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produce apparent contact corresponds to the angular distance which separates them, and is shown on the graduated rim of the sextant. The same arrangement can reflect the sun alongside of the moon or of a star, or bring two headlands together; and, in fact, measure any angle that is within its range. In addition to the much greater accuracy with which reflecting instruments are constructed, they possess the great advantage of bringing the observed and reflected images together. The observer's attention can be concentrated on one, while a motion of his finger brings the other into position. Circles for measuring larger arcs than can be accomplished by the sextant are also constructed, but though useful in experienced hands, they are not in general use.

The text-books of navigation are necessarily uninviting: they bristle with figures, and are ordered in a way which for a time puzzles even expert mathematicians accustomed only to the abstract gymnastics of the schools. We remember once showing to a great mathematician the formula by which seamen work out their longitude. It was entirely strange to him: indeed, it was the first time that he had seen an instance of that which is the distinguishing feature of navigation, viz., high mathematics, disguised in such simple forms that they can be handled easily by weather-beaten old skippers with broad thumb-nails and sou'-wester hats, who would be no more capable of understanding the construction of the formulæ they use than an old woman would be to forge the highly tempered needle with which she sews on her husband's buttons. In navigation, as in astronomy, of which it is the handmaid, materials have been stored up by the patient labour of many hands. First one truth and then another is observed and noted: then comes the philosopher, and reduces the accumulated facts to a system. The mathematician steps in and shows how to utilise observation by deducing the unknown from the known; generation after generation of practical workmen labour to simplify the process, till calculations, which in their first state taxed the full powers of ablest calculators, are reduced to the almost mechanical labour of inspecting tables and following formulæ. It is the glory of navigation that mariners are made heirs of the hoarded wisdom of geometricians; and at last the most abstruse calculations relating to the finding of a ship's place upon the ocean are brought within the compass of ordinary intelligence.

It must always be present to the mariner's mind that the elements of his calculation are in a state of constant change. The degree of accuracy with which he can prick his place on the


chart is exactly proportionate to the success with which he has picked his steps among a crowd of errors, each of which would in its degree vitiate his calculation. He must ascertain the position at a given instant of the true centre of a heavenly body, whirling at high velocity through space, with reference to the true centre of the earth also whirling; an observation true at one instant is from the very conditions of the problem inaccurate a second later; every observation must therefore be reduced to a given instant, and is true only of that instant, and as the theory on which observations are founded is not recondite, success mainly depends upon the painstaking accuracy with which every element of the calculation has been cleared of error; in nautical phrase, 'corrected for the instant of observation.'

But observation of the sun and stars is not the only means used for determining a ship's position. An elaborate series of entries is made in the log which enables the sailor to trace his devious way on the chart with great precision for short intervals of time; yet the errors of dead reckoning constantly increase, and it is now used principally as an auxiliary to bring up the ship's place to the instant of an observation, or to serve as a substitute for observation when clouds obscure the heavens. Dead reckoning was in the time of Anson, and even in that of Nelson, the principal method at the disposal of the mariner. The greatest possible attention was bestowed upon it; young officers kept and wrote out their logs with a care which it would be impossible to excel. We have seen volumes of entries extending over years, in which blot, interlineation, or erasure would be looked for in vain; in which the handwriting resembled copperplate, and every occurrence affecting the ship, from the death of a comrade to the setting of a sail, was described with the utmost minuteness. If the young gentleman' in the cockpit, like other boys of his age, sometimes showed a disposition to 'fudge his day's work,' to copy rather than to work out the final result which each young officer was bound to lay daily on the captain's table, such was not the case with the seniors, who took an anxious pride in their logs, justified in many instances by the care with which they are preserved in old family book-rooms. Nautical astronomy has not superseded, and is not intended to supersede the older method. The two are used in conjunction with each other, and the latitude and longitude by account, as the position determined by dead reckoning is called, enters prominently into the data of all astronomical calculations. Each branch of the science proceeds by its own method, and has its own appliances. Navigation depends upon the compass, the log line, and the chart; to nautical astronomy belong the sextant


and the chronometer. We propose to give a short account of each in order.

point has the patient attention of scientific men been more anxiously directed than to the elimination of errors of the compass. It has long been known that the magnetic needle does not point true north; that the variation differs in amount in different parts of the world, and that it changes slowly from year to year. But it is only of late years when iron may be almost said to have superseded wood in the building of steam-ships and vessels of war, that the full importance of the vagaries of the needle has been felt. Enormous masses of iron, such as are now employed in ship-building, distract the compass-needle, and turn it far from its natural direction. Every compass is affected by variation from the true north, but that is a known quantity, common to all compasses, and equal in all compasses in the same part of the earth; but every compass is also affected by what is called 'local deviation,' owing to the presence of iron in the hull of the ship, and this varies not only in every ship, but in the same ship at different times, and with every position of her head. It will thus be easily seen that to steer by compass, or rather to know what compass course to steer, is not the absolutely simple matter which it appears at first. The sum or difference of variation and local deviation is called 'the error' of the compass, and this error affects not only every point indicated by the compass, but affects each point in a varying degree. Suppose a ship to lie with her head north, her compass is affected with variation 22° W. (that is the ordinary variation in the British Channel); but it is also affected by local deviation owing to iron in the ship's frame, which iron has been so disposed as to deflect the compass (say) 13° E. The error will obviously be the difference between 13° and 22°, that is, 9° W. Therefore when the ship's head is north by compass, her head is in reality N. 9° W. But suppose the ship's head to be turned west, the mass of iron in the ship which deflected the needle 13°, and gave a false north, was then acting directly on the needle and in the direction of its axis. But when the ship's head is west, that same mass of iron is acting on the needle at right angles to its axis, for the needle still points somewhere about north, while the mass of iron has shifted with the ship's head to the west. The error with the ship's head at west will therefore be no longer 9°, but something very different. The distracting cause will obviously vary with every position of the ship's head. But there will be two positions, as she swings right round the compass when the distracting cause and the ordinary magnetic attraction coincide.

Ships, before sailing on a voyage, determine the corrections to be applied to their compass-indications by actual observation. The two plans usually employed in port are by simultaneous reciprocal bearings, and by the known magnetic bearing of a distant object. When the method of reciprocal bearings is adopted, two compasses are selected, which accurately agree with each other when neither is acted upon by local attraction. One of them is taken on board the ship and becomes subject to its local attraction; the other is kept on shore. The ship is then swung round so as to bring her head on each of the thirtytwo points of the compass in succession, and thus to subject the compass to the influence, varying with each direction of the ship's head, of local attraction. As the ship turns to each point, a signal is made to the shore, and the difference between the bearings mutually taken between the compass that is subject to the ship's local attraction, and the shore compass which is removed from that influence, is the measure of the local deviation for each position of the ship's head. Suppose the following case. A ship is swinging to adjust her compass by the method of reciprocal bearings. When her head is Ñ.N.E., both the shore compass and her own point to the true magnetic N.; but when she swings with her head either towards the E. or towards the W., the readings of the shore compass and of that on board no longer coincide. The inference is that the iron on board is so distributed that its greatest attractive power is a little on the port side: as the ship turns toward the Ŵ. the iron on board will battle harder and harder with the true magnetic attraction, until, with her head at W.N.W., it will be at right angles to the line of true magnetic attraction, and cause the maximum deviation. Then its influence will begin to decline until, with the ship's head at S.S.W., the two coincide as before. It is therefore possible to construct a curve showing how much local deviation is to be attributed to the ship's compass for each position of the ship's head, and from this curve to make a table showing the real magnetic significance of each indication of the compass.

Various graphic methods have been devised for this purpose. That most generally used, at any rate in the merchant service, is the plan invented by Mr. Napier. It is very ingenious; it requires no calculation, and only a moderate degree of neat-handedness. 'Napier's diagram' consists of a vertical line of convenient length, say 18 inches, which may be considered as representing the edge of the compass-card cut and straightened out. It is divided into 360° to form a scale for measurement, and is also marked off into thirty-two equal parts representing

representing the points of the compass, commencing at the top with north. The vertical line is intersected at each of the thirty-two points by two cross lines; one inclined to the right, and one to the left at an angle of 60°. The lines inclined to the right are plain, those to the left dotted; thus a series of equilateral triangles is formed, and each triangle has the vertical line as the base, and one leg plain and the other dotted. To leave the vertical for any given distance by a plain line and return to it by a dotted line, is the same thing as marking the length of one of the legs on the vertical. When the ship is swung, her observations for deviation are laid down upon the diagram, by taking from the scale of degrees the amount of deviation at each point, and marking it with a cross; easterly deviations being laid down to the right of the vertical line, westerly to the left. A curve drawn through all the crosses with a pencil shows graphically the curve of deviations. To obtain the true magnetic significance of any compass indication from the diagram, mark the compass indication on the vertical line, and thence follow a dotted line till it strikes the curve. Thence return to the vertical by a plain line, and the point arrived at on the vertical is the true magnetic equivalent of the compass indication.

The rules for using this ingenious diagram have been versified, and afford a convenient memoria technica to many unhappy mariners, who would otherwise be greatly puzzled in their application:

'From compass course, magnetic course to gain,

Depart by dotted and return by plain;

But if you wish to steer a course allotted,

Take plain from chart, and keep her head on dotted.'

If the true magnetic bearing of some distant object be known, the shore compass may be dispensed with; the divergence of the ship's compass from the truth as she swings to each point in succession is the measure of the local attraction. The curve of deviations can then be constructed as before. Other methods of correction, depending upon astronomical observations, are available for use at sea, and are referred to further on.

In old days the distance run by a ship was estimated by throwing overboard a piece of wood attached to a line, and watching how much line ran off the reel while the sands in a quarter-minute glass ran out. Then the rate of the ship, in nautical miles per hour, bore the same proportion to an hour as the length of line run out, to a quarter of a minute; but of late years the actual distance gone through the water is given by Vol. 141.-No. 281. Massey's


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