If a 14 sec. glass be employed, the number of knots read from a log-line constructed with knots of 47.3 ft. each must be doubled.

The log-line is marked with a piece of bunting at the end of the stray line, which should be 12 fathoms long.

One knot at every half knot.

A piece of leather at the first knot.

Two knots at two knots.

Three knots at three knots, and so on.

The log-line should be wetted before being marked, and the lengths of each knot frequently measured to insure the constant correctness of the logline; it is wound on a reel, from which it can be readily paid out without checks. The tenths of a knot can be easily reckoned by hand, when the log is hauled in.

Decimals, Angles, and the Shape of the Earth. There are three points that I will now endeavour shortly to explain, and although it is not necessary that you should at once master the third, it will assist you in understanding the subject of this book, whenever you can do so; they are, 1stly, decimals; 2ndly, angles, and 3rdly, the shape of the earth.

Firstly, Decimals.—I said above that a sea-mile is often divided into tenths, called cables, just as a dollar is divided into 10 dimes, or 10 cent pieces, or a dime into 10 cents. Now 5 miles is written in decimals 5.6 miles, and the dot between the 5 and 6 is called the decimal point.

In adding or subtracting numbers thus written, which are called decimals, always place the decimal points immediately beneath one another, and if there is no figure after the you can always supply ciphers or O's to the right of the point, without altering its value; thus in the last example of subtraction a cipher is added after 14.

In multiplying decimals, multiply as if there were no decimal points, and in the result point off from the right as many decimals as there are in the two numbers multiplied together.

In dividing decimals proceed as with common numbers, and in the result see that there are as many decimals in the quotient and the divisor together, as there are in the dividend.

Secondly, Angles.-The inclination towards one another of two lines which meet is called the angle between them (see Fig. 1, on p. 8).

Thus A OQ is the angle made by the lines A O, QO. In naming an angle, three letters are used, the middle letter being always the one which stands as the point where the two lines meet, and the other two letters being such as stand on some part of each of the lines forming the angle. Thus the angle formed by the two lines A O and QO is called the angle A O Q, or the angle QOA. It must not be called the angle O AQ or the angle A QO. In the accompanying figure let O be the centre of a circle QANES; OA, the radius; EQ, NS diameters; NESQA the circumference of the circle. This circumference is divided into 4 equal parts called "quadrants," by the lines

NS, EQ, each quadrant being subdivided into 90 equal parts called "degrees." Each of the angles Q ON, NO E, EOS, SOQ is called a right angle, and is said to be 90°, also N O is said to be perpendicular to EQ. The angle A O Q is said to be 24° 30′, because AQ, the part of the circumference between A and Q, contains 24 of the 90 equal parts into which the quadrant QA N is

divided. A Q is called an arc of a circle subtending the angle A OQ of 24° 30'. You will now remember that the measurements of latitude and longitude are marked as if they were angles. This is really the case, for both latitude and longitude are arcs of circles, and measure the angles those arcs subtend or are opposite to, at the centre of the earth. This is sometimes called "Angular Measurement."

Thirdly, the Shape of the Earth.-The shape of the earth is like a ball or sphere, only it is slightly flattened at each pole like an orange. In the accompanying figure of an orange therefore please suppose the point N where the stalk is broken off to represent the North Pole, and the other end of the stalk (or core as it is called inside the orange) S, to represent the South Pole.

Let O be the centre of the orange, and represent the centre of the earth, then NOS the core of the orange will represent the axis of the earth, the North end of which always points towards the Pole Star.

Let ER Q be the equator, or such a circle as you would obtain by cutting the orange right across the core into two halves. The edge of either of the halves thus obtained may be considered a great circle, because the centre of the orange is the centre of the circle formed by these edges. Or if you cut the orange in any direction into two equal halves you must cut through the centre of the orange, and obtain a great circle. If, however, you divide the orange into two unequal portions you will not cut through the centre of the orange, and you will obtain at the edges two circles, which in such case are called

small circles, because they are always less than a great circle of the same orange or sphere.

Let NGRS be part of a great circle passing through Greenwich, and the North and South Poles, also let NPT be part of another great circle passing through the North Pole, and any place P on the earth. Join TO and OR. Then NGRS is the meridian of Greenwich, NPT is the meridian of the place P, and the longitude of P west of Greenwich, is measured by the arc TR of the equator subtending the angle TOR at the centre of the earth. Let us suppose the angle TOR to be 15° 6' 16". Then P is said

to be in long. 15° 6' 16" W. Join PO and GO. Then the angle POT, or the arc of the meridian T P, is the latitude of P, and being on the north side of the equator is called N. Let us suppose POT to be equal 51° 28′ 36′′, then P is said to be in lat. 51° 28′ 36′′ N. This is also the lat. of Greenwich Observatory, so that TP and R G are equal.

B

Fig. 3.

G

Construction of Mercator's Charts illustrated.-Now peel off the skin of part of your orange lying between two meridians as T R G P, and let us see what is required to make this into a Mercator's Chart of that part of the earth. Your first difficulty will be that it won't lie down flat as a chart does, and in order to make it do so you will find that you want to stretch P G so as to make it equal to T R, or what is the same thing, you want to make the meridian T P parallel to the meridian R G, or generally, to make the meridians parallel, as you will remember they always are in Mercator's Charts. Let us suppose that you can do this, and that P' G' (read P dash, G dash), see Fig. 3, is made to equal T R by stretching P G sideways, or East and West. You will see now, however, that everything marked upon your peel, or chart as we will call it, is all stretched sideways, and is out of proportion. You require, therefore, to partly restore the proportion by stretching your chart T P′ G′ R in a Northerly direction, just in the same degree as you stretched it East and West; let us therefore stretch T P' to P", and R G' to G", so that P" T and G" R are respectively in the same proportion to P' T and G' R, as P'G' is to PG. This represents what is done in the construction of a Mercator's Chart. Now I hope you will in time be able to discover some clue to the real meaning of lines of Latitude and Longitude upon your chart, and to understand that each of these lines represents part of a circle.

T

If you can refer to a good Atlas with maps of the world showing it in two hemispheres, and also on Mercator's projection, carefully compare one with the other and it will help you to understand Mercator's system.

Rhumb Line.-I may here tell you that the curved line A B C drawn on