Ps or z='s N.P.D=(90°+b)=111° 28' 4" 18 ar. co. log. sin 0.03122 1/ = Hour angle in time, or apparent time before noon, 24 3 52 1 2. Ship Admiral at sea, March 5th, 1850, at 10 o'clock, A. M. Observed altitude sun's lower limb, 27° 44 Height of eye above the level sea, 16 feet. Time at Greenwich, by mean of three chronometers 12 41 12° 49° 54' 00" EXTRACTS FROM NAUTICAL ALMANAC. At mean noon. March 6th, o's semidiameter, 16' 7'9; eq. of time, 3. March 12th, at 4 P.M. Astronomical Account. Alt. of the sun's lower limb, Time at Greenwich by mean of chronometers, Lat. of ship at time of obs. To be subtracted from mean time. + The dec. is of course diminishing till the equinox March 21st. At mean noon. March 12th, eq. of time- 9 5914 semidiam. 16' 6"•3* To find the time at Greenwich requires the aid of additional data, besides those furnished by observations made at the place. The Greenwich time may, indeed, be obtained at once, independently of any observations at the place, by means of a chronometer, carefully regulated to Greenwich time, provided it be subject to no irregularities after having been once properly adjusted. A ship furnished with such a timepiece always carries the Greenwich time with her, and the longitude then becomes reduced to the problem of finding the time at the place. EXAMPLE. Time computed by an altitude of the sun, as at p. 288, was Chronometer showed Greenwich time at the instant of observation to be Difference of longitude of the place of observation from 945" 10' 0 50 20 3 5 10 15 46° 17' 30" The same method applies to examples 2 and 3, p. 289. Still, however, as the most perfect contrivance of human art is subject to accident, and the more delicate the machine the more liable is it to disarrangement, from causes which we may not be able to control, it becomes highly desirable, in so important a matter as finding the place of a ship at sea, to be possessed of methods altogether beyond the influence of terrestrial vicissitudes, and such methods the celestial motions alone can supply. The angular motion of the moon in her orbit is more rapid than that any other celestial body, and sufficiently great to render the portion of her path passed over in so short a time as two or three seconds, a measurable quantity even with a small portable instrument (the sextant).f of * In computing the D's semi-diameter and parallax, second differences need not be used, the consequent error being less than 0.1. THE SEXTANT is constructed upon the same principles as the quadrant. It consists of a graduated It is obvious, therefore, that if the distance of the moon's centre from any celestial body, in or near her path, be computed for any Greenwich time, and this distance be found the same as that given by actual observation at any place, then the difference between the time of observing brazen arc of 60°, numbered double, however, for the same reason as in the quadrant, or to 1200, called the limb, upon which moves a vernier attached to one end of an index, the other end of which is at the centre of the arc. Upon the latter, in a direction parallel with it, and perpendicular to the plane of the limb, is a mirror called the index glass, adjustable by three screws to perpendicularity with the plane of the limb. Opposite the index glass, and parallel with its plane when the index is at zero, is another glass, half mirror and half transparent, called the horizon glass. A small telescope parallel to the plane of the limb is placed before the horizon glass, and directed so as to look through the latter. There are three adjustments. 1. To make the index glass perpendicular to the plane of the limb. This is done by moving forward the index to the middle of the limb, then looking with the naked eye into the index glass; if the part of the limb seen by reflection appear in the same plane with the part seen direct, the index glass is perpendicular to the plane of the limb; if not, it must be adjusted. 2. To make the horizon glass perpendicular to the plane of the limb.-The index glass having been adjusted, hold the instrument in a vertical position, and bring tho direct and reflected images of the same object to coincide; if this can be done exactly, no adjustment is required, but if one image appear at the right or left of the other, the horizon glass must be adjusted by a screw or screws attached to it for the purpose. 3. To make the axis of the telescope parallel to the plane of the limb.-Bring the images of two objects which are more than 90° apart, to coincide upon one of the parallel wires in the telescope, and then by turning the instrument in the hand a little, make the objects appear on the other wire. If the coincidence remains, tho position of the telescope is correct; if not, it must be adjusted by the screws of the ring into which the telescope is screwed. N. B. There are usually two telescopes accompanying the sextant, the one an inverting or astronomical telescope, and the other not. There is also a plane tube without glasses, and either of the three may be screwed into the same ring. There are darkening glasses to be used in observing the sun, four near the index glass, and three before the object glass. They are red and green, of different shades. The latter color is particularly good to take off the glare of the moon. The paler one before the horizon glass may sometimes be used with advantage to take off the glare of the horizon below the sun, occasioned by the reflection of that luminary from the small rippling waves. N. B. The parallelism of the surfaces of the darkening glasses should be tested by inverting them, and observing if the coincidence of objects be preserved. When the index stands at zero the direct and reflected images of the same object ought to coincide. If not, there is index error, the amount of which is determined by observing how far the index stands from zero when the direct and reflected images coincide. The best mode of determining the index error is by measuring the diame the phenomenon and the time at Greenwich, when it was predicted to happen, will give the longitude of the place of observation. Now, in the Nautical Almanac the distances of the moon from the sun, and from several of the fixed stars near her path, are given for every three hours of apparent Greenwich time, and for several years to come, and the Greenwich time, corresponding to any intermediate distance, is obtainable by simple proportion; so that by means of the Nautical Almanac we may always determine the time at Greenwich when any distance observed at sea was taken.* (See Nautical Almanac, pp. XIII. to XVIII. inclusive.) The distances inserted in the Nautical Almanac are the true angular distances between the centres of the bodies, the observer being considered as at the centre of the earth, and to the true distance therefore every observed distance must be reduced; it is this reduction which constitutes the trigonometrical difficulties of this problem. And it consists in clearing the lunar distance from the effects of parallax and refraction; how to do this, it is now our business to explain. ter of the sun by moving the index both forward and backward, the limb being graduated a short distance behind the zero for the purpose. Half this difference of the two measures will be the index error. To measure an angle with the sextant, bring the two objects, the line joining which subtends the angle, the one as seen direct, and the other by reflection, to coincide, by holding the instrument so that the plane of the limb passes through them, and moving the index forward; the reading shown by the index will be the angle required. * The proportion would run thus: As the difference between two lunar distances given in the Almanac, the one greater, the other less than that observed with the sextant, is to 3 hours, so is the difference between the distance observed with the sextant corrected for refraction, &c., and one of those in the Alm., to the difference between the time of observation and the time given by the Almanac corresponding to the latter lunar distance. The Nautical Almanac gives the proportional logarithm of the quotient of the first term of the above proportion, divided by the second term which is constant, viz., three hours. If the distance between the moon and a star increased or decreased uniformly, the Greenwich time corresponding to a given distance would be strictly correct; but an inspection of the columns of proportional logarithms in the ephemeris, will show that this is not the case. A correction for second differences, or for the irregularity in the lunar distances, must therefore be applied. At page 602 of the Nautical Almanac for 1850 is given, besides the ordinary rule and an example under it, a full explanation of the method of employing a table contained in the Almanac for computing the correction on account of second differences in finding the Greenwich time. The theory of second differences has been given (Algebra, Art. 235). At the scientific meeting in New Haven, August, 1850, Prof. Chauvenet of the U. S. Naval Academy presented improvements in the formula and tables for lunars, which it is to be hoped will be perfected and published. proper corrections to these latter, we also deduce the true zenith distances Zм, zs, and with these data we are to determine the true distance, мs, by computation. Put d for the apparent distance.* Then in the triangle мzs we have (Art. 82), R being 1, hence, for the determination of D, we have this equation, viz., * In observing d with the sextant, it is the nearest point of the limb of the moon, which is made to coincide with the other heavenly body, and in observing a with the quadrant, it is the limb also which is made to coincide with the horizon; so that d and a must be corrected for the semidiameter of the moon; similar remarks apply to the sun, if he be the other heavenly body. ↑ Observe that A and A' are the complements of zм and zs. |