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CURRENT SAILING

- 306

OBLIQUE SAILING AND TAKING THE DEPARTURE

Taking a Departure by a Single Bearing and Distance, and by Two Bearings, etc.

Table for finding the Distance of an Object by Two Bearings, and the Distance Run

between them

322

Position by the Isosceles Triangle ; Doubling the Bearing ; Distance by the Altitude

of a High Light seen on the Sea Horizon; Tables showing the various cases of

Plane, Parallel, Middle Latitude, and Mercator's Sailing.

CORRECTION OF COURSES

331

Compass Courses and True Courses ; Correcting Courses for Variation, for Deviation,

for Leeway ; Setting Courses; Correcting Bearings ; Error of Compass, etc.

NAPIER'S DIAGRAM

341

THE DAY'S WORK

345

A Ship’s Reckoning; Summary of Rules for Working a Day's Work, with Ex-

amples; Deviation Card.

FINDING THE LATITUDE

363

Rules for the Sun, for a Fixed Star, for a Planet, for the Moon, by a Meridian Altitude

below the Pole; Numerous Examples.

LATITUDE BY THE REDUCTION TO THE MERIDIAN; Ex-Meridian PROBLEM

379

LATITUDE BY MAXIMUM ALTITUDE

391

LATITUDE BY AN ALTITUDE OF THE POLE STAR OUT OF THE MERIDIAN

394

THE CORRECTIONS OF THE COMPASS

399

Variation, Deviation, and Error of the Compass, by an Amplitude; By Time Azi-

muth; By Altitude Azimuths; Rules and Examples.

LONGITUDE BY CHRONOMETER BY SUN'S ALTITUDE

419

For the Time at Ship and Longitude by an Altitude of a Fixed Star, a Planet or the

Moon

SUMNER'S METHOD OF FINDING A Ship's POSITION AT SEA

434

By Sun's Altitudes; Simultaneous Altitudes of Two Celestial Objects; General

Remarks and Observations to be carefully Studied; Abbreviation of Work in

Computing and Projecting; Rules and Examples.

COMPUTATION OF ALTITUDES

450

LATITUDE BY DOUBLE ALTITUDES

454

General Observations; Altitudes of the same Object with the Elapsed Time ; By

the Sun; By a Fixed Star, etc.; Correction of the Latitude for Change of

Declination in the Interval ; To find the Longitude; Examples.

EQUATION OF EQUAL ALTITUDES

472

To find the Error of the Chronometer; Equal Altitudes of the Sun; Equal Altitudes

of a Fixed Star; Examples.

GREAT CIRCLE SAILING

479

Description, Definitions, and Rules, with Various Problems relating to Great Circle

Sailing; Composite Great Circle Sailing ; Method of constructing a Great Circle

Chart.

NEW NAVIGATION

THE COMPASS ADJUSTMENTS

507

DEVIATION OF THE COMPASS, SYLLABUS OF EXAMINATION FOR MASTER ORDINARY 520

SYLLABUS OF EXAMINATION FOR EXTRA MASTER IN THE LAWS OF THE DEVIATION OF

THE COMPASS OF AN IRON SHIP AND THE MEANS OF COMPENSATING OR CORRECTING

IT. NUMEROUS EXAMPLES

523

PROOFS OF FORMULÆ, TRIGONOMETRY

570

SPHERICAL TRIGONOMETRY

REQUISITE ELEMENTS FROM THE NAUTICAL ALMANAC

585

NAVIGATION,

INTRODUCTION.

NAVIGATION is the Art which instructs the mariner how to conduct a ship over the wide and trackless ocean, from one port to another, with the greatest safety, and in the shortest time possible.

Navigation may be divided into two branches: viz., Seamanship, comprehending the method of managing a vessel by disposing her sails, rudder, &c., so that she may move in any assigned course or direction the wind or weather will permit; and Navigation Proper (the part we intend to treat of in the present work), which comprebends those methods by which a mariner determines at any time the situation of his vessel, the course she is to be steered, and the distance she has to run, to gain her intended port: hence the requisites for a mariner, in order to understand this branch of the Nautical Art, are a competent knowledge of the figure of the earth, with the various imaginary circles drawn upon it, so as to be able to ascertain the distance and situation of places with respect to each other; the method of finding the ship's latitude and longitude, either by her course and distance run, or by astronomical observations; the use of various instruments, as the log, compass, log-glass, quadrant, sextant, chronometer, &c.; the different allowances necessary to be made in estimating a ship's way, as for leeway, the variation and deviation of the compass, and currents; the method of finding the time of high water at any place; the use of charts, with the method of constructing them : all of which particulars, depending upon mathematical and astronomical principles, we shall endeavour, in the following pages, to explain and illustrate in such a manner as to render every part as clear, concise, and methodical as possible.

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ARITHMETIC OF NAVIGATION The Arithmetic of Navigation can be explained in a few pages, and these the beginner would do well to carefully read: It is, of course, supposed that he is well up in the four rules of simple arithmetic-addition, subtraction, multiplication, and division—which are as constantly required in Navigation as in daily business transactions.

Beginning with the arithmetic of the Circle and of Time, it is to be noted that the parts of both are divided sexagesimally, or, in other words, sixty of a less denomination make one of a greater. Two short TABLES furnish the basis of computation.

(A) DIVISIONS OF THE CIRCLE, OR ANGULAR MEASURE 60 second(")

make

I minute (0) 60 minutes

I degree and these terms are respectively marked so that 5° 51' 28" is to be read 5 degrees, 51 minutes, 28 seconds.

(B) MEASUREMENT OF TIME 60 seconds (s.)

make

I minute (m.) 60 minutes

1 hour (h.) but in this instance the terms are respectively marked h. m. s., so that 6h. 31m. 24s. is to be read 6 hours, 31 minutes, 24 seconds.

It will here be perceived that though the lower denominations in both tables are known by similar names-seconds and minutes—yet have they different signs to distinguish them, and in speaking of them, the former are called seconds and minutes of arc, and the latter, seconds and minutes of time; nor are these signs (which represent values) interchangeable, for, as will (in due course) be shown, a second of time has fifteen times the value of a second of angular measure, and so also as regards the minutes.

This appears to be the proper place for drawing attention to the ARITHMETICAL SIGNS which are most frequently used in computation; they are as follows

equal to, is the sign of Equality; as 60 minutes = 1 hour ; that is,

60 minutes are equal to 1 hour.
+ plus (more), is the sign of Addition; as 8 + 7 = 15; that is, 8

added to 7 is equal to 15.
minus (less) is the sign of Subtraction; as 9 – 3 = 6; that is, 9

lessened by 3 is equal to 6.
x multiplied by, is the sign of Multiplication; as 9 X 12 = 108; that

is, 9 multiplied by 12 is equal to 108. divided by, is the sign of Division; as 84 - 12 = 7; that is, 84

divided by 12 is equal to 7. Divided by is also expressed by placing one number over the other; as if = 7; that is, 84 divided by 12 is equal to 7. In all cases, the upper number is to be divided by the lower number.

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