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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.
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.
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(")
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.)
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.
added to 7 is equal to 15.
lessened by 3 is equal to 6.
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.