274 NAVIGATION same altitudes, but in the inverse order. It is more convenient to take the first set of sights, five or more, in the ordinary manner, that is, leaving the observer free to use the tangent screw and cry stop when he secures the contact. In the afternoon it will be desirable to begin a minute or two before the time for the greatest altitude, and to continue observations till past the lowest altitude of the forenoon. In other words, take one more at each end, the mean of which is likely to correspond nearly with the mean of the forenoon set. If desirable cut off one of the extremes and rectify any small disagreement by simple proportion till the exact altitude is obtained, with the equivalent time. Examine (fig. 21). September 9, 1882. On the Mole of Palermo, 38 8 15" N., 13 22 50" E.( = 53 m 31 S 3), at 10 A.M. apparent time, the chronometer showed 9 h 43 m 15 s - 5 as a mean when the five alti tudes of the sun were taken by the artificial horizon, which gave a mean (after all corrections) of 47 20 22". Precisely the same mean of altitudes was procured in the afternoon when the chronometer showed l h 42 m 51 s 2. The chronometer was supposed to have been 39 m 30 s fast on Greenwich mean time, gaining 1 s "8 daily. This last information is only useful for reducing the equa tion of time and declination ; it gives 9 h 4 m (nearest minute) Greenwich mean time for the first and l h 3 m P.M. for the second sight, or in Greenwich apparent time 10 h -long. 53 m = 9 h 7 m , and 2 h - 53 m = l h 7 m . The declination at apparent noon was 5 15 52" N., decreasing 56" - 7 hourly, which for three hours less seven minutes before noon, gives a correction +2 43" ; for one hour and seven minutes after noon it is - 1 3". The equation at apparent noon was 2 m 46 S 4 (to be subtracted from apparent time), increas ing O s- 85 hourly, which for the above periods gives -2 s- 4 and +l s . The latitude, the reduced declination (marked - because it is on the same side of the equator as the latitude), and the zenith dis tance can now be used as in the calculation with fig. 18 to find the hour angle, or time from apparent noon. For the forenoon it is exactly two hours (10A.M.); for the afternoon, the declination being 3 46" less, the latitude and zenith distance the same as before, the hour angle will be l h 59 m 38 s 8. In order to make the mode of arriving at the error of the chrono meter perfectly clear, the figures will be given in full: Hour angle.. Morning. 2 11 O m s ) Afternoon. Iii59 m 38 s -8 -0 2 47-4 Apparent tim Equation e 10 -0
2
44 1 3 Mean time. .. 10 -0 57 53 16 31 1
56 53 51 31 4 3 Longitude.... Greenwich mean time Chronometer No. 1 showed 9 9 3 43 44 15 7 5 1 ] 3 42 20 51 1 2 Chronometer fast 39 39 31 1 Here there is a perfect agreement in the result ; as the chrono meter was supposed to be gaining 1 s 8 daily, four hours would show an increase of three-tenths. As the altitude and latitude were assumed, they are necessarily faultless ; but in actual practice such a result would rarely occur. The latitude of such a place as Palermo Mole, which was once used as a base from which to take chrono- metrical lines, is undoubted, but the error of one minute in the alti tude would in this example produce a difference of fourteen seconds between the two results ; the mean, however, would be quite correct. There is no ambiguity in this mode of finding the errors of a dozen chronometers and of the sextant (if it has any) at the same time. The two separate sets of logarithms also afford a desirable check upon the work. The principal reason why ship s chronometers are not always rated in this manner is that double the boat-work is required, perhaps from a distance. Various shorter methods have been devised : Norie s is very short, but he uses a special table, with logarithms A and B, with rules respecting the correction being + or - ; Inman s rule is very confusing. Chronometers can be rated with greater ease by means of a transit instrument, but that does not come within the reach of an ordinary navigator ; nor can telescopes be used on board ship to find the longitude by Jupiter s satellites, by occupations, or eclipses of sun or moon in a practical and satisfactory manner. Variation. The variation of the compass has been slightly touched upon when speaking of the most desirable mode of acquir ing the longitude, altitude, and variation by the same daily observa tions. ; In addition to azimuths taken casually with reference to the direction of the ship s head, it is occasionally necessary to take a round of observations of some kind in order to test the change which altered circumstances have produced in the attraction of iron in the ship (compare METEOROLOGY, section on Terrestrial Mag netism). The standard compass by which the ship s course is governed should always be placed in a position which is least affected by the ship s iron, and whence azimuths and all other bearings can be con veniently taken. Whenever an azimuth or amplitude is taken the direction of the ship s head should be noted and logged with the variation. The most simple mode of obtaining the variation is by amplitude observing the bearing of the sun s centre when it is more than the whole diameter above the horizon, as the refraction will be thirty-four minutes, and the dip four or five more. To find the true bearing at sunset or sunrise, add together the log. secant of lat. and log. sine of declination ; the sum will be the log. sine of the amplitude, that is, the number of degrees to the right or left of the east or west point according to the declination. To an observer on the equator the declination is also the bearing. Under the true bearing, however found, place the compass bearing ; the difference will be the variation, which is called east or west accord ing to the position of the north point, with regard to the meridian, or true north. By keeping that point in view mistakes will be avoided ; the same applies to local deviation. The true bearing may also be taken from the amplitude tables. The best mode of ascertaining the amount of local attraction or deviation is by means of a second prismatic compass, placed on shore near the ship, free from guns or other metal. While the ship is slowly hove round by hawsers and stopped at each point, simultaneous bearings are taken, noted, and timed. The difference between the two compasses is attributed to error caused by the ship s influence while her head was on each successive point. If landing cannot be effected, the thing may be done by observing a distant object, or by a succession of azimuths. If the latter case it may be found more convenient to use apparent time only for finding the true bearing about every twenty minutes, and the intermediate bearings by simple proportion. In a time azimuth the apparent time from noon, the co-latitude and co-declination are given to find the angle opposite the latter. As the change in hour angle is the chief thing affecting the azimuth, two or three minutes in declination may be disregarded, and the declination may be treated as constant for two or three hours. Accurate bearings cannot be taken when the sun is more than 25 or 30 above the horizon. Burdwood s azimuth tables are very use ful ; from them the true bearing can be taken out by inspection. When a round of azimuths have been taken for the purpose of ascertaining the deviation of the compass, the variation should also be obtained on shore, or taken from a recent authority, in order to separate the amount due to the ship. It has been found very con venient to gum a diamond of paper about T ths of an inch broad on each point, bearing the number of degrees deviation to be allowed when the ship s head is in that direction, westerly devia tion being marked in blue or black and easterly in red. There is a very simple graphic method, when the deviation has been found upon six or eight scattered points only, of deducing therefrom the amount due to the intermediate points. Draw a central line through the length of a sheet of foolscap as a datum line, and about forty lines at right angles to it, three-tenths of an inch apart, to represent the thirty-two points of a compass, and a few repeated at each end. At the left side of the paper write on those lines the names of the points, commencing at north-west and so through north, east, south, and west to north and north east. Lay off the amount of deviation found on any point upon the corresponding line, taking any convenient scale of equal parts, perhaps one or two tenths of an inch to a degree, according to the amount of deviation ; there is no connexion between this scale and that by which the points are represented. Place the easterly deviation on the right of the datum line and the westerly on the left, till all the points secured have been marked. With a pencil form curves which will pass through those marks, or between them if they are close together and disagree, attributing the difference to errors in observation. Ultimately ink an approved curve and remeasure it, as the corrected scale of deviations. The result of this rough method will be found the same as that by a highly scientific calculation, which would be out of place here. See Admiralty Manual. To insure the true bearing of a distant object it is necessary to take an angle from the sun (or a star) to the object, and find the bearing of the sun as above by amplitude or azimuth. If the former and the distant object be on the horizon, there is nothing to be done but apply the distance from the sun s centre. Also if the sun has considerable altitude and the distance be measured by a theodolite or standard compass arc acting as such, or if the distance measured be 90 no correction is necessary. Otherwise the distance measured by the sextant is one side of a spherical triangle, the sun s zenith distance another, and the distant object to the zenith the third ; and from these the angle at the zenith must be found. The position of a ship when in the vicinity of land is usually determined by cross-bearings ; but if greater accuracy is required, and three objects are visible which are not in the circumference of a circle passing through the ship s position, sextant angles should be taken between them, and laid off on a piece of tracing paper as a substitute for a station-pointer. When the three lines are brought to coincide with the three positions prick the point of junction, winch will be the ship s true position ; or, without tracing paper or station-pointer, lay off the angle from 90 opposite each station towards the other which was observed with it ; those lines will
