2o. If the Compass Bearings be of different names:

(a) If some of the Bearings are reckoned from North and the others from South:

Take either set from 180°, and they will all be reckoned from the same point North or South; the name as to East or West remains unaltered; add all the bearings together and divide by 8, the result is the correct magnetic bearing, of the same name as the unaltered bearings.

(b) If some of the Bearings are towards the East and others towards the West:

Find the sum of those which are reckoned towards East; and also the sum of those which are towards the West; then take the less from the greater, and mark the difference of the same name as the greater; the result divided by 8 gives the Correct Magnetic Bearing of the distant object, which is of the same name as the difference.

NOTE. On the form given at the Marine Board Examinations there is not sufficient space to perform the last mentioned addition and division: there is only room to find the first two sums; the rest, however, can be finished in the margin.

3°. To find the Deviation for each of the given Courses. (a) If the Correct Magnetic and Compass bearings are of like names : Take their difference.

(b) If one is reckoned from North and the other from South, first take the Correct Magnetic Bearing from 180°, and the remainder will have the same name as the compass bearing, then take the difference between the Correct Magnetic and Compass Bearings.

(c) If both bearings are from North or both from South, but one is towards East and the other towards West, take their sum:

The difference or sum will be the deviation.

4. To Name the Deviations.-If the Correct Magnetic Bearing is to the right of the Compass Bearing the deviation is East, but if to the left it is West.

EXAMPLE I.

In the following Table give the correct magnetic bearing of the distant object, and thence the Deviation.

NOTE.-The above is the form in which the Table is given at the Local Marine Board Examinations. The Table is printed, excepting the columns of Bearings, which the Examiner fills up in writing. The following is the above example worked :

Here we first add together the eight given bearings of the distant object, making 336°, and divide the sum by 8, giving as the result S. 42° W., the correct magnetic bearing of the distant object.

We next take the difference between the correct magnetic bearing thus obtained and each bearing given in the table; thus, with the ship's head at North, the bearing by compass is S. 41° W., and the difference between this and the correct magnetic bearing S. 42° W. is 1°, and because the correct magnetic bearing is to the right hand of the standard compass bearing the deviation is East. Again, with the ship's head at N.E., the compass bearing is 8. 59° W., and the difference between this and the correct magnetic bearing S. 42° W. is 17o, but now the correct magnetic bearing is to the left of the compass bearing, hence the deviation is West, and so on with the remaining bearings, and the work will stand as follows:

NOTE.-In the above work, the deviations are obtained by subtracting the less bearing from the greater, because they are all of the same name. (See XCIII, 3o and 4o, page 374).

QUESTION 8. LIST B. (See Rule XCII, Problem II, page 372.

From the above table construct a NAPIER'S Curve, and give the courses you would steer by standard compass to make the following courses correct magnetic:

(1.) S.E.

(2.) N.E.E.

(3.) S. 10° W.

(4.) E. N.

To Construct the Curve from the Table.-With a pair of dividers take from the central line 1o, the deviation for ship's head North; and lay it off from North, on the central line along the dotted line passing through the given point, and towards the right—being East; at the extremity of the distance make a dot or cross. Next take 17° from the central line, and with one foot of the dividers on N. E. on the central line, lay off this distance on the dotted line passing through the given point and to the left, because the deviation is West. Proceed in like manner with the deviation 22° W. at East; with 18° W. the deviation at S.E.; and with 4° at W. the deviation at South. The deviation at S. W., West, and N.W. being easterly, must be applied to the right of the central line along the dotted lines proceeding from those points. Now draw with a pencil a curve passing as nearly as possible through the points found, and when satisfied with its uniformity, draw it in ink,

To find the Standard Compass Course.-(1.) Place one foot of a pair of dividers on S.E. on the central line, and the other foot on the point where the plain line extending from S.E. is cut by the curve; then keeping the first foot fixed and lift that on the curve, moving it in a direction parallel to the nearest dotted line, towards the central line; the compass course that makes correct magnetic S.E. is shown on the central line to be S. 29° E., or S.S.E. ‡ E., (easterly).

(2.) Take N.E. E. on the central line, then placing one foot of the dividers on that spot, extend the other foot from this point and parallel to the nearest plain line till it cuts the curve; then keeping the first foot fixed, move the one on the curve parallel to the nearest dotted line and towards the central line; the compass course that makes correct magnetic N.E. E. is shown on the central line to be E. by N. & N.

(3.) Place one foot of the dividers on S. 10° W. on the central line, and extend the other foot parallel to the nearest plain line, and to the right until it meets the curve; then keeping the foot on the central line fixed, move the foot on the curve thence parallel to the nearest dotted line until it arrives at the central line, which shows that the compass course to be steered is S. 9° W., nearly, in order to make S. 10° W. correct magnetic.

(4.) One foot of the dividers being placed on E. N., move the other foot to the left from that spot and parallel to the nearest plain line until it is cut by the curve; from thence, keeping the first foot fixed on the central line, move parallel to the nearest dotted line till the central line is reached; the compass course that makes correct magnetic E. N. is shown on the central line to be S. 72° E.

QUESTION 9. LIST B.

Suppose you steer the following courses by the standard compass, find the correct magnetic courses from the curve drawn :-(See Problem I, Rule XCI, page 371).

(1.) S.S.E. E.

(2.) S. W.

(3.) E. by N. N.

(4.) N. W.

(1.) To find the Correct Magnetic Course. With one foot of the dividers on S.S.E. & E. on the central line, move the other foot on a line to theft and parallel to the nearest dotted line until it cuts the curve; then keeping the first foot fixed, move the foot on the curve from thence parallel to the nearest plain one and towards the central line; the correct magnetic course is at once seen to be S. 451° E.

(2.) Placing one foot of the dividers on S. W. on the central line, move the other foot on a line to the right, parallel to the nearest dotted line and cutting the curve; from thence, keeping the first foot fixed on the central line, move in a direction parallel to the nearest plain line until the central line is reached; the correct magnetic course is thus shown to be S. 10° W.

(3.) Take the point on the central line representing E. by N. & N., place a leg of the dividers on that point and move the other leg in a direction parallel to the dotted lines, and after meeting the curve, return parallel to the plain lines, until the central line is again reached; the correct magnetic course is thus found to be N. 48° E.

(4.) One leg of the dividers being fixed on N. W. found on the central line, move the other leg in a direc ion parallel to the dotted lines till the curve is reached; and from thence returning to the central line in a direction parallel to the plain lines, we find correct magnetic course is North.

QUESTION 10. LIST B.

312. Given the Bearings of two (or more) distant objects by the Standard Compass and also the Azimuth of the Ship's Head: required the correct magnetic bearing of these objects,

RULE XCIV.

1o. Find the Deviation corresponding to the direction of the ship's head, taking it from the Napier's Deviation Curve with a pair of dividers.

2°. Apply the Deviation thus found (keeping the legs of the dividers the same distance apart) to the Bearing of distant object by Standard Compass, thus-Place one leg of the dividers on the part of the central line which represents the Standard Compass Bearing, and lay the other leg on the central line.

Upwards if deviation for ship's head is W.

Downwards if deviation for ship's head is E.

The number of degrees there indicated will be the correct magnetic bearing from N. or S. towards the E. or W.

The following bearings of distant objects have been taken by the Standard Compass as above; with the ship's head as given, find the correct magnetic bearing.

On the central line find the given course, West, and with a pair of dividers measure the distance from the point to where the curve cuts the dotted line proceeding from the course; this distance taken to the central line gives deviation 24° E. for ship's head at West.

We next apply the deviation to East-the bearing of distant object by standard compass -by placing one leg of dividers on central line at East and laying the other leg on the central line downwards (the deviation being East), the number of degrees there indicated; whence the correct magnetic bearing of distant object is S. 66° E.

Again, ship's course S.S.E. is found on the central line; with dividers measure from thence to where the dotted line proceeding from given course is cut by the deviation curve; this distance, taken from the central line, gives deviation 13° W.

The standard compass bearing of distant object taken when ship's head was at S.S.E. is E. by S. S., or S. 76° E., to which apply deviation, found as above, by placing one leg of dividers on S. 76° E. on the central line, and applying the other leg upwards on the central line (deviation being West); the result is the correct magnetic bearing 8, 89° E.

The deviation due to E. & N.—the direction of the ship's head-is found on deviation curve to be 221° W.

Apply this deviation to compass bearing N. W., or N. 8° W., upwards on the central line (deviation being West), which gives correct magnetic bearing of distant object N. 30° W.

N.E. E. is the next given direction of the ship's head, and applied to the central line, the deviation for which on curve is found to be 18° W.

The deviation thus found being applied upwards from W. S., or S. 87° W., gives the correct magnetic bearing of distant object S. 69° W.

EXAMPLE II.

I. In the following Table give the correct magnetic bearing of the distant object, and thence the Deviation :

Ship's Head
by
Standard
Compass.

(Correct Magnetic Bearing of distant object = N. 89° 4′ W.)

In this example the bearings given in the left hand column are reckoned from S. towards W., while the bearings in the right hand column are reckoned from N. towards W.; therefore, before adding up the latter column, each bearing must be subtracted from 180°, and the remainder, in each case, is the bearing reckoned from S. towards W.

Subtracting N. 87°W. from 180°— S. 93°W. which put in the place of N. 87° W.
N. 75 W. 180 S. 105 W.

N. 68 W.

=

180 S. 112 W. N. 72 W. 180

N. 75 W.
N. 68 W.

S. 108 W.

We may, however, proceed as above, viz.:-add up the Bearings reckoned from N. towards W.; and since there are four bearings so reckoned (from N. towards W.); take the sum from 720 (180 X 4); the remainder is the sum of the bearings to be reckoned from 8. towards W. It is evident that to subtract the sum of the four bearings from 720° is the same thing as to subtract each bearing from 180° and to add the remainders.

II. From the above Table construct a NAPIER's curve, and give the courses you would steer by standard compass to make the following courses correct magnetic :—

(3.) E. N.
(3.) N. 60° E.

(4) S.E. 8.
(4.) S. 49° E.

(1.) W. by S. S. (2.) N. E. Answers :-(1.) West. (2.) N. 1° E. NOTE.-For the method of constructing the curve, see No. 305, page 367, and for rule to find standard compass course to steer, see Rule XCII, page 372.

III. Suppose you steer the following courses by standard compass, find the correct magnetic courses from the curve drawn :

(1.) North. (2.) S.S.W. W. (3.) Answers:-(1.) N. 3° E. (2.) 8. 15° W.