PROB. V. Having the latitude of the station or ship, the day of the month, and an approximate knowledge of the apparent time of sun-rising or setting; to find the sun's amplitude. Let WNE represent the horizon of the station, z its centre the zenith; w and E the east and west points, and WME the equator, S n P ८ T E N M have ST the sun's declination (which may be found from the Nautical Almanac sufficiently near the truth by means of the approximate knowledge of the time of rising or setting) the angle SET, which being measured by the arc MN of the meridian is equal to the colatitude of the station, and the right angle at T; therefore SE, the true amplitude, may be found (art. 60. (e)) by the formula Rad. sin. ST sin. E sin. SE, or sin. SE sin. ST sin. E Now, to find the change of amplitude in consequence of refraction; imagine s' to be the place of the sun when, by refraction, his centre would appear in the horizon; then, refraction taking place in a vertical direction, the apparent place of rising is c, and cs' (the refraction in the horizon) is equal to about 32 minutes of a degree. In the right angled triangle scs', which may be considered as plane, there are known cs', the right angle at c and the angle css' (=the complement of EST, which may be computed (art. 60. (ƒ)) from the formula Rad. cos. SET sin. EST cos. ST, or sin. EST= COS. SET COS. ST therefore (Pl. Trigo. art. 57.) sin. css': sin. cs's (=cos. CSS') :: cs'cs, and hence we obtain cs the correction of the amplitude, which correction must (in the case represented by the diagram) be added to Es, in order to have the apparent amplitude. If the sun had been on the opposite side of the equator, cs must have been subtracted from ES to give the apparent amplitude. 343. On placing the compass so that the alidad may be directed to the sun's centre at the moment of apparent rising, it may be found that ezs (second fig., art. 340.) expresses the apparent amplitude by the compass; if then sZE express the apparent amplitude by computation, the difference Eze will be equal to PZn the variation of the needle. It may be added here that ET (fig. to the Prob.) expresses the number of hours which elapse between the true time of sun-rising and the sixth hour of the morning (apparent time): or, ME being a quadrant, MT expresses the number of hours between the time of sun-rising and apparent noon. The last expression also denotes the hour of sun-setting in apparent time. The value of ET may be found by the formula rad. sin. ET=cotan. SET tan. ST. (art. 62. (e')). If the hour circle Pt be drawn through c, the apparent place of the sun at rising, Tt will express the difference between the apparent, and true time of sun-rising. Let Pt cut the parallel of declination in n; then in the triangle csn, considered as plane, cs having been found in seconds of a degree as above, we have cs cos. Css's n, and in seconds of a degree. sn COS. ST =Tt Ex. May 1. 1844, in latitude 51° 20′ 33′′ N., the sun being supposed to rise about 4 hours A. M.; it is required to find his amplitude, and the true time of rising. The sun's declination at apparent noon The sun's declination at the time of rising log. sin. ST (15° 6′) log. sin. E (38° 39'.27" subt. 15 11 36 N. 5 36 15 6 0N.(=ST) The true amplitude north of east. 15) Hour of sun-rise before VI. A.M. lho. 18'51" 6 Apparent time of true sun-rise 4 41 9 Computation of the corrections for refraction. In the spherical triangle SET, log. cos. SET 9.8925921 log. cos. ST, subtr. 9.9847400 344. About the year 1824, Mr. Barlow of Woolwich discovered a means of correcting partially the attractions exercised on the compass by the iron in a ship. The apparatus for this purpose consists of two thin circular plates of iron about twelve inches diameter, between which is interposed a circular board in order to increase the stiffness without much increasing the weight: the plates are pressed together by screws near their edges, and by a screw at each end of a brass socket passing through the centre. A brass rod about two feet long passes through this socket perpendicularly to the plates, and is inserted at one end into the box, or the stand supporting the compass. The plate is capable of being slided on the rod so as to be placed at any required distance from a vertical line passing through the pivot of the compass. One of the methods put in practice by Mr. Barlow in order to find, on board a ship, the effect of local attraction on a needle, in different directions tending from the compass, was to have the ship moored in a convenient situation with a short cable, and to observe with the compass on board, the several bearings of a terrestrial object, when the head was directed to the different rhumb points of the horizon in succession as the ship was warped round upon its mooring; the terrestrial object being not less than six or seven miles from the ship in order that the parallax arising from the change of her place might not create any sensible error. The local attractions cause the bearings of the object to differ from one another when the head lies in different directions; and, on examining the registered bearings, it will be found that there are two opposite points of the compass at which the bearings are nearly the same; it will be found also that these either coincide with, or differ by 180 degrees from the bearing of the ship, which is supposed to have been observed at the object. Consequently one of these equivalent bearings, or the mean of both, may be considered as the true bearing of the object; and the differences between this true bearing and those which may be observed in the other positions of the ship's head will express the effects of local attractions in the different positions. Instead of this method, the bearings of the sun may be observed by the compass when the ship's head is in different directions; and these may be compared with the sun's azimuth computed from the altitudes observed at the times when the bearings were taken. The line passing through the two opposite points of the compass at which the bearings of the object are the same is called the line of no deviation; and the difference between the bearing of the object and of the ship's head at the times when the equal bearings were observed, is the angle which the line of no deviation in the ship makes with a vertical plane passing through the keel: the position of such line is consequently found. Mr. Barlow observes, however, that in all the ships on which he has made observations the line of no deviation is directly fore and aft. The place on the pedestal of the compass at which the plate must be fixed in order that it may correct the local deviations produced by the iron of the ship is to be found by trial thus:-the compass with its pedestal being on shore, the former must be turned on its vertical axis till the north end of the needle coincides with the north line in the compass box; then eight holes being bored horizontally in the pedestal, towards the vertical axis, at distances from one another equal to one eighth of the circumference and at the distance of about twelve inches below the level of the needle; eight others at the distance of an inch below the former, eight others at an inch lower, and so on; the brass rod carrying the plate is to be inserted in each of these holes to various depths, so that the plate may stand from 12 to eighteen inches from the vertical axis. In all these different positions of the plate the effects of the latter in creating a deviation of the needle must be observed and registered; and it will be found that the deviations observed when the rod was fixed in the positions N. E. and N. W. will be nearly equal to one another; so likewise will be those which are observed when it is in the positions E. and w., and in the positions s. E. and s. w. The like equalities nearly will be found to exist in the deviations observed on board the ship at the corresponding positions with respect to a plane passing through the keel, or rather to a vertical plane passing through the line of no deviation. Taking therefore a mean of the deviations when this line of no deviation was N.E. and N. W., E. and W., S. E. and S. W., there will be found among the different positions of the plate, one, with respect to the distance of the rod vertically below the needle and to the distance of the plate from a vertical line passing through the pivot of the needle or the axis of the compass, which, with like bearings, produces nearly equal deviations. In this position on the pedestal must the plate be fixed, on board, with its axis in the line of no deviation produced towards the stern, in order that the local deviations may be corrected. The Astronomer Royal has given, as a general rule for the application of iron to correct local attractions, that, if a mass of iron be placed opposite an equal mass, both in azimuth and elevation (with respect to the compass), the disturbing effect of one mass is doubled. If one mass be placed opposite the other in azimuth and at the same elevation or depression; or if it be placed in the same azimuth but with an elevation when the other is depressed, and vice versâ, it destroys the disturbing force only in part. And if one mass be placed on the same level as the compass, its effects may be destroyed by placing another mass at the same level but differing in azimuth 90 degrees on either side. It is ascertained that Barlow's plate leaves a part of the disturbing force uncorrected; and, in order to render the correction complete, when the iron-work of a ship is nearly equally diffused above and below a horizontal plane passing through the compass, it would be necessary to have, besides the plate, a mass of iron on the same level as the compass and either on its starboard or larboard side. The situation of this mass should be found by trial, so that the compass may point correctly when the ship's head lies N. E., S. E., S. W., and N. W. from the magnetic meridian. (Phil. Trans. 1839.) 345. The most accurate process, at least on land, for obtaining the time of day, and the error of the watch, is that of taking equal altitudes of the sun before and after noon; since then, the watch being supposed to go regularly during the interval between the times of observing, the observations are independent of refraction and parallax (unless the former should change in that interval) and the index error of the instrument. For this purpose, the index must be fixed on the arc of the sextant a few moments previously to the time when the celestial body is expected to attain the altitude denoted by the index; and the times shown by the watch. when the upper limb, the centre, and the lower limb have |