EXAMPLES FOR PRACTICE.

From the following Compass Courses find the True Courses :-

236. It is often of the utmost importance in various branches of physical science to represent tables of related numbers by means of curve lines, or other figures that show to the eye the nature of the relations or laws expressed, or rather concealed, within the mass of figures constituting the tables. Not only does such a mode of representation at once manifest these laws-almost rendering them palpable-but it further points out in what cases natural laws are not represented, and therefore what the cases are that require a greater amount of observation. These modes of representation are com

monly known as Graphic Methods.

graphic methods" of delineating the deviation have been devised; but the method introduced here is due to J. R. Napier, Esq., F.R.S., and is one peculiarly adapted for this purpose, as it is equally applicable whether the points on which the observations have been made are or are not precisely equidistant. It requires no calculation, and only a moderate degree of neat-handedness.

The method consists of two parts, the diagram and the curve. The diagram is the same for all vessels.

Construction of the Diagram-In this method the diagram consists of a central or vertical line of convenient length-say 18 inches-which 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

S

W

N

This line 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. The vertical line is then intersected at each of the 32 points by two straight lines inclined to it at an angle of 60°: one of these is a plain line inclined to the right; the other a dotted line inclined to the left; that is, on the right side of the vertical line, the dotted lines incline downwards, and the plain lines upwards. The reverse is the case on the left.

The central line is further divided in 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 circumference of the compass-card, from o° at North and South, up to 90° at East and West.

237. 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.

238. 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 similiarly whilst under steam or sail at sea, a number of azimuths of the sun may be observed, and hence the deviation obtained.

* Graphic methods for correcting the ship's course for the Deviation of the Compass have also been designed by Rear Admiral Ryder, Mr. Archibald Smith, F.R.S., and Mr. W. W. Rundell. Admiral Ryder's, which is an extension of Napier's diagram, is published by the Admiralty. Mr. Smith's, known as the straight line method, is published by the Board of Trade, and also furnished to H.M. ships for fleet tactics, for which it is well adapted. Mr. Rundell's is known as the circular method. They are all useful in practice.

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

239. Construction of the Curve of Deviation.-Easterly deviations are laid down to the right of the central line, Westerly deviations to the left. The plain and dotted lines make an angle of 60° with the central line and with each other, and so forming a set of equilateral triangles with the central line; the scale on each is the same, and the amount of the deviation may therefore be 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.

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

I. 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 64°, and from North on the vertical line lay off the deviation on the dotted line which passes through that point towards the left-the deviation being West; 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.

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