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 incomplete without reference to the extended use of Lord Kelvin’s sounding machines, either in the original form, where the increased pressure at different depths is recorded by discoloration of chemical tubes, or in the later form known as the “depth recorder,” where similar results are obtained by the automatic record of the position of a piston forced upwards in a tube by this increased pressure. Very satisfactory results can be obtained at speeds of 15 or 16 knots, enabling that great safeguard of navigation in many places, viz. a continuous line of soundings, to be accurately and rapidly obtained. In connexion with this should be mentioned a most ingenious invention known as the “submarine sentry,” which on being set for any desired depth and towed overboard remains at that depth whatever the speed of the ship may be. On striking bottom it at once floats to the surface and rings a warning bell. Such an instrument is of obvious value in ships where, owing to the small number of available men, it is difficult to maintain a continuous line of soundings. To avoid an unnecessarily wide détour in rounding points and shoals, extensive use is now made of both horizontal and vertical danger angles; the former is the angle on the arc of a horizontal circle passing through a point at the required distance from the danger, and through two previously selected, easily recognized, fixed objects. Should circumstances enable the selection to be made of an angle of about 90°, the ship by continually measuring the angle may be steered on the arc of such a circle with great precision, and may even be safely taken through a channel between two dangers. The vertical danger angle enables similar results to be attained by measuring the vertical angle subtended by a known height; but except where the selected object is one whose height is well determined, such as a lighthouse, this method is not so trustworthy as the former.

Before losing sight of land the latitude and longitude of the last well-determined position found by the methods referred to is taken from the coast chart, transferred to the ocean or small scale chart, and considered to be the “departure” or starting-point of the ocean voyage, and from that point the course and distance run by the ship is laid down, being rectified on every occasion when the position is more accurately determined by astronomical means. To obviate the inevitable inaccuracies attending this graphic method and as a corroboration of the ship’s position, the changes of latitude and longitude involved in each alteration of course are daily calculated by plane trigonometry, such calculations being materially abbreviated by the use of the Traverse Table, which is a tabulated expression of the solutions of right-angled plane triangles.

The foregoing modes of keeping account of a ship’s position are technically known as “dead reckoning.” The general introduction of compasses with short needles and slow periods of vibration has done very much towards improving the accuracy with which a ship’s “dead reckoning” is kept. The original model of these was that patented by Lord Kelvin in 1876, and since adopted in the British navy as the standard. In this instrument we have a compass specially designed to enable the principles of compensation or correction proposed by Sir G. B. Airy in 1837 to be accurately carried out, while its slow period of swing renders it in all circumstances extremely steady.

The record of distance run is always obtained from the patent log, usually in the form of the Cherub or Taffrail log introduced in 1878. The common or hand log has ceased to be regarded as anything but the very roughest of guides, and the patent log in its original form, in which it recorded the revolutions of a small screw towed by the ship, does not give satisfactory results at great speeds, nor can anything more favourable be said of those forms where pressure on known areas is employed. The revolutions of the engines, with due allowance made for the condition of the ship’s bottom, afford now perhaps the best means of estimating speed (see ).

Astronomical observations afford the most accurate means of ascertaining positions at sea, other methods (dead reckoning) being only relied upon when the weather does not admit of the practice of these, though by utilizing twilight and night observations of moon, stars and planets, the navigator in most parts of the world need seldom proceed far without the means of astronomically rectifying his position either in latitude, longitude or both at the same time.

The practical problems involved are precisely those employed at astronomical Observatories, but it is not possible to attain similar accuracy of results, for though the sextant (the instrument always employed at sea in making such observations) is capable of marvellous accuracy, yet, as practically all such observations depend directly upon altitudes measured above the sea horizon, the uncertainty and variability of the true position of this, due to the changing effects of refraction, much affect observations made' at any one time. This error in practice is greatly reduced by methods of combining several observations made at different times and using their mean or average result.

A notable feature of the progress of the art of modern navigation is the greatly increased practice of star navigation, and many of the supposed difficulties of night observations are found to be removed by experience. Determinations of positions at sea by twilight observations, when the brighter stars become visible while the horizon is still well defined, are probably the most accurate means we possess; and the careful navigator, by combining for latitude stars passing north and south of the zenith, and for longitude those near the prime vertical both east and west, can generally depend upon a good result, especially if suitable stars can be found for each pair at about the same altitudes. For these purposes the armillary sphere is extremely useful: this is a small celestial globe on which are depicted the principal stars visible to the naked eye. On elevating the pole to the approximate latitude of the observer, and turning the sphere until the sidereal time is under the fixed meridian, a correct representation of the heavens at the time of observation is obtained; the stars are then easily identified by their bearings and altitudes. This valuable instrument is not merely useful when at twilight, only a few of the brighter stars being visible, the constellations to which they belong are difficult of recognition, but it enables arrangement to be made in advance for such observations as are desired to be taken during the night. By marking in pencil on the globe the positions of the planets in right ascension and declination, the same sphere is also available for their identification. The heavenly bodies commonly observed at sea are: The Sun, Moon, Venus, Mars, Jupiter, Saturn, the Pole star, and the larger (or first magnitude) fixed stars, the positions of all of which in the heavens are given in the Nautical Almanac for fixed epochs at Greenwich, with the requisite data for computing their positions at all other times in all other places.

The chief astronomical observations made at sea are those for ascertaining (1) latitude, (2) time and thence longitude, (3) error of compass, and (4) latitude and longitude simultaneously.

To ascertain latitude by itself altitudes of heavenly bodies are measured above the horizon when they are on or near the meridian and therefore exactly or nearly north or south of the observer; in the case of the sun, of course, this means at or near noon, and in the case of other bodies such local times are previously accurately ascertained by a simple calculation made from the Nautical Almanac or more roughly found from an armillary sphere. The principle involved is the simple one that by subtracting the observed altitude when on the meridian from 90° the distance of the zenith or point overhead north or south of the heavenly body is found; then by combining with this the distance, obtained from the Nautical Almanac, of the body considered north or south of the celestial equator at the same instant, it is found how far the zenith is north or south of the celestial equator, and this is exactly the same as the latitude of the observer since the celestial equator is merely the imaginary extension of that of the earth. Such observations are not necessarily restricted to that which can be taken at the instant when the body observed is on the meridian (meridian altitude); equally accurate and multiplied observations can be made on either or both sides of the meridian if the body is somewhat near it (ex-meridian and circum-meridian altitudes), and a simple calculation or reference to a specially constructed table or graphic curve gives the required result.

Errors arising from uncertainty as to the true position of the horizon are with twilight and night observations largely counteracted by taking the means of results obtained from observations made of heavenly bodies crossing the meridian both north and south of the observer, taken as nearly at the same time as convenient. In northern latitudes the pole star is so near to the pole that