column as the distance in miles C is off when abeam, and in the difference of latitude column will be found 5 miles, the distance the ship will have to sail from B before bringing it abeam.

40° as course and C' B, 10 miles, in distance column give 6.4 miles in departure column as the distance C' is off when abeam, and in the difference of latitude column will be found 7.7 miles the distance the ship would have to sail from B before bringing it abeam.

VERTICAL AND HORIZONTAL DANGER ANGLES.

Neither of these methods gives a fix, but they are of great service in keeping the navigator outside the danger zone.

Vertical angles.-The heights of lighthouses, headlands, hills, and mountains are to be found in the List of Lighthouses and on charts. If the altitude is measured on and off the arc with a sextant the mean will be the angle required. By taking the angle off and on the arc any index error is eliminated.

The formula is

Dist. height of object x cot. of angle.

=

If the height of the object is in feet the distance will be in feet. To get miles, subtract the log. of 6,080 feet from the log. of the distance in feet. The distance can be found by inspection from "Distance by Vertical Angle" Table in Norie's Tables.

The formula for finding the angle is

Tan. 0 =

height in feet distance in feet'

where the Vertical Angle.

The angle can also be found by inspection from the above Table.

Horizontal Angles. For this method two objects in a horizontal plane are required whose position and distance apart are known. The problem. depends upon the fact that any chord of any arc subtends the same angle from any point on the circumference of the circle (Euclid III. 21). In practice the distance outside of which the danger is to be passed is marked on the chart as at C. A and B are prominent objects on shore marked on the chart; the angle between A and B subtended at C is measured by the compass, protractor, or rulers; in this case it is 34°.

340

The angle is placed on the sextant to the nearest half-degree. As the ship approaches the danger zone, steering towards the east in this case, A will be seen to approach B. When A is upon B the circle is reached at some point on the arc A C B, and a perfect arc of a circle can be maintained by conning the ship so that A is kept upon B; or if steering the opposite way, then by keeping B upon A. It is the finest, safest way of navigating an outlying danger we have, as it takes into account any set of tide or current and it is impossible under any circumstances to touch the danger so long as the data is correct and the objects are not at any time allowed to open. A fix by Station Pointer is explained under Station Pointer. In all cases the greatest accuracy is obtained by using the compass error on the course steered, converting the compass bearings into true bearings and using the meridian and Field's rulers to make the desired angles. You are then independent of the magnetic compass, the small figures of which are mixed with the soundings on the chart, and in a bad light are difficult to read. You are also independent of the alteration due to change in the variation.

E

C

Find the course to steer from A to B to counteract the effect of a current which set N.E. magnetic at the rate of two miles per hour, ship steaming 9 knots, and supposing the ship to have left A at 4 p.m. ; find the time of arrival, the distance steamed, and distance made good.

Join A and B, and from A draw A C of any convenient length in a north-easterly direction; on A C lay off A D equal to 4 miles, the drift in 2 hours; take from the graduated meridian in the compasses 18 miles, the distance the ship steams in 2 hours, and with one foot on D cut the line A B in E and draw E D, then will the direction of E D represent the true or magnetic course to be made good, which turn into a compass course in the usual way.

Draw B F parallel to E D, then will B F represent the distance steamed and A B the distance made good.

The number of miles in B F divided by the speed of the ship will give the time taken on the passage, which, added to 4 p.m., will give the time of arrival.

In this example B F measures 25 miles, and this divided by 9 knots gives 2h. 46 m., which added to 4 p.m. gives 6h. 463m. p.m. as the time of

arrival; the distance made good is 29.3 miles.

If the scale of the chart be small, and the current makes an acute angle

with the line joining the points of departure and destination, it is better to lay off the current for a longer period than it would take to perform the passage, when finding the course to make good, as it gives longer lines to work with, which is a great advantage and gives better results than using short lines.

Making allowance for "set and drift" experienced in the earlier part of the run.

While steaming from A to B it was found that after steaming for 2 hours at the rate of 10 knots the position was found to be at F; from this position find the compass course to steer to counteract the effect of a current similar to that experienced in the earlier part of the run, and give the distance made good in two hours towards B, the ship steaming at the rate of 12 knots.

Draw A B and lay off from A towards B 20 miles, let this point be marked C; from C draw the line C D of any convenient length through F, then will C F represent the set and drift of the current in the earlier part of the run. Now rub out the dotted portion of A B represented by C B, and draw F B, then F B will represent the direct course from F to B; from F, in the direction of D, lay off the current for 2 hours; this will equal F N. From the graduated meridian take 24 miles in the dividers, and with one leg on N cut the line F B in Z with the other leg, then N Z will be the course to make good, which find in the usual way, and F Z will be the distance made good in 2 hours towards B, and N Z measured on the graduated meridian will be the distance steamed.

A

N

F

THE DEVIATION CARD AND ITS USE

The compass on board ship is always more or less affected by the iron and steel in the ship's construction, and in a much less degree by iron in the cargo; so the ship must be swung and a table of deviations made, one with the ship's head by compass, the other with the ship's head magnetic.

The card is used in two ways-to correct bearings, and correct the course. The first case is simple. The deviation is sought for the direction of the ship's head when the bearing was taken, and it is applied in the usual way, as when correcting courses in the Day's Work; but to set a course the process is inverted, since the true or magnetic course is first found from the chart or by calculation. Here again there would be no difficulty if the deviation with ship's head magnetic were used, but as the first way is most commonly employed (when deviation card is used) a small calculation is necessary.

To find the Deviation to apply to the Magnetic Course from Chart in order to find the Compass Course to steer

Take a compass course from the deviation card and apply the deviation opposite to it in the same way as in correcting courses in a day's work. If this should agree with the magnetic course from the chart, that will be the required compass course and also the deviation; if it does not agree with the magnetic course, select a compass course which will give a greater magnetic course and also one that will give a lesser magnetic course, and proceed as in the following examples, using deviation card for compass direction of ship's head.

Ist compass course N. 20° E. Dev. 6 E. Lesser magnetic course N. 26° E. Mag. course from chart N. 36° E. Lesser mag. course N. 26 E.

diff. 10°

41° E.

2nd compass course N. 30° E. Dev. E. Greater magnetic course N. Greater mag. course N. 41° E. Lesser mag. course N. 26 E. diff. 15°

Now, if 15° give a change of deviation of 5°, what will 10° give?

5°

ΙΟ

15°)50(3°
45
5

Dev. II" E.
Dev. 6 E.

diff. 5°

Example 2.-What is the deviation and the course to steer by compass, the magnetic course being north?

Now, if 18° give a difference of 8°, what will 7° give?

Example 3.-Find the deviation and compass course to steer in order to make good a magnetic course of S. 60° W.

Now, if 6° give a change of deviation of 4o, what will 2° give?

Example 4.-What is the deviation and the course to steer by compass in order to make good a magnetic course of S. 17° W. ?

Example 5.-What is the deviation and the course to steer by compass in order to make good a magnetic course of N. 7° W. ?

Mag. course N. 7° W.
7 W.

Deviation as per card

=

Compass course to steer, North.