NAVIGATION 273 Fig. 20. accompanying calculations). 1 The true distance being over 90 will come out as a small cosine, the change in which (at that angle) is only one unit in the sixth place of figures for seven seconds. It is desirable to avoid angles of this description, which can be done by dropping a perpendicular from Z to the required side ms, which would then be found in segments, by two right-angled spheri cal triangles, as exempli fied with fig. 15. The sum of the two segments, 93 48 36", is ten seconds more than the result obtained directly from the oblique-angled tri angle, and is more likely to be correct. Take the true distance as 93 48 30", and find in the Nautical Almanac an approximate distance, which was 93 40 45" at midnight of the 18th; the difference is 7 45". As the moon was approaching the star the greater distance was before midnight. There are tables of proportional logarithms arranged for finding readily the proportion which three hours or three degrees bear to any part of either, or one part to another. The Nautical Almanac gives after each distance the logarithm due to the amount of change during the next three hours, to four places of figures. As the distance in the present instance is so close to one of the periods, namely midnight, it is necessary to take the mean of the two log arithms before and after, which is 2314. The difference between it and the logarithm for 7 45" = 1 3659 is 11345, =13 m 12 S 5 ; or it may be found by simple proportion. Greenwich mean time was therefore ll h 46 m 47 S 5, and ship mean time as found by the star gh 45m 5is-5 . difference 3 h O m 56 s = 45 14 W. long. There are various graphic methods for finding the correction to the distance due to parallax and refraction, for which space cannot here be spared, as they are at best but approximations, and belong rather to the progress of the art. See Kelly s Spherics. The moon is occasionally used for finding the longitude with the aid of a chronometer, and the method is then similar to that with a planet or star, except that the parallax is so great and the change in right ascension and declination so rapid that the greatest care is necessary in taking out the corrections to the nearest minute of Greenwich time. A star appears to be far preferable for the purpose. The horizon under the moon sometimes assumes a bright sharp appearance which appears tempting ; but caution is necessary, as a bank of cloud below the moon sometimes cuts off the more distant part of the water and presents a false horizon. It should be mentioned that extraordinary refractions some times occur in the daytime which make the horizon appear many minutes of angle higher than it really is. That has been observed in a very remarkable manner in the Baltic. The results of apparently good observations of the sun for the chrono meter were found to be very erroneous, and, a short time after, the island Gottsko Sando was seen presenting a second water- line above what had previously appeared to have been the horizon. On another occasion, April 21, 1854, the low islands and land east of Stockholm were seen from a distance of 12 miles as if inverted on the sky, presenting the appearance of level table land, with dark cliffs, about half a degree above the horizon. On approaching, the upper line gradually disappeared, leaving the low islands covered with fir trees, in their natural state. It was calm at the time, and there was much ice in the Gulf of Bothnia. Fortunately such a state of the atmosphere is not frequent. In the Standard of August 12, 1882, mention is made of an extra ordinary mirage at Alexandria on the previous evening, which caused the forts about Aboukir Bay, distant 15 miles, to be plainly visible. Artificial Horizon. The artificial horizon is a most useful con trivance whereby the effects of mirage or fog are avoided, but unfor tunately it can only be used on solid ground, though many attempts have been made to overcome the effect of the ship s motion. The artificial horizon in common use is composed of a wooden or copper trough 5 or 6 inches long by 3 to 3i inches broad and 1 inch deep. This being placed on a solid stone or hard ground, 100 yards from vehicular traffic, and at least 20 yards from foot passengers, mercury is poured into it from a small-necked bottle, till the bot tom of the trough is covered. In pouring, the neck of the bottle should be kept well down in order to keep back the scum. A metal frame carrying two pieces of plate glass, which are fixed at 45 from 1 The corrected positions of the moon and star in fig. 20, and the dotted line representing the true distance, are not according to scale, as it would be impossible to draw lines fine enough. the horizon, and at right angles to each other, is placed as a screen over the trough and mercury, to keep off the wind. 2 By this ar rangement of the glasses forming the screen, the refractions which a ray of light suffers when passing obliquely through the glasses destroy each other. The observer may be seated close to the hori zon if the sun or star be high, and the whole disk of the sun will be seen ; but with a low altitude the image passes into the box so obliquely that the observer must place himself at a distance and be content with seeing the upper half of the sun s reflected image, to which is brought by the sextant the reflexion of the sun s lower limb. An object with less altitude than 6 or 7 cannot be taken, nor a greater angle than 60. By using suitable shades the two reflected disks will appear so sharp that a very accurate contact may be made, and repeated as desired. Eating Chronometers. Observations in port with the artificial horizon are used to rate chronometers. For this purpose a good watch should be compared with each before leaving the ship, and immediately on returning. The angle measured by the artificial horizon must be halved, after instrumental corrections have been made, and from the altitude thus obtained the mean time at the place can be found just as at sea. But in the present case the longitude is known, and Greenwich mean time will be found from the local mean time by adding or subtracting the longitude in time, according as the latter is W. or E. The difference between it and the time shown by each of the chronometers at the same instant will be their errors, which taken from the last error found and divided by the number of days and fractions of days will give the rate. The errors of chronometers should be ascertained at every port, and every ten days if a ship remains long at one yort. The results being tabulated, the character of a watch during a year can be seen at a glance. Chronometers should be kept in a dry place and equal tempera ture, free from vibration, not too softly padded (for fear that the motion of the balance-wheel should be imparted to the body of the watch) ; and they should not be carried about for any purpose. "Equal altitudes" is a term which signifies a mode of obtaining the time by means of altitudes of the sun or a star taken at each side of the meridian ; it is more accurate in result than any other method, as all errors, personal or instrumental, are neutralized by the repetition, as are also errors in latitude. If the object observed were perfectly stationary with regard to the celestial concave, as a star may be considered to be, one-half the elapsed time added to the time of the first observation would be the time of transit ; and, the difference between the star and sun in right ascension being applied to this, the apparent time at place would be obtained. The motions of the planets vary in amount, and must be treated accord ingly. Jupiter s orbitual motion is so slow that the change during an interval of three or four hours may be disregarded, excepting where great accuracy is required. When equal altitudes of the sun are observed, a considerable correction has usually to be made in consequence of the change of declination during the interval. Thus in the example illustrated by fig. 21, though the zenith distance was pre cisely the same before and after noon, the sun in creased its distance from the pole, and instead of passing by the upper dotted line from S to s it is found to join the curve representing the zenith distance farther south, say at d. During three or four days at each solstice the change in declination is very slight, and may therefore be dis regarded; also when the sun bears nearly east or west the change of a few minutes in declination will not affect the hour angle. If when on the meridian the sun be nearly vertical, and a sea horizon available, an altitude correctly timed ten minutes before noon and ten after will give the time of transit without any calculation. In order to secure a set of observations which shall have their mean exactly on either side the meridian, it is customary to fix the arc of the sextant in positions five or ten minutes apart (according to the motion of the sun, and whether the artificial horizon is used or not) in anticipation of the contact, calling " top " when it takes place, and to repeat a similar operation in the afternoon with the 2 The older form of the artificial horizon, as described in Robertson s Naviga tion (1755), was a box placed on gimbals, containing 1 Ib of quicksilver, with a parallel glass floating on it. It has been attempted to use a top with a polished plane surface rotating horizontally which would remain steady on the principle of the gyroscope asanartifici.il horizon on sTiipboard. An instiument of this kind, the invention of a Mr Serson, was described in 1752 ; and Brunei proposed a similar device to be used on the " Great Eastern." XVII. - 35
