302. Construction of the Diagram.-In this method the diagram consists of a central or vertical line of convenient length-say 18 incheswhich may be considered as representing the margin of the compass card cut at the north point, and straightened and extended in the following way:

N

E

W

N

This line, which may be taken to represent no deviation, is divided into 32 equal parts, representing the 32 points of the compass, commencing at the top with North, and ranging in the order of N. by E., N.N.E., &c., and ending with North at the bottom. The central line is then intersected at each of the 32 points by two straight lines, one a plain line and the other a dotted line. The plain and dotted lines make an angle of 60° with the central line and with each other, and with the parts of the central line intersected form a set of equilateral triangles, and so converting the diagram into a simple addition and subtraction table. On the right side of the central line the dotted lines incline downwards, and the plain lines upwards. The reverse is the case on the left. In other words the central line is intersected at the angle of 60° by dotted lines drawn upwards from right to left, and at the same angle downward from right to left by plain lines. The central line is further divided into 360 equal parts, representing degrees, and these divisions are numbered from o° at the top to 360° at the bottom. They are also numbered, according to the usual mode of dividing the compass card, from o° at North and South, up to 90° at East and West. This division of the central line into degrees serves also as a scale by which the deviations are laid off.

It is very important to remember that the plain lines always represent Magnetic Courses, and the dotted lines Compass Courses.

303. Requisite Observations to be made.—The least number of observed deviations available for obtaining a complete curve are the deviations on 4 points distributed equally, or nearly so, round the compass; but, if possible, the deviations should be observed on 8 or more points. If the .observations are observed on 4 points only, these should be at or near N.E., S.E., S. W., and N.W., and from these it is possible to form a fairly approximate curve. The points next in importance are North, East, South, and West. If the deviations have been observed at or near the eight principal points, a curve can be drawn which will give the deviation on every point of the compass within very small limits of error.*

304. Cases may also occur in which by the ship swinging round at her anchors in a tide-way or to the wind, or by the aid of a steam-tug, the deviation may be observed on various directions of the ship's head, not being necessarily exact points of the compass; or, similarly, whilst under steam or sail at sea, a number of azimuths of the sun may be observed, and hence the deviation obtained.

The examiation of a collection of curves made from actual observations, as in the report of the Liverpool Compass Committee, &c., will show that there is so much regularity that these interpolated deviations may generally be relied upon, although certain cases, such as the U.S.S. Roanoke (Report of Nautical Academy of Sciences, 1863), the irregularities are considerable.

In these cases the Graphic Method here described furnishes a ready and effectual mode of obtaining a result on which the errors of individual observations are as far as possible compensated and any egregious errors eliminated.

305. Construction of the Curve of Deviations.-Easterly deviations are laid down to the right of the central line, westerly deviations to the left.*

The amount of the deviation is taken from the scale of degrees on the central line; then, if the deviation has been determined with the ship's head on an exact compass point, lay off the amount of the deviation on the dotted line which passes through that point; but if not observed on the exact point, then on a line parallel to the dotted line, the compass course or direction of the ship's head being still taken from the central line, and mark the point so determined with a cross, or dot encircled in ink. Perform the same operation for each observed deviation. Then with a pencil and a light hand draw a flowing curve, passing as nearly as possible through all the crosses, or dots encircled; and when satisfied that the curve is good, draw it in ink. This is the curve of deviations.

If any of the pencil marks be out of the fair curve, it may be assumed that an error has been made in the observation for that point.

NOTE. When the curve alters its form considerably near the North point as in several CURVES, EXAMPLES FOR PRACTICE, it will be advisable to bring the North points of the diagram together in the form of a drum and then draw the curve.

The process will be best understood by explaining the projection corresponding to the observations as given in the following table:

1. The first compass course on which an observation has been made is North, and the observed deviation is 6° 30′ W. With a pair of dividers take from the central line a distance equal to deviation 63°, and from North on the central line lay off the deviation on the dotted line which passes through that point towards the left-the deviation being W.; at the extremity of the distance make a dot or cross.

In Rear Admiral RYDER's plan, the central line is the diagonal of a square and the other lines make angles of 45° with it, and at right-angles to each other and to the sides of the square, which sides are divided into 360°; the top and bottom representing correct magnetic courses, the sides compass courses. By this method the correct magnetic course corresponding to a given compass course, or the compass course corresponding to a given correct magnetic course, is found as by a table of double entry. The two methods, it will be seen, are the same in principle. Mr. NAPIER's will perhaps be found more convenient in construction by the expert; Admiral RYDER's more simple in use by the inexpert.

+ If the table of deviations are given for the correct magnetic courses and not the compass courses or direction of the ship's head, the same process is gone through, except that the deviations are in that case laid off on the plain lines. It is, however, now generally understood that this procedure is contrary to practice and may lead to error,

2. The second compass course on which an observation has been made is N.E., and the observed deviation is 13° 0' W. With dividers take from the central line a distance equal to deviation 13°, and from N.E. on the central line lay it off on the dotted line-to the left-deviation being W.: and the point so determined mark with a cross or dot.

3. The third compass course on which an observation has been made is East, and the observed deviation is 22° 15′ W. Take from central line 2240, and from E. on central line and on the dotted line passing through it, lay off the observed deviation to the left-deviation being W.; and mark the point so determined with a dot or cross.

4. Compass course S.E., observed deviation 23° 30′ W. Take from the central line a distance equal to deviation 231o, and from S.E. on the central line lay off on the dotted line passing through the same point the amount of deviation-to the left-the deviation being W.; make a dot.

5. Compass course South, deviation 5° 30′ E. Measure on the central line a distance equal to deviation 51° and having found compass course South on the central line, lay off the amount of deviation on the dotted line which passes through it towards the right— deviation being E.; and make a dot or cross.

6. Compass course S.W., deviation 28° 35′ E. From the central line take a distance equal to observed deviation 284°, and having found S. W. on the central line, lay off on the dotted line passing through that point the amount of deviation to the right—deviation being E.; make a dot or cross.

7. Compass course West, observed deviation 19° 15′ E. Measure on the central line a distance equal to deviation 1940, and from West lay off on the dotted line passing through that course the amount of deviation towards the right-deviation E.; and make a dot or

cross.

8. Compass course N.W., deviation 3° 0' E. Take from central line a distance equal to 3o, and lay off on the dotted line passing through N.W. the amount of deviation (3°) towards the right-deviation E.; and make a dot.

9. Then, with a pencil and a light hand, draw a flowing curve, passing as nearly as possible through all the crosses or dots, and if satisfied with the curve in pencil, draw it in ink.

NOTE.-The learner should take a pair of dividers and go through the above process on the diagrams here given (see Plate I). He should then take the blank diagram (see Plate II), and make the curve on it.

Ex. 2. Construct a curve of deviations, using for the purpose the following observations :- (See Deviation Curve A in Diagram).

I. With a pair of dividers take from the central line a distance equal to deviation 1o 15', or 12o, and from North on the central line, lay the distance off on the dotted line passing through that point and towards the left-being W.; at the extremity of the distance make a dot or cross.

2. Take from the central line a distance equal to 22}° (22° 30′), and lay it off on the dotted line, from N.E. towards the right—being E,; make a dot or cross,