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', M'T', north. The Difference of iMtitude ))etween any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction; thus, the difference of latitude between T and T' is Tn' or T'u, noVth from T or south from T'.

The longitude of a place on the surface of the earth is the arc of the equator intercepted between its meridian and that of some place from which the longitude is reckoned. Longitude is measured East or West through 180° from the meridian of a designated place, such meridian being termed the lYtine 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 PCJQP', then the longitude of the point T is QM, east, and of T', QM', east. The Difference of Longitude lietween any two places is the are of the equator inter- cepted 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 quantities previously defined, departure is reckoned in miles; the departure l)etween 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 correspomling to the distance Tn in the latitude of T, or to n'T' in the latitude of T'.

12 DEFINITIONS BELATING TO NAVIGATION.

The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Hhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure, tliis line is represented by TrT'. 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. It is equal to one minute of latitude — that is, to the length of that portion of a meridian which subtends at the earth's center the angular measure of one minute; since, however, on account of the fact that the earth is not a perfect sphere, this distance is not exactly the same in all latitudes, a mean value is adopted for the length of the knot, and it is regarded as equal to 6,080.27 feet. For the purposes of navigation, the variation from this value in different latitudes is so small that it may be neglected, and the knot may be assumed equal to a minute of latitude in all parte of the earth; hence, when a vessel changes her position to the north or south by one nautical mile, it may always be considered that the latitude has changed 1'. Owing to the fact that the meridians all converge toward the poles, the difference of longi- tude produced by a change of position of one mile to the east or west will vary with the latitude; tlius a departure of one mile will equal a difference of longitude of I'.O at the equator, of I'.l in the latitude of 30°, and of 2'.0 in the latitude of 60".

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 'R/T'. From the properties of a great circle (which is a circle upon the earth's surface formed by the inter- section 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 alwavs differ from the rhumb line, and the great circle track will intersect each intervening meridian at a different angle.

INSTRUMENTS AND ACCESSOBIES IN NAVIGATION. 13

CHAPTER II.

INSTEUMENTS AND ACCESSORIES IN NAVIGATION.

DIVIDERS OR COMPASSES.

7. This instrument consists of two legs movable about a joint, so that the ix>ints at the extremitiee of the legs may be set at any requirerl distance from each other. It is used to take and transfer dis- tances and to describe arcsand circles. When used for the former purpo.se it is termed diriders, and the extremities of both legs are metal points; when used for describing arcs or circles, it is called a cmn- pass, and one of the metal points is replaced by a jiencil or pen.

PARALLEL RULERS.

8. Parallel riilerx are used for drawing lines parallel to each other in any direction, and are particu- larly 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 ."hape in which it may be made. ( For a description of the Three Armed Protractor, see art. 432, Chap. XVII. )

THE CHIP LOO.

10. This in.strument, for measuring the rate of sailing, consists of three parts; viz, the log-chip, the log-line, and the log-glags. A light substance thrown from the ship ceases to partake of the motion of the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain inter- val, if the distance of the ship from this stationary object te measured, the approximate rate of sailing will l)e given. The log-chip is the float, the log-line is the measure of the distance, and the log-glau defines the interval of time.

The log-chip is a thin wooden quadrant of aliout 5 inches radius, loaded with lead on the circular edge sufficiently to make it swim upright in the water. There is a hole in each comer 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 jieg to fit snugly into the socket before the log-chip is thrown; as soon aa the line is checked this peg pulls out, thus allowing the log-chip to Ije hauled in with the lea.st resistance.

The log-line is al)out 1.50 fathoms in length, one end made fast to the log-chip, the other to a reel upon which it is wound. At a distance ot from 1.5 to 20 fathoms from the log-chip a permanent mark of red bunting aV)out 6 inches long is placed to allow sufficient gtrau line for the log-chip to clear the vessel's eddy or wake. The rest of the line is divided into lengths of 47 feet 3 inches called knots, by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the number from stray-line 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 tlie numterof seconds which the log-glass measures; the length of each knot must liear the same ratio to the nautical mile (^V ot a degree of a great circle of the earth or 6,080 feet) that the time of the glass does to an hour.

In the United States Kavy all log-lines are marked f6r log glasses of 28 seconds, for which the proportion is:

3600 : 6080 = 28- : a:, X being the length of the knot.

Hence, .

a: = 47".29, or 47" 3'°.

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

The Ujg-glam is a sand glass of the same shape and construction as the old hour-glass. Two gla-sses 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 indicated 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 peg must be found to fit sufficiently tight to keep the log-chip upright; the log-line 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 stationary 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.

14 INSTRUMENTS AND ACCKS80RIES IN NAVIGATION.

THE PATENT LOG.

1 3. 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 tow line; the rotator is a small .spindle with a number of wings 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 pro- peller; the rotator is towed from the vessel by means of a log or tow line from 20 to 50 fathoms in length, made fast at its apex, the line teing 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 regis- tering device is so constructed as to show upon a dial face the distance run, according to the numlx'r 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 tlie rotator will be towed clear of the wake.

14. Though not a perfect instrument, the patent log affords the most accurate means available for determining the ves-sel'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 erior should be determined by careful experiment and applied to all readings.

Various causes may operate to produce ina(«uracy of working in the patent log, such as the bending of the wings of the rotator by accidental blows, fouling of the rotator by sea weed or refuse from the ship, or mechanical wear of parts of the register. The length of the tow-line has much to do with the working of the log, and by varying the length the indications of the instrument may sometimes be adjuste<l 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.

16. A number of instruments based upon different })hysical principles have been devised for recording the speed of a vessel through the water and have been used with varying degrees of success.

1 7. The revolutions of the screw propeller afford in a steamer a valuable check upon the patent log and a means of replacing it if necessary. To be of service the number of revolutions per knot must be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foul- ness of bottom.

THE LEAD.

18. This device, for {iscertaining 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 hand-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. , 17 fathoms from the lead, same as at 7 fathoms^

20 fathoms from the lead, w-ilh !J lkriot8.<^« 25 fathoms from the lead, with 1 knot. *"

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

30 fathoms from the lead, with 3 knots. 35 fathoms from the lead, with 1 knot. 40 fathoms from the lead, with 4 knots. An<l so on.

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 intermediate 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 verilied. The distance from the leadsman's hand to the water's edge should l>e ascertained in order that proi)er 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.

SO. This machine possesses advantages over tlie deep-sea lead, forwhich 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 iMrd 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 <]f the sounding corresponding to this line is read off from a scale. TuImjs that have been used in comparatively shallow water may be useil again where the water is known to be deeper.

IKSTRUMENTS AND ACCESSORIES IN NAVIGATION.

15

22. A tube whose inner surface is (fround has been substituted for the chemical-coated tube, ground glass, when wet, showing clear. The advantage of these tubes is that they may be used an indefinite number of times if thoroughly dried. To facilitate drying,arubbercapi8 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 com- pression 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 30.00 30.50 30.75	One-fortieth. One-thirtieth. One-twentieth. One-fifteenth.

THE KAKINER'S COMPASS.

25. The Marinefg Compaes is an instrument consisting either of a single magnet, or, more usually, of a series of magnets, which, being attached to a graduated circle pivoted at the center and allowed to

• Fio. 2.

swing freely in a horizontal jdane, has a tendency 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 <ourse and of all visible o>)ject8, terrestrial or celestial.

16

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

46. The circular tard of the compass (fig. 2) is divided on its periphery into 360°, numbered from 0° at North and South to 90° at East and West; also into thirty-two divisions of lip each, called yjoi'nte, the latter being further divided into half-poii)ts and quarter-points ; still liner sulxlivisions, eighth-points, are sometimes 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 the figure. This system is in use by the mariners of some 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. Jlidway between each cardinal and inter-cardinal point, at an angular distance of 22J°, or 2 points, is a point whose name is made uj) 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 11|°, from each cardinal and inter- cardinal point (and therefore midway between it and the 22J°-division last described), is a point which bears the name of that cardinal or inter-cardinal point joined by the word hy to that of the cardi- nal point in the direction of which it lies: North by East, Northeast by North, Northeast by East, et(^

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; fot instance, NE. by N. J N. and NNE. J E. would describe the same division. It is the custom in the United States Navy to box /j-ojji 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 N. J E., N. by E. J E., NNE. J E., NE. J N., etc. Some mariners, however, make it a prac- tice to box from each cardinal and inter-cardinal point toicard a 22}°-point (NNE., ENE., etc.) ; as N. I E., N. by E. J E., NE. by N. J N., NE. J 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 shows also the degrees, minutes, and seconds from North or South to which each division corresponds:

N. toE.

N. to W.

S. toE.

S. to W.

Pts.

Angular measure.

North:

N. JE

N. JE

N. IE

N. byE

N. byE. JE...

N. byE. JE...

N. byE. |E... NNE

NNE. JE

NNE. JE

NNE. |E

NE. bvN

NE. iN

NE. JN

NE. t N

NE

NE. JE

NE. JE

NE. IE

NE. byE

NE. byE. J E..

NE. byE. JE..

NE. bvE. i E..

ENE ....:

ENE. JE

ENE. JE

ENE. |E

E. bvN

E. JN

E. JN

E. JN

East

North:

N. iW

N. J W

N. }W

N.by W

N. byW. iW.

N. bvW. JW.

N. by W. }W. NNW

NNW. JW...

NNW. J W...

NNW. J W... NW. by N

NW. JN

NW. +N

NW. i N

NW

NW. i W

NW. J W

NW. i W

NW. by W

NVV.byW.JW

NW. by W. JW

NW.byAV. |W WNW

WNW. i W...

WNW. J W...

WNW. J W... W. byN

W. JN

W. J N

W. IN

West

South:

S. JE

S. JE

S. }E

S.byE

8. byE. JE.

S. byE. JE.

S. by E. J E . SSE ,

SSE. JE

SSE. JE

SSE. JE.... SE. bvS

SE. JS

SE. JS

SE. JS

SE

SE. JE

SE. JE

SE. JE

SE. byE

SE. by E. J E

SE. by E. J E

SE. by E. J E ESE

ESE. JE....

ESE. JE....

ESE. JE.... E. byS

E. JS

E. JS

E. JS

East

South:

S. J W

S. JW

S. J W

S. by W

S. bvW. JW...

S. bvW. JW...

S. by W. JW...

ssw

i

i 1

U li

2 SSW. JW '• 2J

ssw. J W . SSW. J W

SW. byS

SW. J s . . SW. JS.. SW. JS..

SW

2J

2J

3

3J

3J

3J

4

4J

SW. J w.... SW. JW....

SW. JW I 4|

SW. byW I 5

SW. byW. JW. 5 J

SW. hyW. JW.I 5J

SW. bvW. JW.I 5J

WSW....". 6

WSW. JW 6J

WSW. JW ! 6 J

WSW. JAV ! 6J

w.

by S . W.

JS.

W. JS.

AV. J S .

West

7 7J

7*

2 48 45 5 37 30 8 26 15 11 15 00 14 03 45 16 52 30 19 41 15 22 30 00 25 18 45 28 07 30 30 56 15 33 45 00 36 33 45 39 22 30 42 11 15 45 00 00 47 48 45 50 37 30 53 26 15 56 15 00 59 03 45 61 52 30 64 41 15 67 30 00 70 18 45 73 07 30 75 56 15 78 45 00 81 33 45 84 22 30 87 11 15 90 00 00

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

2S. According to the purpose which it is designed to fulfill, a compass is designated as a Standard, Steering, Check, or Boat Compass.

INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 17

30. There are two types of compass in use, the vet or Umiid and the dri/; in the former the bowl is filled with liquid, the card l)eing 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 deflectetl by reason of 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 7J-inch Liquid Compass. — This consists of a skeleton card 7J 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 Ijetween tlie poles of a jiowerfiil electromagnet. They are afterwards placed in a cylindrical ca.se, 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 soliil 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 througli their extremities. These magnets penetrate the air vessel, to which they are soldered, and are further secured to the Iwttom of tlie 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 arc secured to the bottom of the ring of the card.

The card is of a curved annular type, the outer riu" being convex on the upper and inner side, and is graduated to read to one-fourth point, a card circle lieing 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 laying the course to degrees.

The card is ]irovi(le(l with a concentric spheroidal air vessel, to buoy its own weight and that of the magnets, allowing a ])res.sure 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, ojieu at its lower end, and provided with the pivot bearing, or cap, containing a sapi)hire, which rests upon the pivot and thus sujiports the card; the cap is provided with adjusting screws foraccurately centering the card. The pivot is fastened to the center of the lK)ttom of the bowl by a flanged plate and scivws. Through this plate and the bottom of the bowl are two small holes which communicate with the expansi<m chamber and admit of a circulation of the liiiuid between it and the Ik>w1. 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 evaporatiim or leakage of the liquid, which entirely fills the Ixiwl. This liquid is com- posed of 45 per cent pure alcohol and 55 per cent distille<l water, and remains liquid below — 10° F.

The lubber's line is a fine line drawn on an enameled ])late on the inside of the bowl, the inner ."urface of the latter l>eing covered with an insoluble white paint.

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

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

!J2. The Dky Compass. — The Lord Kelrin Cotnjyiim, which may l)e regarded as the standard for the nonliquid type, consists of a strong jiaper card with the central parts cut away and its outer edge stiffened bj- a thin aluminum ring. The pivot is fitte<l with an iridium point, u])on which rests a small light aluminum 1m)SS fitted with a sapphire bearing. Radiating from this boss are 32 silk threads whose outer ends are made fast to the inner edge of the compa.ss card; these threads sustain the weight of the suspended card, and, as they ])os.ses8 some elasticity, teml to ilecrea.se the shocks due to motion.

Eight small steel w ire needles, 3| to 2 inches long, are secured normally to two i)arallel silk threads, and are slimg from the aluminum rim of the card by other ."ilk threads which pass through eyes in the ends of the outer pair of needles. The needles are below the radial threads, thus keeping the center of gravity low.

33. The Azimuth CiKcle. — This is a necessary fitting for all compasses employed for taking bearings — that is, noting the directions — of either celestial or terrestrial objects. The instrument varies widely in its different forms; the essential features which all share consist in (o) a pair of sight vanes, or equivalent device, at the extremities of the diameter of a circle that revolves concentrically with the compass bowl, the line of sight thus always passing through the vertical axis of the compass; and (h) a system, usually of mirrors and prisms, by which the point of the coiuiiass card cut by the vertical plane through the line of sight — in other words, the compa.ss direction — is brought into the field of view of the person making the observation. In some circles, for obser\ ing azimuths of the sun advantage is taken of the brightness of that body to reflect a jtencil of light uix)n the card in such a manner as to indicate the bearing; such an azimuth circle is used in the United .States Navy.

34. Binnacles. — Comi)a.sses are mounted for use in stands known as lihinacleK, of which there are two principal tjpes — the ('uiiipensathtg and the yon-Compeiiiidthui Bhnmclr, so designated according as they are fir are not e(|Hii)ped with appliances by which the deviation of the compa.ss, or error in its indications due to disturbing magnetic features within the ship, may be compensated.

Binnacles may be of wood or of some nonmagnetic metal; all contain a compass chamlier within which the compass is susjiended in its gimbal ring, the knife edges upon which it is suspended resting in V-shaped bearings; an appropriate method is supplied for centering the compa,ss. A hood is provided for the protection of the compass and for lighting it at night. Binnacles must be rigidly secured to the deck of the vessel in such position thet the lubber's line of the compass gives true indications of the direction of the ship's head.

The position of the various binnacles on shipboard and the height at which they carry the compass must be chosen w ith regard to the purpose which the compass is to ser\'e, having in mind the magnetic conditions of the ship.

Compensating binnacles contain the appliances for carrying the various correctf)rs used in the ccm- pensation of the deviation pf the compass. These consist of (a) a system of permanent magnets for 24972°— 12 -2

18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

semicircular deviation, placed in a magnet chamber lying immediately beneath the compass chamber, so arranged as to permit variation in the height and direction of the magnets employed; (6) a pair of arms projecting horizontally from the compass chamber and supporting masses of soft iron for quad - ran tal deviation; (c) a central tuV)e in the vertical axis of the binnacle for a permanent m^net used to correct the heeling error, and (d) an attachment, sometimes fitted, for securing a vertical soft iron rod, or "Flinders bar," used in certain cases for correction of a part of the semicircular deviation. An explanation of the various terms here used, together with the method of compensating the compass, will be given in Chapter III.

THE PELORT7S.

35. This instrument consists of a circular plate, mounted liorizontally in gimbals upon a vertical standard, at some point on board ship affording a clear view for taking bearings; radial scores upon a raised flange on the periphery of this plate indicate true directions from its center parallel with the keel line of the vessel and perpendicular thereto — in other words, lines of bearing directly ahead, astern, and abeam. Revolving about a common center, which is also the center of the plate, are (a) a dumb com- pass card, usually engraved on metal, whose face is level with the raised periphery of the plate on which are marked the scores, and (6) a pivoted horizontal bar carrying at its extremities a pair of sight vanes so arranged that the line of sight always passes through the vertical axis of the instrument, and having an index showing the point at which the line of sight cuts the dumb compass. The dumb compass and the sight-vane bar can each be rigidly clamped.

The insiruraent is used for taking bearings, and may be more convenient than the compass for that purpose because of the better view that it affords, as well as because it may be made to eliminate the compass error from observed bearings. Suppose that the dumb compass be revolved until the degree or division which is coincident with the right-ahead score of the plate is the same as that which is abreast the lubber's line of the ship's compass. Then all directions indicated by the dumb comi^ass will be parallel to the corresponding directions of the live one, and all bearings taken by the pelorus will lie identical with those taken by the compass (leaving out of the question the diffence due to the distance that separates them). Suppose, now, that it is known that the ship's compass has a certain error and that the correct direction that we seek (which is the one indicated on the charts) is a certain angular distance to the right or left of that which the compass shows; if, in such a case, instead of setting tlie pelorus for the direction indicated by compass, we set it for the correct direction in which we know the ship to be heading, all Isearings observed by the pelorus will be correct liearings as given by the chart and may be plotted directly thereon without the necessity for the intermediate process of correction to which the bearings shown by compass are subject. It will at once be evident that the indications of the pelorus will be accurate only when bearings are taken at an instant when the ship is heading exactly in the direction for which it is set, and care must be taken accordingly in its use.

The most modern types of pelorus are fitted for illuminating the dumb compass, thus greatly facili- tating night work.

THE CHABT.

!I6. A nautical chart is a miniature representation upon a plane surface, in accordance with a defi- nite system of projection or development, of a portion of the navigable waters of the world. It generally includes the outline of the a<ljacent land, together with the surface forms and artificial features tliat are useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the land, by somidings that are fixed in po.sition 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.

37. There are three principal systems of projection in use: (a) the Mercator, (h) the polyconic, and (c) the gtiommfiic; of these, the Mercator is by far the most generally used for purposes of navigation proper, while the polyconic and the gnomonic charts are employe<l for nautical purposes in a more restricted manner, as for plotting surveys or for facilitating great circle sailing.

3§. The Mercator Projection. — The Mercator I'rojection, so called, may be said to result from the development, vmm 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 bear- ing 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 develop- ment; 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, maintaining 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.

39. 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.

INSTRUMENTS AND ACCKS80RIE8 IN NAVIGATION. 19

Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of tlie same length, it becomes necessary, in order to preserve the proportion that exists at different parts- of the earth's surface l)et\veen 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 Parte 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 pro- jection and for solving problems in Mercator sailing.

4©. To CoxsTRucT A Merc.\tor 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 parallel to be drawn 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 down on the chart by means of any properlv divided scale of yards, meters, feet, or miles, after having been reduced to the scale of proportions adopted for the {•hart.

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 eiiuator, a diagonal scale may first be constructed, on which ten meridional parts, or ten minutes of arc on the eijuator, have a length of half an inch.

It mav 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 multi- plied. This quantity will represent the urate of the chart. If it occurs that the limits of longitude are a governing consideration, the case may be similarly treated.

E.vami-le: Let a projection be re^iuireil 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 l)etween 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 ninning down to the line of 25', will be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc lietween these latitudes, for which 1' of arc of the equator is taken as the unit. On the intended projection,

lAiD

therefore, V of arc of longitude will measure -^.~„ = 0.0152 inch, which will be the scale of the 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 lie the parallel of latitude 20° 30'; this will lie 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 0.015 X 60 X 7 = 6.3 inches; and through the points thus obtained draw parallel lines 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. 8ubtra<:ting 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 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:

0'".015X (1344.9-1248.9) =1.440 inches, 0'°.015X (1409.5-1248.9) =2.409 inches, 0'».015X (1474.5-1248.9) =3.384 inches, etc.

Thus will be shown the parallels of latitude 22° 00', 23° 00', 24° 00', etc. Finally, 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 0'°. 015X60=0'". 9. J^ay off, therefore, on the low- est parallel of latitude drawn on the chart, on a middle one, and on the highest )>arallel, measuring from the middle meridian toward each side, the distances of 0'".9, ]'".8, 2'". 7, 3'". 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 subdivide the degrees of latitude and longitude as minutely as the scale of the chart will ])ermit, the sulxlivisions 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 deseril)ed, though it will generally be found sufficiently exact to make even subdivisions of the degrees, as in the case of the fongitude.

The subdivisions between the two eastern as well as those between the two western neat lines will serve for measuring or estimating terrestrial distances. Distances Vjetween points l)earing North and South of each other may be ascertained by referring them to the suV)divisions between the same paral- lels. Distances represente<l by lines at an angle to the meridians (loxodromic lines) may l)e measured

20

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

by taking between the dividers a small number of the subdivisions near the middle latitude of the line to be mea.sured, 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' l)e required, the distance shown on the neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may be taken between the dividers and stepjied off on that line.

41. 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 corre- sponding parallels of latitude and meridians over botli charts so close to eacli 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 l)y 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 tlie jirojection.

42. The Poi.ycoxic Pko.iection. — This projection is based upon the development 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 tlie general distortion of the figure is less than in any other method of projection, the relative magnitudes ))eing closely preserved.

A straight line on the jiolyconic chart represents 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.

This method of projection is especially adaj)ted to the plotting of surveys; it is also employed for nearly all of the charts of the United States Coast and Geodetic Survey.

43. Gnomo.nic 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 the plane of projection. In a gnomonic chart, a straight line between any two points is projected as an arc of a great circle, and is therefore 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 methodoLdoing which will be explained in Chapter \'.

44. Meeidi.\xs E.virLOYED in Ch.vrt Constklction. — The United States, England, Germany, Italy, Eussia, Norway, Sweden, Denmark, Holland, Austria, Portugal, and Japan adopt as a prime meridian the meridian of Greemvich.

France adopts the meridian of Paris in Long. 2° 20' I4".5 E. of Greenwich.

Spain adopts the meridian of fktn Fernando, Cadiz, in Long. 6° 12' 20" W. of Greenwich.

The Pulkowa Observatory of St. Petersburg (sometimes referred to in Russian charts) is in Long. 30° 19' 39".6 E. of Greenwich.

The Royal Observatory of Naples (sometimes referred to in Italian charts) is in Long. 14° 14' 06" E. of Greenwich.

The meridian of Genoa is 8° 55' 21" E.; of Lisbon, 9° 08' 36" W.; of Rio de Janeiro, 43° 10' 21".2 W.; of Amsterdam, 4° 53' 03".8 E.; of Washington, 77° 03' 56".7 W.

45. Quality of Bottom. — The following table shows the qualities of tlie bottom, as expressed on charts .of various nations:

I'nited States.

English.

French.

Italian.

Spanish.

German.

Olav Coral Gravel . . . Mud	C. Co. G. M. Sh. St. ....Wd. fne. crs. stf. sft.	Clay Coral Gravel . . . Mud Rock.... Sand Shells ... Stones.... Weed.... Fine Coarse . . . Stiit Soft Black .... Red Yellow..	cl. ....crl. g- m. ....rk. 8. ....fh. .St. ...wd. t. c. ....stf. ....sft. ...blk. ....rd. y-	Argile.... Corail.... Gravier .. Vase Roche.... Sable Coquille . Pierre Herb Fin Gros Dure Molle.... Noire Rouge ... Jaune	....A. ...Cor. ....Gr. ....V. ....R. S. ..Co^. ....H. ...fin. m. n. r. j.	Argila Cor411o RenaorGhiaja	Arcillo or Barro Coral CascAjo Fangoor Luno. Piedra or Roca . Arena Conchuela Piedra Alga Fina Gruesa...	.cl. Co. ..F. ..P. .A. .ca. ..P. .A. ..f.	Lehm Korallen . . . Grob sand . . Schlemm .. Fels Sand	h. K. ....g. s. Sch.
Rocky	Roccia	F.
Sand	S4bia or Artoa	. S
Shells....	Muschel . . . Stein. Gras Fein Grob Zahe Welch Schwarz... Roth. Gelb.	M.
Stone	pietre
Weed	Alga	G.
Fine	Fino	i.
Coarse . . .	Grosso	f-
Stiff
Soft	Molle	Muelle	\v.
Black....	bk. rd. yi. gy.	Nero	Negro	, .schw.
Red
Yellow...	Giallo	Amarillo
Gray

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

21

46. Measures op Depth. — The following table shows the measures of depth employed in the charts of certain foreign nations, with their equivalents in English measures:

I English feet.

Austrian fathom (klafter) . .

Danish and Norwegian fathom (farn)..

Dutch fathom ( vaden) . .

French /fathom ( brasse) . .

\meter (metre)

Portuguese fathom (braga) . .

Prussian fathom ( faden) . .

Russian fathom (sajen) . .

Spanish fathom (braza) . .

Swedish fathom (famn) . .

6.222 6.175 5.575 5.329 3.281 6.004 O.906 6.000 5.492 5. 843

Englisli fathoms.

1.030 1.029 0.929 0.888 0.547 1.000 0.984 1.000 0.915 0.974

II

i

The Dutch elle, the Spanish, Portuguese, and Italian metro, and the French mrtre are identical.

Xpied ««i(f/= 13. 124 inches, or 1.094 feet. A mPtre is 'S pieds; a, pied da roi =12.7896 inches; t/)-asse is used upon old French charts instead of metre. Tpon some Italian charts soundings are in French pieds.

THE BABOKETEB.

47. The barometer is an instrument for measuring the pressure of the atmosphere, and is of jxreat service to the mariner in affording a knowledge of existing meteorological con- ditions and of the probable changes therein. There are two classes of barome- ter— merc.imrd and aneroid.

48. The Mercuri.^l Barometer. — This instrument, invented by Torricelli in 1643, indicates the pressure of the atmosphere 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 completely filled with pure mercury, antl then placed, open end down, in a cu|) of^ mercury (the open end having been temporarily sealed to retain the liquid during the process of inverting) , it will be found that the mercurv in the tube will fall until the top of the colunm is about 30 inches above the level of that which is in the cup, leaving in the upper part of the tute a perfect 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 in position — namely, thatof the atmosi)heric air — it follows that the heightof the column is subject to variation upon variation of that ])res8ure; hence the mer- cury falls as the pressure of the atmosphere decreases and rises as tliat j)res- sure iucrea-ses. The mean pressure of tlio atmosphere is equal to nearly 15 pounds to the square inch; the mean heightof the barometer is about 30 inches.

49. 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 suspen.^ion, and at the bottom in a flange, to which the several jiarts forming the cistern are attached. The up])er part of the brass tui)e is partially cut away to expose the mercurial column for observation ; abroa.«t this opening is fitted a scale for measuring the height, and along the scale travels a render 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, by which the adjustment is made. In the middle of the brass 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 air; tlie central IX)sition of the column is selected in order that the mean temperature may be obtained — a matter of importance, as tlie teni])eratureof the mercurial column must be taken into account in every accuratt; application of its reading.

•50. In the arrangement of further details menturial barometers are di- vide<l into two classes, according as they are to be used a.s Stii>id<irds (fig. 4) on shore, or as Sea Barouielen (fig. 3) on shipboard.

In the Standard Barometer the scale and vernier are so graduated as to enable an oVjserver 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 evi- dent that as the mercury in the tube rises, upon increase of atmospheric pres- sure, themercury 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 Pj^_ 3 rise of level will occur. As the heightof tlie mercurial column is required pj,. 4

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 l)ag, against t\\i\ bottom of which presses the i)oint of a vertical screw, the milled

22

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

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 graduations; 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 any small bubl)les of air from finding their way upward. The instrument aboard ship is sus- pended 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.

51. The wrnicc 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 e(iual to some whole number of divisions of .the scale of the mstrument and that this length shall ))e 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 to 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 31 divisions of the vernier \)e 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 colunui 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 of such a division; the division marked "1" will fall short of a scale division by one- tenth of 1 divison 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 the zero coincide with a scale ao 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 jV 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.

52. The Sea Barometer is arranged as described for the instrument a.ssumed 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 capa- ble 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 maybe read to 0.002 inch.

53. 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 mer- cury 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 night. When observing the barometer it should hang freely, not being inclined by holding or even by touch, l)ecause any inclina- tion will cause the column to rise in the tube.

54. 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 temi>erature 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. 56), 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.,

Fig. 5.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

23

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. !
o	Inch.	o	Inch.	o	Iruih.	0	Inch.
20	-1-0. 02	40	-0.03	60	-0.09	80	-0.14
22	-1-0. 02	42	-0.04	62	-0.09	82	-0.14
24	-1-0. 01	44	-0.04	64	-0.09	84	-0. 15
26	H-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

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

Observe<l lieight of the mercury 29. 95 '

Correction for temperature (74° ) —0. 12

Height of the mercury at standard temjierature 29. 83

55. Thk Aneroid Barometer. — This is an instrument in which the pressure of the air is measured by means of the elawticity 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 consequence 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 magnifie<l many times, a very minute movement of the box making a considerable difference in the indication of tlie pointer. The graduations of the aneroid scale aie 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 correction for temperature can be applied with certainty. Aneroids, as now manufactured, are almost perfectly comjiensated for temperature by the use of different metals liaving unequal coefficients of expansion; they ought, therefore, to show the same pressure at all temperatures.

The aneroid barometer, from its small size and theea.se with wliich it may be transported, 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 jiressure. It can, however, be reliefl upon only when frequently com- pared with a standard mercurial barometer; moreover, considerable care is re<]uired 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 plaeetl 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.

56. Co.MP.\RisoN OF B.\Ro.METERs. — To determine the reliability of the ship's barometer, \\hether 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 gla.ss tube, or similar causes; in an aneroid, which is less accurate and in which there is even more necessity for fretiuent comparisons, errors may be due to derangement of any of the various mechanical featur«i upon which itH 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 sliipboard at those times, and, if a mercurial instrument is used, to note the attached thenuometer and apply the correction for temperature (art. 54). 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 Ijy the Weather Bureau and Branch Hydrographic offices.

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.

57. DpKRMiNATiox OF HEIGHTS BY' Babometer. — The barometer may be used to determine the difference in heights between any two stations by means of the difference in atmospheric pressure

24

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

between them. An approximate rule ia to allow 0.0011 inch for each difference in Jevel of one foot, or, more roughly, 0.01 inch for every 9 feet.

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

Diff. in height=CX

B„-B

B.+B' if the temperatures be taken by a Farhenheit thermometer.

<'

900

>

— — . .. ^ ^ — ,«(- — — — ^^ ..J — — ., — .^.v. .. [^.jj.

! are three classes of thermometer, distinguished according to the method of graduating the Hows: the Fahrenheit, in which the freezmg point of water is placed at 32° and its boiling

C (in feet) = .52, 494 I i_|_ if a centigrade thermometer is used,

0 (in meters) = 16,000^1+?^^^^.

THE THERMOMETER.

58. The Thermometer is an instrument for indicating tenii)eraturc. 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 mer- cury contained in the tube moves in a vacuum produced by the expulsion of the air through l)oiling tlie mercury and then closing the top of the tube by means of the blowpipe.

There! scale as follows . point (under normal atmospheric pressure) at 212°; the' Ceiitif/mile, 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).

59. 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 temperature 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.

60. 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 Cf)mpared with a<"curate standards, and not accepted if their read- ings vary more than 1° from the true at any point of the scale.

CI. The dry-bulb thermometer gives the tempera- ture of the free air. The wet-bulb thermometer, an exactly similar instrument the bulb of which is sur- rounded by an envelope of moistened cloth, gives what is known as the temperature of ernporntion, which is always somewhat less than the temperature of the free air. Froin 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 )ioint at which it will be obliged to precipitate some of its moisture (water vapor) in the form of liijuid. With the envelojie of the wet bulb removed, the two ther- mometers should read precisely the same; otherwise they are practically useless.

The two tliermoTneters, the wet and the dry bulb, shciuld be hung within a few inches of each other, and the surroundings should be as far as possible identical. In ]iractice the two tliermometers are generally in<'losed within a small lattice case, such as that shown in figure 6; the case should be placed in a position on deck remote froiii any source of artificial heat, sheltered from the <lirect rays of the sun, and from the rain and spray, but freely exposed to tlie circulation of the air; the door should be kept closed excei>t during the ])roc- ess 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. Tlie wick which serves to carry the water from the cistern to the bulb should consist of a few threads of lampcotton, 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 iU)t dripping.

When the temperature of the air falls to 82° F. the water in the wick freezes, the capillary action is at an end, the bulb in consequence soon becomes (piite dry, and the thermometer no longer shows the temperature of evaporation. At such times the bull) should be thoroughly wetted with ice-col<l water shortly before the time of observation, using for this purpose a caiiiers hair tirusli or feather; by

Fig. 6.

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

25

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 water, the thermometer will act in the same way fts if it had 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.

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

Tempera- ture of the air, dry-		Difference between dry-buJb and wet-bulb reading	s.
bulb ther- mometer.	tv	2°	3°	4°	5°	CO	7°	8°	9°	10°
o	Perrt.	Perct.	Per el.	Per et.	Peret.	Peret.	Peret.	Perct.	Perct.	Perct.
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	86	79	72	65	58	51	45	38	32
48	93	86	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	a5

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 ilifference teing 4°, look in the cohmm heade<l "Temperature of the air" for 60°, and for the figures on the same line in column headed 4°; here 78 will 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 tlie atmosphere is 78 per cent of the total amount that it could <'arry 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 precipi- tated 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.

63. 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 thermome- ter should remain immersed in the water at least three minutes before reading, and the reading should be made with the bulb immersed.

THE LOG BOOK.

64. The Tx)g Book is a record of the ship's cruise, and, as such, an imjjortant accessory in the navi- gation. It should afford all the data from which the position of the ship 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.

65. A convenient form for Tecording the data, which is employed for the log books of United States naval vessels, is shown on page 26; beside the tabulated matter thus arranged, to which one page of the book is devoted, a narrative of the miscellaneous events of the day, written and signed by the proper officers, appears upon the ojiposite jiage.

26

IN8TBUMENTS AND ACCESSORIES IN NAVIGATION.

State of sea by symbols.
1	o S o
is
111
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Reading of patent log.
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S S 2

3^ CG 00 Xi a

6C M tic 2 5

INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

27

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

67. 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 closehauled. The scale, with the estimated velocity of the wind in both statute and nautical miles per hour, is as follows:

		Velocity.	Mean pressure
	Conditions.			in pounds per square
Foroe of wind.	Statute miles per	Nautical miles per
		hotir.	hotir.	foot.
0 Oalm	Full-riwred ship, ail sails set, no headway . Just sufficient to give steerage way Speed of 1 or 2 knot.'i, "full and by "	0 to 3 8 13	0 to 2.6 6.9 11.3	0.03
	0.23
■J.— Light breezo	0.62
3.— Gentle breeze	Speed of 3 or 4 knots, "fuUaud by"	18	15.6	1.2
4.— MtMlerate breeze..	Speed of 5 or 6 knots, "full and by "	23	20.0	1.9
	28	24.3	2.9
6.— Strong breeze	Topgallantsailsoversingle- reefed topsails	34	29.5	4.2
7.— Moderate gale — *.— Fresh gale	40	34.7	5.9
Treble-reefed topsails (or reefed upper-	48	41.6	8.4
	topsails and courses).
9. — Str* »ng gale	Clase-reefedtopsailsandcourses(or lower topsails and courses).	66	48.6	11.5
10.— Whole gale	Close-reefed main topsail and reefed fore- sail (or lower main topsail and reefed foresail).	&5	56.4	15.5
		' 75 90 and over.	65.1 78. 1 and over.	20.6
		29.6

6». When steaming or sailing with any considerable speed, the apparent direction and force of the wind, as determined from a vane, flag, o"r pennant aboard ship, may differ materially froin 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 of two vessels, each steaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The former ve'<8el will be moving with the same velocity as the air and in the same direction; the velocity of the wind relatively to the ship will thus Ije zero; on the vessel an apparent calm will prevail and the pennant will hang up and down. The latter vessel will l)e 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 28 knots an hour, and the direction from which it comes will be NVV. If, therefore, the effect of the the speed of the ship is neglected the wind will te recorded as N\V., 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.

69. We.vther. — To designate the weather a series of symbols devised by the late Admiral Beaufort is employed. The system is as follows:

//. — Clear blue sky. r. — Clouds.

)l. — Drizzling, or light rain. /. — Fog, or foggy weather. g. — (iloomy, or dark, stormy-looking weather. //.—Hail. /. — Lightning. )/(. — Misty weather. 0. — Overcast.

p. — Passing showers of rain.

q. — Squally weather.

r. — Rainy weather, or continuous rain.

s. — Snow, or snowv weather.

/.—Thunder. u. — Ugly appearances, or threatening weather.

r. — Visibility of distant objects. «'. — Wet, or heavy dew.

z. — Hazv.

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

?0. Cloi'ds. — The following are the principal forms of clouds, named in the order of the altitude above the earth at which they usually occur, teginning with the most elevated. The symbols by which each is designated follows its name:

1. Cirrus, {(1.). — 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 eflect of perspective, converging toward one or two opposite points of the horizon.

2. Cirro-Stratl's, (Ci.-S.). — A thin, whitish sheet, sometimes completely covering 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 haloa around the sun and moon.

3. CiRRO-CuMULUs, (Oi.-ft*.).— 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 liner flakes. They'often spread themselves out in lines in one or two directions.

28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.

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 coronpo. This form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great.

6. Strato-C'i'mi-lus, (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- (Ximulus is not, as a rule, very thick, and patches of blue sky are often visible through tlie 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 describe<l as Fracto-Nimbus (Fr.-N. ), the " scud " of sailors.

8. Cumulus, {C'ti.). — Wool-pack clouds; thick clouds of which the upper surface is dome-shajjed 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 protuter- ances. 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 superifir 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 Fraeto-Cumulus (i^.-C((. ).

9. CuMULo-NiMBus, ( On. -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 shower* of rain or of snow (occasionally hail or soft hail).

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

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

72. State of Sea. — The state of th^ 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.

6. — Ground swell. S. — Smooth sea.

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

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li

THE COMPASS ERROR. 29

■^

CHAPTER III THE COMPASS ERROR.

<.^ CAUSES OF THE ERROP.

7:1. When two magnets are near enough together to exert a mutual influence, their properties are such an to cause those poles whicli possess similar magnetism to repel, and those which possess magnet- ism of opposite sorts to attract one another.

The earth is an immense natural m^net, having in each hemisphere a pole lying in the neighlx>r-

•>^ ii< i\ of the geographical pole, though not exactly coincident therewith; consequently, when a magnet,

^^^such as that of a compass, is allowed to revolve freely in a horizontal plane, it will so place itself as to

be parallel to the lines fif magnetic force in that plane created l)y the earth's magnetic poles, the

end which we name north pointing to the north, and the south end in the opposite direction. The

north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end

which has o|)j>osite polarity to the earth's north magnetic pole, this latter possessing the same sort of

-Vnagnetism as the so-called south pole of the compass.

74. By reason of tlie fact that the magnetic pole diffefsin position from the geographical pole, the ^t compass needle will not indicate true directions, but each compass point will differ from the corres[)ond-

ing true point by an amount dependent upon the angle between the geographical and the magnetic pole at the position of the observer. The amount of this difference, expressed in angular measure, is the Variation of the Compass (sometimes callefl also the Derlination, though this term is seldom employed by navigatfirs).

The variation not only changes as one travels from point to point on the earth, being different in

different localities, but, as it has been found that the earth's magnetic poles are in constant motion, it

" '«rgoes certain changes from year to year. In taking account of the error it produces, the navigator

. therefore be sure that the variation used is correct not only for the place, but also for the lime

■r consideration. The variation is subject to a small diurnal fluctuation, but this is not a material

conitKeration with the mariner.

75. Besides the error thus produced in the indications of the compass, a further one, due to Loral Attraction, may arise from extraneous influences due to natural magnetic attraction in the Vicinity of the

; vessel. Instances of this are quite common 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 at sea in localities wfiere the mineral substances in the earth itself possess magnetic qualities — as, for example, at certain ])laces in Lake Superior and at others off the coast of Australia. When due to tlie 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, if ever, be determined; if known, it might jiroperly be included with the variation and treated as a part thereof.

76. 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 ship itself. This is known as the Di-riation 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 undergo modification as a vessel proceeds from one geographical locality to another.

APPLYING THE COMPASS ERROR.

77. From what has been explained, it may be seen that there are three methods by which bearings or courses may be expressed: (a) tr>ie, whentheyreferto the angular distance from the earth's geographical meridian; (';) magnetic, when they refer to the angular distance from the earth's magnetic meridian, and must be corrected for variation to be converted into true; and (c) hy compass, when they refer to the angular distance from the north indicated by the compass on a given headmg 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 circum- stances is one of which the navigator must make himself a thorougli master; the various problems of conversion are constantly arising; no course can beset nor liearing plotted without involving the applica- tion of this problem, and a mistJake in its solution may produce serious consequences. The student is therefore ui^ed to give it his most careful attention.

30

THE COMPASS ERROR.

78. 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 icest, ormarlied ~.

Figures 7 and 8 represent, respectively, examples of easterly and westerlj^ errors. In both cases

consider that the circles rep- resent theobserver's horizon, N and S being the correct nortli and south points in each case. If N' and S' repre- sent the corresponding points indicated by a com pass whose needle is deflected by a com- pass 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 com- pass error will be westerly or negative.

Considering ligure 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 {'orrect bearing of north, which is one point to the left; and this rule is general throughout the circle, the corret'ted direction being always to the left of that shown by the compass.

79. Having once satisfied himself that the general rule holds, the navigator may save the necessity of reasoning out in feach 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-righl-east, in such a case, would be the key to all of his solutions. If he had a compass course to change to a corrected one with easterly deviation, he would know that to obtain the result the error must be applied to the right; if it were desired to change a correct course to the one indi- cated by compass, the error being westerly, the converse presents itself— the correct must be to the left— the uncorrected will therefore be to the right; if a correct bearing is to be compared with a com- pass bearing to find the compass error, when the correct is to the right the error is east, or the reverse.

SO. It iiHist be remembered that the word east is equivalent to riyht 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 easterlv 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 .„j.ay— north end up — S. by W. would l)e the point arrived at, and a mistake of two points would be the result. . .

81. In the foregoing explanation reference has been made to " 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 .^ubjei-t in its general bearing without confusion of details.

Actually, as has already been pointed out, directions given may be true, magnetic, or bj; compass. By applying variation to a magnetic bearing we correct it and make it true, by applying 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. Whichever 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 N. 76° K.; variation, 0° W.; required the true bearing. N. 71° E.

A bearing taken by a similar compass is NW. bv W. i W.; variation, i pt. W.; require<l the true bearing. NW. by W. | W. . . , , ,.

A vessel steers S. 27° E. by compass; deviation on that heading, 8° W.; variation in the locality, 12° E.; required the true couree. S. 18° E.

A vessel steers S. bv W. i W.; deviation, i pt. W.; variation, SSW. i W.

It is desired to steer the magnetic course N. 38° W.; deviation, pass. N. 42° W.

The true course between two points is found to be W. ; X. required the compass course. W. | S.

True course to be made, X. 5.5° E.; deviation, 7° E. ; variation, 14° W. compass. N. H2° E.

1 ,,t

4° E.

E. ; required the true course, required the course by coin- variation U pt. E.; no deviation; requirefl the coui'se by

THE COMPASS EKKOR. ' 31

A vessel passing a range whose direction is known to be S. 20° W., magnetic, observes the bearing by compass to be S. 2° K. ; re(|uired the deviation. 22° E.

The sun's observed bearing i)y compass is S. 89° E. ; it is found by calculation to be N. 84° E. (true) ; variation, 8° W. ; required the deviation. 1° E.

FINDING THE COMPASS EBBOB.

82. The variation of the compa.«!J for any given locality is found from the charts. A nautical chart always contains infonnation hom 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.

83. 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 observation 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 thirty-two points. At later swings, esjiecially after correctors have been applied, or in the case of wooden ships, sixteen points will suffice — or, indeed, only eight. In case it is not practicable to make observations on exact compass points, they should be made as near thereto as practicable and platted on the Napier diagram (to' be explained hereafter), whence the deviations on exact points may be found.

84. In swinging ship for deviations the vessel should he on an even keel and all movable masses of iron in the vicinity of the compa.ss secured as for sea. The vessel, upon being placed on any heading,' should be stea<lied there for three to 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 a.ssure 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 anchor, where the action of the tide tends to turn them in azinuith (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.

85. The deviation of all (ompas-ses on the ship may be obtained from the same swing, it teing required to make observations with the 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 point of the standard; applying the deviation, as ascertained, to the hea<ling by standard, gives the magnetic heads, with which the direction of the ship's Iiead 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.

86. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal hearings, by bearings of the sun, by rntigen, and by a distant object.

87. Reciproc.m, Be.\rin<;s. — One observer is stationed on shore with a spare compass placed in a jiosition 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 repre- sents the deviation of the latter.

In determining the deviations of compasses placed on 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 bv a theodolite in which, for convenience, the zero of the horizontal graduated circle may be ternie<l 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 devia- tions, we obtain the correct values.

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

88. Bearings of the Six. — In this method it is required that on each heading a Ijearing 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 exi)laine<l in Chapter XI\', the true bearing of the sun may be ascertained from the known data, and tiiis, compared with the compass tearing, gives the total compass error; deducting from the compass error the variation, there remains tlie deviation. The variation used may l)e 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 meth(xl is important as being the only one available for determining the compass error at sea.

89. Ran<ie.s. — 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 deviations may be obtained, the deviation of each heading being equal to the difference between the compass and the magnetic bearing.

90. Distant Ohiect. — A conspicuous object is selected which must be at a considerable distance from the ship and upon which there should l)e 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 maybe assumed to be the mean of the compass tarings.

32

THE COMPASS ERROK.

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 tliffer 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 .S(K.

91. 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 whict the deviation is determined on that heading, and finally write the deviation itself. When the result of the swing has been worked up another table is constructed showing simply the headings and the corresponding deviations. This is known as tlie DerkUlon 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 navigation of the ship.

92. Let it be assumed that a deviation table has been found and that the values are as follows:

Deviation table.

Ship's head by standard compass.

Devia- tion.

Ship's head by standard compass, j

Devia- tion.

North

N. by E .

NNE....

NE. by N NE

NE. by E

ENE....

E. by N .

- 1 50

- 3 00

- 5 15

- 7 10 -10 15 -13 05 -17 10

1 00 i East -19 55 '■ South

E. by S... -22 00

ESE -23 30

SE. by E .'-24 00 SE -23 30

SE. bvS.. -20 30 SSK. '..... -16 00 S.by E... - 8 50

Ship's head by standard compass.

Devitt-

tiOD.

Ship's head by Devia- standard compass. tion.

0 00 West.

W. by N...

WNAV

NW. bvW.

S.bv W... -flO 20

SSW +17 00

SW. by S.. +21 50 i SW^ +24 30 NW.

SW. bv W . 4-26 20 ' NW. Ijy N .

WSW" +25 00 NNW

W. hv S . . . Lo;; ;{o X. bv AV. . .

+19 30

+17 00 + 13 00

+11 10 + 7 40 -I- 5 05 + 3 00 + ! 00

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 mag- netic heading. But if we are given the magnetic direction in which it is desired to steer and have to find, the corres]ionding 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 te 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 N. 79° W., magnetic.

The deviation corresponding to N. 79° W., per compass, is + 17° 00'. If we apply this to N. 79° W., magnetic, we have S. 84° W. as the compass course. But, consulting the table, it may be seen that the deviation corresponding to S. 84° W., per compass, is -f 21j°, and therefore if we steer that course the magnetic direction will be N. 74J° W., and not N. 79° AV., as desired.

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

Mag. course required . . Try dev. on N. 79° W.,

p. c

FIrxt trial.

. . N. 79° W.

17° E.

. . S. 84° W. 21i°E.

g. course made good N. 74J° W.

Since this assumption carries the course 4J° too far to the right, assume next a deviation on a course 5° farther to the left than the one used here.

Trial comp. course

Dev. on S. 84° W., p. c

Mag. course required . Try dev. on S. 79° W.,

Trial comp. course Dev. on S. 77r W.

p. c

p. c...

Second trinl. N. 79° W. 23i° E.

S. 77J° W. 24° E.

Mag. course made good N. 78 j ° W.

This is as close to the recpiired ccairse as the ship can be steered. It may occur that further trials will be necessarv in some cases.

93. TnE Napier Diaokam. — 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 con- necte<l with compass work it should be clearly understood by the navigator. This device admits of a graphic representation of the table of deviations of the compass V)y means of a curve; besides furnishing a ready means of converting compass into magnetic courses and the reverse, one of its chief merits is tliat if the deviation has been determined on a certain nundier of headings 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 85.

THE COMPASS ERROR.

33

94. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and itraightened into a vertical line; for convenience, it is usually divided into two sections, representing, respectively, the eastern and western semicircles. The vertical line is of a convenient length and divided into thirtv-two equal parts corresponding to the points of the compass, beginning at the top with North and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked.

DEVIATION

WEST

DEVIATION

EAST

Fio. 9.

The vertical line is intersected at each compass point by two lines inclined to it at an angle of 60°, that line which is inclined upward to the right bein^ 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 ««Hpf(ji« courses (as is usually the case with th^. standard compass), measure off on the vertical scale the number of degrees corre.sponding to the deviation and lay it down — to the right if easterly and to the left if westerly — on the doited line passing through the point representing the ship's head; or, if the observation was not made on an even point, then lay it down on a line drawn parallel to the dotted ones through that division of the vertical line which represents the compa.s8 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 points 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.

24972°— 12 3

34

THE COMPASS EBKOR.

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 point are enough to estab- lish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on every point.

the curve shown in the full line on figure 9 corresponds to the table of deviations given in article 92,

From a giren compass course to find the corresponding magnetic course, through the point of the vertical line representing the given compass course, draw a line parallel to the dotted linen 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 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 measured 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 1 ho 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 92 may be solved by the diagram, and the result will be found to accord with the solution previously given.

THE THEORY OF DEVIATION."

95. Features of the Earth's Magnetism. — It has already been stated that the earth is an immense natural 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 undisturbeil 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 mechan- ically arranged to move only in a horizontal plane, it becomes necessary, when investigating the effect of the earth's mag- netism upon them, to resolve the total force into two com- ponents which in the figure are represented by AC and AD. These are known, respectively, as the horizontal and vertical components oi 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 6.

It is clear that the horizontal component will reduce to zero at the magnetic poles, where tlie needle points directly downward, and that it will reach a maximum 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 Vie found from special charts.

96. 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 said to be induced, and the properties of induc- tion 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 te 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 thoroughly will induced magnetism be dissipated when the source of influence is withdrawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted to it ip 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 magnetic qualities under the varying influences to which it is subjected.

97. 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 the position of the metal with reference to the earth's total force, upon its character, and upon the degree of hammering, bending, and twisting that it undergoes.

n 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 remnindcr of this chapter at first and return to it later.

Fig. 10.

THE COMPASS ERROR. 35

An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an angle thereto it -nould 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 ecjually near the poles 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 mag- netism of a permanent character is impressed upon it, which is never entirely lost unless the bar is subjected to causes eijual 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 distri- bution of magnetism will depend upon the horizontal and vertifal 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 inci- dents of construction, and upon the nature of the metal employed.

98. Causes tii.\t Prodcce Deviation. — There are three influences that operate to produce devia- tion; namely, («) siibperm<ment mngnetisiii; (fc) transient magnetism induced in vertical soft iron, and (c) transient magnetism induced in horizontal soft iron. Their effect will be explained.

Subpermanent magnetism is the name given to that magnetic force which originates 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 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 polaritv (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 aetion 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, Ijeing 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. Ita 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 jwles of these forces do not usually lie in the horizontal plane of the compa-ss needle, but as this needle is constrained to act in a horizontal i)lane, 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, when without this plane, deflects the needle, and the amount of such deflection constitutes the deviation.

99. Classes op Deviation. — Investigation has developed the fact that the deviation produced as described is made up of three parts, which are known respectively as semicircular, (juadrantal, and con- stant 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.

too. iSemicircular 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 com- ponent of the earth's force. If we r^ard the effect of these two forces as concentratefl 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 <leviation; now consider that, from this position, the ship's head swings in azi- muth 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 diametrically 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 etjual and opposite effect it is given the name of semicircidar deviation.

\ In figure 9, a curve is depicted which 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.

101. 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 tt; 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 deflec- tion due to a given disturbing force. On the other hand, that part of the semicircular force due to magneti.sm induced in vertical soft iron varies as the earth's vertical force, which is proportional to the

36 THE COMPASS ERROR.

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

... 1 ■ 1 f , . . . sin &

deviation arising troni this cause on change of latitude is „„„ g, or tan 9.

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 pro- duced by subperinanent magnetism varies as ^^, and that due to vertical induction as tan 0. But for

xl

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

102. If we now resume our former assumption, that all the forces tending to produce semicircular deviation are concentrated in a single pole exerting an attracting influence upon the north pole of the compass, we may consider a line to be drawn joining that theoretical pole with the center of the com- pass, then the angle made by this line with the keel line of the vessel, measured from right ahead, around to the right is called the starboard ani;le. From this it follows that the disturbing force producing semicircular deviation may be considered to have the same effect as a single magnet whose center is in the vertical axis of the compass, and whose south pole (attracting to the north pole of the compass) is in the direction given by the starboard angle; if, therefore, a magnet be placed with its center in the ver- tical axis of the compa-ss, its north (or repelling) pole in the direction of the starboard angle, and its distance so regulated that it exerts upon the compass a force equal to that of the ship's combined sub- permanent magnetism and vertical induced magnetism, the disturbing effect of these two forces will be counterbalanced, and, so far as they are concerned, the compass deviations will be corrected, provided that tlie ship does not change her magnetic latitude.

103. It is evident that the force of the single magnet may be resolved into two components — one fore-and-aft, and one athwartship; in this case, instead of being represented by a single magnet with its south pole in the starboard angle, the semicircular 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 respec- tively 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 theconditions that have been de.scrihed. If O be the center of the compass, XX' .. --'* and YY', respectively, the fore-and-aft and athwart- ship lines of the ship, and OS the direction in which the attracting pole of the disturbing force is exerted, then XOS is the starboard angle, usually designated a. Now, if OP be laid off on the line 0.S, represent- ing the amount of the disturbing force according to some convenient scale, then Oh and Oc, respectively, 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 athwartship one when the ship heads north or south by compass, and the longitu- dinal one when the heading is east or west. On any other heading than those named the deviation produced ))y each force will bea fraction of its maximum whose magnitude will depend upon the azimuth of the ship's head. The maximum deviation 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 nega- tive to port. These coefficients are expressed in degrees."

Referring again to figure 11, it will be seen that: or ( what may be shown to be the same thing):

Oc tan a=-^-^,

. sm C.

tan «= . ~|i

sinB

and when the maximum deviations are small, this becomes:

tan o'=vi. B

Since the starboard angle is always measured to the right, it will be seen that, for positive values of B and C, a will be between 0° and 90°; for a negative B and a positive C, between 90° and 180°; for

a 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 also A, D, and E, to be mentioned later, and the eiact coefficients denoted by the corresponding capital letters of the German alphabet. In the practical discussion of the subject here given, the question of the difference need not be entered into.

THE COMPASS ERROB.

37

negative values of both B and C, between 180° and 270°; and for a positive B and negative C, between 270° and 3«0°.

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 previouslygiven(art. 92), Biseoualto -19° 55', or to —19° 30', or to J (—19° 55' —19° 30')= —19° 43'.

The coefficient O 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 —1° 00' or 0° 00', or i (-1° 0O'±0° 00')= -0° sc

105. The value of the subpermanent magnetism remaining practically constant under all condi- tions, it will not alter when the ship changes her latitude; but that due to induction in vertical softiron undergoes a change when, by I'hange of geographical 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 circumstances, it is possible, by solving equations, to determine whateffect each force has in jjroducingthe semicircular deviation; having done which, the subpermanent magnetism can be corrected by permanent magnets after the method previ- ously 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 bar.

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. iluadrantal Deviation is ihaX 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 ath wart- ship 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-soutli 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 athwartship and the fore-and-aft iron having simply exchanged positions) ; and (h) the direction of the deviation produced is opposite in successive quadrants. The action of unsymraetrical soft iron is not quite so readily apparent, but investigation shows that part of its effe<;t is to profluce a deviation which becomes zero at the inter-cardinal points and is of opposite name in successive quadrants. From the fact that deviations of this class change sign every 90° throughout tlie circle, they gain the name of quadratdal deriatturm. One of the curves laid down in the Napier diagram (fig. 11) is that of quadrantal deviations, whence the nature of this disturb- ance of the needle may te 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 maxinuun is regarded as a coefficient, as in the case of semicircular deviations. The coeffi- cient due to symmetrical soft iron is designated as D, ancl is considered positive when it produces easterly <leviations in the quadrant betvveen North and East; the coeflicient of deviations arising from unsymraetrical 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 midship line.

108. D is approxiniately etpial to the mean of the deviations on NE. and SW.; or to the mean of those on SE. and N\V., with sign reversed; or to the mean of those means. In the table of deviations given in article 92, D is equal to J (—7° 10' + 24° 30') = )- 8° 40'; or to J (+23° 30' - 7° 40') = + 7° 55'; or to J ( 4- 8° 40' + 7° 55') = -p 8° 23'. By reason of the nature of the arrangement of iron in a ship, I) is almost invariably positive.

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 i (-1°00'±0°00') =-0°30'; or to i (-f- 19° 55' - 19° .30') =+0° 13'; or tot (~0° 30' J- 0° 13') = - 0° 09'.

109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic latitude; being due to induction in horizontal softiron, the magnetic force exerted to produce it is propor- tional 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.

no. 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 quad- rantal disturbing force, vary directly with the earth's horizontal cdmponent, the compensation once properly made will be effective in all latitudes.

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.

Fig. 12.

38 THE COMPASS ERBOB.

111. Constant Dmation is due to induction in horizontal soft iron unsymmetrically placed about the compass. It has already been explained that one effect of such iron is to produce a quadrantal deviation, represented by the coefficient E; another effect is the constant deviation, so called tjecause 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 represented by a coeffi- cient; this coefficient is designated as A, and is considered plus fpr 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 lieadings, North, East, South, and West, and would then be equal to i (-1° 00'-19° 55'±0° OC+IQ" 30')=-0° 21'; or from all of the 32 headings, when it would equal +0° 16'.

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 con- stant deviation will remain uniform in amount in all latitudes.

No attempt is made to compensate 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 approxi- mate 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 bin- nacle or altering the surrounding iron. The following relation exists between the coefficients and the deviation:

d=A + B sin 2' + C cos 2' -f D sin 22' -f E cos 22',

where d is the deviation, and 2' the ship's heading by compass, measured from compass North.

115. Me.\n Directive Force. — The effect of the disturbing forces is not confined to causing devi- ations; 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 largelv 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.

1 16. 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 inclination from the vertical certain new forces arise, and others previously inoperative become effective. These forces are (a) the vertical component of the subperma- nent magnetism acquired in building; (h) 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 subiiermanent magnetism will vary, on change of latitude, as , 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.

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 opjwsite 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 will next be given.

120. Order of Correction. — The following is the order of steps to he followed in each case. It is assumed that the vessel is on an even keel, that all surrounding masses of iron or steel are in their normal positions, all correctors removed, and that the binnacle is one in which the semicircular deviation is corrected by two sets of permanent magnets at right angles to each other.

1. Place quadrantal correctors by estimate.

2. Correct semicircular deviations.

THE COMPASS ERBOB. 89

3. C!orrect quadrantal deviations.

4. Swing 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 com- ponent of the semicircular force, whose effect is represented by the coefficient C If East or West, the only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is repre- sented 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);

• (i = Bsinz' + Ccosz' + Dsin2y.

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 90° 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 approxi- mate as closely as possible to those that exist when the compensation is completed; therefore the quad- rantal 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 understood 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 semi- circular force, which is to be corrected by permanent 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. VVhen 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 com- ponent 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 com- pletely 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 comjiensation, and 2z' , 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. Deter.min.\tion op Magnetic Headixos. — To determine when the 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:

{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 forone quadrant, and thus find the com- pass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal point, as North, NE., and East, magnetic." Then put the ship succ&ssively 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 com- pass. Variations of this method will suggest them.selves 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 com- pa.ss the headings by the auxiliary may be noted and a curve for the latter constructed, as explained in article 94, and the required headings thua 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 compa.oses; apply to these the variation and obtain the magnetic bearings; record the times and bearings in a convenient tabular form; set the watch accurately for the local apparent time; then -when it is required to steer any given ma^etic course, set that jwint 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 Ije altered at intervals to accord with the table of times and bearings.

(c) Construct a 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 cour.se will then be the required one. As an example, suppose that the 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. If on N. 11° W., for example, turn the circle to N. 76° E.; leave the vane

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

40 THE COMPASS EEROK.

nndisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjust- ment may be made accordingly.

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

123. SuMM.\HY OF Ordinary Corrections. — To summarize, the following is the process of correct- ing a compass for a single latitude, where magnets at right angles are employed for compensating the semicircular deviation and where the disturbances 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 complete. 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 N. ends to starboard to correct easterly deviation and to port to correct westerly^and the reverse if heading South. If heading East, enter N. ends forward for easterly and aft fo^fwfesterly deviations, and the reverse if heading West. (Binnacles differ so widely in the methods of cftrrying magnets that details on this point are omitted. It may be said, however, that the magnetic intensity of the correctors may be varied by alterini' either their number or their distance from the compass; generally speaking, several magnets at a distance 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 intereardinal 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.

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

125. To Correct Semicircular Deviation with a Single Magnet. — In certain binnacles provision is made for correcting the semicircular deviation by a single magnet (or series of magnets) in the star- board angle, the magnet tray having motion in azimuth as well as vertically. In this case the process of correcting semicircular deviation is somewhat different from that described for correction by rectangular magnets. Either of the two following methods may be employed :

(a) By computation determine the starboard angle. An approximate method for doing this is given in article 103, and a more exact one may be found in works treating this subject 'mathematically. Head the ship on a cardinal point (magnetic); enter the magnets in the tray and revolve it until their N. ends lie at an angular distance from ahead (measured to the right) equal to the starboard angle; raise or lower the tray until the deviation disappears.

(6) Head the ship on a cardinal point (magnetic), enter the magnets, and turn the tray to an east- and-west position, the N. ends in such direction as will tend to reduce the deviation; raise or lower the tray until the deviation disappears. Alter course 90° and head on an adjacent magnetic cardinal point; observe the amount of deviation that the compass shows; correct half of this by altering the starlioard angle and the other half by raising or lowering the tray. Return to first course, note deviation, and correct one-half in each way, as liefore. Continue the operation, making a series of trials until the deviations disappear on both headings, when the compensation will be correct. This operation may be considerably hastened by finding the first position of the magnets from a rough calculation of the starboard angle (art. 103).

126. 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 azi- muth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly rolling.

127. 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 equator. 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 induc- tion disappears and that the whole of the existing semicircular deviation arises from subpermanent magnetism. If, then, when 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.

THE COMPA88 ERROB. • 41

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 tompass or directly abaft it, disregarding the effect of components to starboard or port. It is tnerefore 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.

128. When it is not possible to correct the compass at the magnetic equator there is no ready practical method by which the Flinders bar may be placed; the operation will then depend entirely upon computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work the details of procedure will not be gone into; the general principles involved are indicated, and students seeking more must consult t1i%, 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 sub- permanent factor varying as ti and of a vertical induction factor varying as tan (I. If we indicate by the subscripts , and ,., respectively, the parts due to each force, we may write the equations of the coefficients:

B=B, X jj + B, X tan 8; and

0 = C,Xh + 0, X tanO.

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

Bi = B,Xg- + B,.Xtan6„

B, = B, X g-f B, X tan 6.^ ; and

C, = C, X-i + C, Xtane,,

ill

Cj = C. X jj- + C, X tan 6.,.

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

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

129. To CoKRECT Adjustment on C'h.vxge of Latiti-de. — The compensation of quadrantal devia- tion, once properly made, remains effective in all latitudes; but uidess 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 pa-ssage and must expect that the table of residual deviations obtained in the magnetic latitude of compensation will undergo considerable change as that latitude is departed from. The new deviations may l)ecoine so large that it will be found convenient to readjust the semicircular correcting magnets. This process is very simple.

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

When correctors in the starboard angle are used, arrange as before for heading on two adjacent cardinal magnetic courses. Steady on one of these, observe amount of compass error, correct half by changing the starboard angle and half by raising or lowering magnets; steady on the adjacent cardinal point and repeat fhe operation. Continue until adjustment is made on both headings, then swing for residual deviations.

42 PILdTING.

CHAPTER IV.

PILOTING.

130. Definition. — Piloting, in the sense given tiie word by modern and popular usage, is tiie art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to navigation are available for fixing the position, and where thedepth of wateraud 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.

131. Requisites. — As requisites to successful piloting, the navigator should be provided with the best available chart of the locality to be traversed, together with the sailing directions and descrip- tions of aids to navigation; and all of these should be corrected for the latest information, published in notices to mariners or otherwise, that bear upon the locality. The vessel should be equipped with the usual instrumentsemployed in navigation. The deep-sea sounding-machine, if provided, should be ready for use when there is a chance that it may be needed. The lead lines should be correctly marked, and a.s shoal water is entered one or two men should be stationed to sound. The index errors of the sextants should be known, and, above all, there should be at hand a table showing correctly the deviation of the compass on each heading.

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

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

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

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

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

obtain the true bearing, or deviation only to obtain the magnetic; if

/'y observed by pelorus, that instrument sliould be set for the true or mag-

(Va netic heading, according as one or the other sort of reading is required,

jf^ and no further correction will be necessary. Draw on the chart, by

v' ( means of the parallel rulers, lines which shall pass through the resjjec-

y' \ tive objects in the direction that each was observed to bear. As the

jT \ 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

•^/ \ c both conditions.

— yKr i"* ^^ figure 1.3, if A and B are the objects and OA and OB the lines

y^ \^ j passing through them in the observed directions, the ship's position

/ \^ 1 will be at O, their intersection.

\^ 1 135. If it be possible to avoid it, objects should not be selected

\^ \ for a cross bearing which subtend an angle at the ship of less than 30°

N^ or more than 150°, as, when the lines of bearing approach parallelism,

p^B a small error in an observed bearing gives a large error in the result.

V\. For a similar reason objects near the ship should l)e taken in prefer-

^ > ence to those at a distance.

Fig. 13. 1 36. 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 00 of the object C in the figure), the navigator may have a reasonable a.ssurance

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.

PILOTING.

43

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

138. Bearing and Distance op a Known Object. — When only one object is available, the ship's position may be found by observing its bearing and distance. Follow the preceding method in the mat- ters of taking, correcting', and plotting the bearing; then, on this line, lav off the distance from the object, which will give the point occupied by the observer. In figure 14, if A represents the object and AO the bearing and distance, the position sought will Tie at O.

139. It is not ordinarily easy to find directly the distance of an object at sea. The most accurate method is when its height 'is known and it subtends a fair-sized angle from the ship, in which case the angle may be measured by a sextant," and the distance computed or taken from a table. Table 3.3 of this work gives distances up to 5 miles, corresponding to various heights and angles. Captain Lecky's "Danger Angle and Offshore Dis- tance Tables" carries the computation much further. The use <5f this method at great distances must not be too closely relied upon, as small errors, such a.s those due to refraction, may throw •out the results to a material extent; but it affords an excellent approximation, and as this method of fixing positjon is employed only when no other is available the best possible approximation has to suffice.

In measuring vertical angles, strictness requires that the observation should l)e so made that the angle at the foot of the object should equal 90° and that the triangle be aright triangle, as OMN, figure 15, where the line OjVl j; truly horizontal, and not as in the triangle O'MN, where the condition is not fulfilled. This error is inai)preciable, however, save at very close dis- tances, when it may be sufficiently corrected by getting down as low as possible on board the vessel, so that the eye is near the water-line. One condition exists, however, where the error is material — that shown in figure 16, where the visible shore-line is at M', a considerable distance from M, the point vertically below the summit. In this case there is nothing to mark M in the observer's eye, and it is essential that all angles be measured from a point close down to the water-line.

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

There is another meth(xl for determining the distance of an object, which is available under certain circumstances. This consists in observing, from a position aloft, the angle between the object and the line of the sea horizon beyond. By reference to Table 34 will be found the distance in yards corresponding to different angles for various heights of the observer from 20 to 120 feet. The method is not accurate beyond moderate distances (the table being limited to 5.000 vards) and is obviously only available for finding the distance of an isolated object, such as an islet, vessel, or target, over which the horizon may be seen. In employing this method the higher the position occupied bv the observer the more precise will be the results.

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

141. When the methods of finding distance by a vertical or a.horizon angle are not available, it must be obtained by such means as exist. Estimate the distance by the appearance; take a sounding, and note where the depth falls upon the line of bearing; at night, if atmospheric conditions are normal, consider that the distance of a light when sighted is equal to its maximum range of visibility, remem- bering that its range is stated for a height of eye of 15 feet; or employ such method as suggests itself under the circumstances, regarding the result, however, as an approximation only.

142. The Bearing op a Known Object and the Angle between two Known Objects. — This method is seldom employed, as the conditions always permit of cross bearings being taken, and the latter is generally considered preferable.

Take a bearing of a known object by compass or pelorus and observe the sextant angle between some two known objects. The line of bearing is plotted as in former methods. In case one of the objects of the observed angle is that whose bearing is taken, the angle is applied, right or left as the case may be, to the bearing, thus giving the direction of the second object, which is plotted from the compass rose and parallel rulers. If the object whose bearing is taken is not one of the objects of the angle, lav off the angle on a three-armed protractor, or piece of tracing paper, and swing it (keeping the legs or lines always over the two objects) until it passes over the line of tearing, which defines the position of the ship; there will, except in special cases, be two points of intersection of the line with the circle thus described, and the navigator must know his position with sufficient closeness to judge which is correct.

143. Two Bearings of a Known Oriect. — This is a most aseful method, which is frequently employed, certain special cases arising thereunder teing particularly easy of application. The process

aThe use of the sextant is explained in Chapter VIII.

44

PILOTING.

is to take a careful bearing and at the same moment read the patent log; then, after running a convenient distance, take a second bearing and again read the log, the difference in readings giving the intervening run; when running at a known speed, the time interval will also afford a means for determining the distance run.

The problem is as follows: In figure 17, given OA, the direction of a known object, A, at the first observation; PA, the direction at the second observation; and OP, the distance traversed between the two; to find AP, the distance at the second observation. Knowing the angle POA, the angular distance of the object from right ahead at the first bearing; OPA, the angular distance from right astern at the second bearing; and OP, the distance run; we have by Plane Trigonometry:

PAO = ]80°-(POA + OPA); and

AP=OP X

sin POA sin PAO'

Fig,

If, as is frequently the case, we desire to know the distance of passing abeamr we have:

AQ = AP X sin OPA.

Tables 5A and 5B give solutions for this problem, the former for intervals of bearing of quarter points, the latter for intervals of two degrees. The first column of each of these tables gives the value of AP, the distance of the ship from the observed object at the time of taking the last bearing, for values of OP equal to unity; that is, for a run between bearings of 1 mile. The .second column gives AQ, the distance of the object when it bears abeam, likewise for a value of OP of 1 mile. When the run between bearings is other than 1 mile, the number taken from the table must be used as a multiplier of that run to give the required distance. Example: A vessel steering north takes a bearing of a light NW. J W.; then runs 4.3 miles, when the bearing is found to be WSW. Required the distance of the light at the time of the second bearing. Difference between course and first bearing, 4J pts. Difference between course and second bearing, 10 pts. Multiplier from first column. Table 5A, 0.88. 4.3 miles X 0.88 = 3.8 miles, distance at second bearing. Example: A vessel on a course S. 52° E. takes the first bearing of an object at S. 26° E., and the second at S. 2° W., 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 colunm, Table 5B, 0.76. 0.8 mile X 0.76 = 0.6 mile, distance of passing abeam. 144. As has been said, there are certain special cases of this problem whei'e 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 tlie first bearing, the distance of the object from the ship at second bearinf; 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° - 2a, and POA = a:

PAO = 180° -{POA + APO), = 180° —(a: + 180° — 2a:), = a.

Or, since tli« angles at O and at 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 bow.

145. 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.

146. AVhen the first bearing is 263° from ahead, and the second 45°, the -pjj, -j^g distance at which the object idll be passed abeam yfill eqna.1 the run between bear- ings; this may be proved by computation or by reference to the tables and is a

very convenient fact to remember, as it shows the navigator at once, if about to pass a point, how wide a berth he is going to give the offiving dangers. '

147. There is 0. graphic method of solving this problem that is considered by some more convenient than the use of multipliers. Draw upon the chart the lines OA and PA (fig. 19), passing through the object on the two observed bearings; set the dividers to the distance run, OP; lay down the parallel rulers in a direction parallel to the course and move them toward or away from the observed object until some point is found where the distance between the lines of bearmg is exactly equal to the distance between the points of the dividers; in the figure this occurs when the rulers lie along the line

PILOTING.

45

Fig. 19.

OP, and therefore O represents the position of the ship at the first bearing and P at the second. For any other positions O'P', 0"P", the condition is not fulfilled.

148. Another graphic solution is given by the Distance Finder, devised by Lieut. J. B. Blish, U. S. Navy. This consists of a semicircle whose circumference is graduated in degrees. Two pieces of thread, made to swing about a pin-head at the center, are laid down to represent the lines of bearing, and ease in measuring distances is afforded by series of cross lines similar to those on a piece of profile ^ paper.

149. The method of obtaining position by two bearings of the game object is one of great value, l^y reason of the fact that it is frequently necessary to locate the ship when there is but one land- mark in sight. Careful navigators seldom, if ever, miss the oppor- tunity for a lx)W and beam bearing in passing a light-house or other well-plotted object; it involves little or no trouble, and always gives a feeling of added security, however little the position may be in doulrt. If about to pass an object abreast of which there is a danger — a familiar example of which is wlien a light-house marks a point off which are rocks or shoals — a good assurance of clearance should be obtained before bringing it abeam, either by doubling the angle on the bow, or by using the 26J°— 1.5° liearing; the latter has the advantage over the former if the object is sighted in time to permit of its use, as it may te a.ssumed that the 4h° (bow) bear- ing will always be observed in any event, and this gives the distance abeam directly, saving the necessity of plotting the position at second Ijearing (as obtained by doubling the angle) and then carry- ing it forward.

1 50. It must be rememiaered that, however convenient, the fix obtained by two bearings of the same object will be in error unless the course and distance are correctly estimate<l, the cours-e "made

good" and the distance "over the ground" ijeing required. Difficulty will occur in estimating the exact course when there is bad steering, a cross current, or when a ship is making leeway; errors in the allowed run will arise when she is being set ahead or back by a current or when the logging is inaccurate. To take a not extreme case, a vessel making 10 knots through the water, running against a 2-knot tide, will overestimate her distance one-fifth of its true amount in taking a bow and beam bear- ing if no allowance is made for the tide, or she will underestimate her distance by one-fifth of its apparent amount if going with the same tide. Therefore, if in a current of any sort, due allowance must be made, and it should be remembered that more dei)endence can be placed upon a position fixed by simultaneous liearings or angles, when two or more objects are available, than by two bearings of a single object.

151. Sextant Angles between Three Known Oriects. — This method, involving the solution of the tlirre-point problem, will, it the objects be well chosen, give the most accurate results of any. It is largely eniployed in surveying, because of its precision; and it is especially valuable in navigation, because it is not subject to errors arising from imperfect knowledge of the compass error, improper log- ging, or the effects of current, as are the methods previously described.

Three objects represented on the chart are selected and the angles measured with sextants of known index error tetween the center one and each of the others. Preferably there siiould be two observers and tlie two angles be taken simultaneously, but one observer may first take the angle which is changing more slowly, then take the other, then repeat the first angle, and consider the mean of the first and last observations as the value of the first angle. The position is usually plotted by means of the three-armed protractor, or station-pointer (.see art. 432, Chap. XVII). Set, the right and left angles on the instrument, and then move it over the chart until the three beveled edges pass respectively and simultaneously through the three objects. The center of the instrument will then mark the ship's position, which may i)e pricked on the chart or marked with a pencil point tiirough the center hole. When the three-armed protractor is not at hand, the tracing-paper protractor will prove an excellent substitute, and may in some ca,«es be preferable to it, as, for instance, when the objects angled on are go near tlie olwerver as to be hidden by the circle of the instrument. A graduated circle printed upon tracing paper permits tlie angles Iieing readily laid off, but a plain piece of tracing paper may be u.s'ed and the angles marked by means of a small protractor. The tracing- paper protractor ])ermits the laying down, for simultane- ous trial, of a number of angles, where special accuracy is sought.

1 .52. The three-point problem, by which results are obtained in this method, is: To find a point such that three lines drawn from this point to three given points shall make given angles with each other.

Let A, B, and C, in figure 20, be tiiree fixed objects on shore, and from the ship, at D, suppose the angles CDK and ADB are found equal, respectively, to 40° and 60°.

With the complement of CDB, 50°, draw the lines BE and CE; the point of intersection will be tlie center of a circle, on some point of whose circumference the ship must be. Then, with the complement of the angle ADB, 30°, draw the lines AF and BF, meeting at F, which point will be the center of another circle, on some point of whose circumference the ship must be. Then D, the point of intersection of the circumference of the two circles, will be the position of the ship.

Fig. 20.

46

PILOTING.

The correctness of this solution may be seen as follows: Take the first circle, DBC; in the triangle EEC, the angle at E, the center, equals 180°— 2X50°= 2 (90° -SO'' ), twice the complement of 50°, which is twice the observed angle; now if the angle at the center subtended by the chord BC equals twice the observed angle, then the angle at any point on the circumference subtended by that chord, which equala half the angle at the center, equals the observed angle; so the required condition is fulfilled. Should either of the angles exceed 90°, the excess of the angle over 90° must be laid off on the opposite side of the lines joining the stations.

153. It may be seen that the intersection of the circleG Decomes less sharp as the centers E and F approach each other; and finally that the problem becomes indeterminate when the centers coincide, that is, when the three observed points and the observer's position all fall upon the same circle; the two circles are then identical and there is no intersection; such a case is called a "revolver," because the protractor will revolve around the whole circle, everywhere passing through the observed points. The avoidance of the revolver and the emjiloyment of large angles and short distances form the keys to the selection of favorable objects.

Generally speaking, the observer, in judging which objects are the best to be taken, cau picture in his eye the circle passing through the three points and note whether it comes near to his own position. If it does, he must reject one or more of the objects for another or others. It should be remembered that he must avoid not only the condition where the circle passes exactly through his position (when the problem is wholly indeterminate), but