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Navigation has been defined as the art of conducting—in the sense of piloting or guiding—a ship from one port to another; and this piloting on-the open ocean, far out of sight of beacons, landmarks and lighthouses, rests on the determination of Direction, Distance, and Relative Position,—combining observation with calculations that are the practical application of Geometry and Astronomy. It is the purpose of this little work to explain the use of the instruments, and the kind of calculations, that are required in Navigation,) as well as the usual methods that are adopted from day to day during a voyage to find what is called the Ship's Place At Sea, which is the basis on which rests the direction of her course towards the port of destination. . . -•

ARITHMETIC OF NAVIGATION.

The first thing to be considered is—Do you understand the Arithmetic ol; Navigation?—if you do not, it can be explained in a few pages, and these the. beginner would do well to carefully read; he who is proficient in this knowledge can pass on to the next subject—" Circles and Angles." .

It is of course taken for granted that you are 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, . '.

Let us begin with the arithmetic of the Circle and. of Time, the parts of which in both are divided sexagesimally, or, in other words, sixty of a less denomination make one of a greater. Two short Tables furnish us with the basis of computation.

(A) Divisions Op The Circle, Or Angular Measure.
60 seconds (") .... make .... 1 minute (')
60 minutes „ .... 1 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 . . . . 1 minute (m.)
60 minutes ..... „ .... 1 hour (h.)

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

B

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Navigation has been defined as the art of conducting—in the sense of piloting or guiding—a ship from one port to another; and this piloting on-the open ocean, far out of sight of beacons, landmarks and lighthouses, rests on the determination of Direction, Distance, and Relative Position,—combining observation with calculations that are the practical application of Geometry and Astronomy. It is the purpose of this little work to explain the use of the instruments, and the kind of calculations, that are required in Navigation,) as well as the usual methods that are adopted from day to day during a voyage: to find what is called the Ship's Place At Sea, which is the basis on which rests the direction of her course towards the port of destination.

ARITHMETIC OF NAVIGATION.

The first thing to be considered is—Do you understand the Arithmetic of Navigation ?—if you do not, it can be explained in a few pages, and these the beginner would do well to carefully read; he who is proficient in this knowledge can pass on to the next subject—" Circles and Angles." (

It is of course taken for granted that you are well np in the four rules of simple arithmetic—addition, subtraction, multiplication, and division—which are as constantly required in Navigation as in daily business transactions.

Let us begin with the arithmetic of the Circle and. of Time, the parts of .which in both are divided sexagesimally, or, in other words, sixty of a less denomination make one of a greater. Two short Tables furnish us with the basis of computation.

(A) Divisions Of The Circle, Or Angular Measure.
60 seconds (") .... make .... 1 minute (')
60 minutes „ .... 1 degree (°)

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

(B) Measurement Of Time.
60 seconds (s.) .... make . . . . 1 minute (m.)
60 minutes ..... „ .... 1 hour (h.)

bnt in this instance the terms are respectively marked h. m. s., so that
6b. 31m. 24s. is to be read 6 hours, 31 minutes, 24 seconds.

B

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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; nor are these signs (which represent values) interchangable, for, as will be presently shown, a second of time has 15 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:—

ea equal to, is the sign of Equality; as 60 minutes =» 1 hoar; that is, 60 minutes are

equal to 1 hour. + pltu (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 j 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 j that is, 9 multiplied

by 12 is equal to 108. •$- divided by, is the sigh of Division; as 84 -j- 12 m 7; that is, 84 divided by 12 is

equal to 7.

Reduction.

One of the earliest processes in our arithmetic will be Reduction, which is the converting or changing a quantity from one denomination to another without altering its absolute value. Take an example from money: we know that 100 shillings make £5; that is, the shillings here indicated have the same value as the pounds; to get the £5 we divide the 100 by 20 (since 20 shillings make £1); for the reverse process we multiply the 5 by 20, which gives us the 100 shillings, hence the following rule:—

General Rule For Reduction.—Consider how many of the less denomination make pne of the greater; then multiply the higher denomination by this. number, if the reduction is to be to a less name; or divide the lower denomination by it, if the reduction be to a higher name.

In Angular Measure and in Time (by Tables p. 1), 60 of the less denomination make one of the greater; hence, as the case requires, we must multiply or divide by 60.

Ex.—In 5h. 48m. lis., how many seconds?

5h. 48m. lis.
60

348 minutes.
60

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20,891 seconds.

Here, 5 multiplied by 60'gives 300," to which add 48, and the result is 348 minutes. Then 348 multiplied by 60 gives 20,880, to which add 11, and the final result is 20,891 seconds.

And similarly for any other quantity. Thus, 18' 42' reduced to ' give 1,122*.

JVote.—Before proceeding to the next rules, it will be sufficient to remark, once for all, that like denominations (as in every other computation of compound quantities) must stand directly under each other; thus, degrees must be placed under degrees, ' under' and * under '; and so with hours, minutes, and seconds.

Here, for simplicity, by striking off the 0 from 60, we must also strike off the unit (last) place from 505; then say 6 into 50 goes 8 times. and 2 over; write down 8, and bring down the 5, placing the 2 before it; the result will be 8° 25'.

And similarly for any other quantity. Thus, 763s. reduced to minutes give 12m. 43s.

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