TO FIND THE APPARENT TIME, AND THEREBY REGULATE THE GOING OF THE WATCH. IT tical. T is neceffary here to premife, that there are three divifions of time in ufe, the Civil, the Aftronomical, and the NauThe Civil day begins at mid ight, and ends at the midnight following, being divided into two equal parts of 12 hours each; the fift 12 being marked A. M. that is, ante meridiem, or before noon; the latter 12, P. M. that is, poft meridiem, or afternoon. This divifion of time is moft generally ufed. The Aftronomical Day, fo called from its being used by aftronomers, begins at the noon of the civil day, and continues to the noon of the civil day following (the hours being counted in regular fucceffion from 1 to 24) so that the first part of the aftronomical day is the laft part of the civil day; and the last part of the aftronomical day includes the first part of the civil day following, The Nautical Day, in ufe among ft feamen, is, in one refpect, the direct reverse of the aftronomical day, as it ends when the aftronomical day begins. This it has in common with the civil day, that it is divided into two equal parts of 12 hours each, but the first twelve hours are marked P, M. and the latter 12 A M, An example will beft illuftrate this. By the fea reckoning, Tuesday begins immediately after meridian on Monday; all occurrences happening from Monday noon to midnight, though the first part of Tueflay by the nautical reckoning, are marked as happening at fuch an hour P. M.; and all occurrences happening from midnight to Tuesday noon, are marked as happening at fuch an hour A.M. Thus it appears that the hours in the nautical day are regulated by the civil day, but the nautical day itself begins 12 hours before the civil day. I have been the more explicit on this fubject, as I do not remember to have seen it clearly eluci dated in any book of navigation extant. From what has been faid, it will appear, that the noon of the civil day, the beginning of the aftronomical day, and the end of the nautical day, take place at the fame time, The different kinds of time are two, mean and apparent. Mean time is that fhewn by a clock or watch, regulated to mean folar time. Apparent time is reckoned from the paffage of the fun over the meridian of any place. Mean and apparent time will fometimes differ from each other near a quarter of an hour, owing to the irregularity of the earth in her orbit, or the variation in the inclination of her axis. This difference is cal ed the equation of time, and is contained in page 2, in the Nau. Alm. It is only requifite to take notice of it in determining the longitude by a time keep r, but not in any other nautical obfervation, as the calculations in the Nau. Alm. are adapted to apparent time. To To find the apparent Tim by equal Altitudes of the Sun. Take the fun's altitude at any convenient time in the forenoon, 2, 3, 4, or 5 hours diftant from the meridian; fet down the altitude with the correfponding time by watch exactly; fet the index to the fame altitude, and wait till the fun comes to that altitude in the afternoon; note the time by watch; half the fum of these two times is the apparent time fhewn by the clock or watch, when the fun was on the meridian of that place. But it must here be obferved, that if the change of declination be confiderable during the elapfed time, it must be allowed for, by adding the difference to, or fubtrating it from, the fecond altitude, according as it is increafing or decreafing. Left that an altitude taken in the forenoon, cannot, by the interpofition of the clouds, have a correfponding one in the afternoon, it is advifeable to take feveral in the forenoon, in order to fecure a correfponding one in the afternoon. And if feveral equal altitudes can be taken on both fides of the meridian, it will be beft to find the noons for each pair, and the mean of all the noons thus found, for the true noon. EXAMPLES. May 20, 1806, suppose that at 8 h. 40 m. in the forenoon, and 3 h. 16 m. afternoon, by watch, the fun had equal altitudes, and the going of the watch be required? Add together gives noon per watch True noon Watch flow H. M. 12 March 18, 1806, suppose at 8 h. 11 m. foren. and at 3 h. 58 m. 32f aftern. you have equal altitudes of the fun Required the going of the watch? 'I he diftance of the time from noon when the firft alt. was taken, ois 3 h. 49 m., and the daily de8 40 creafe of decl. at this time is 3 16 23′43′′ 1423", which, multiplied by the number correfponding to 3 h. 49 m. (T. XVII) cut off four figures to the right 11 58 hand, leaves 4537′ 33′′. 2)23 56 12 Hence the index of the quadrant must be fet 7' 33" forward 2 on the arch, to correfpond with the morn. alt, whence the watch will be found 4'45" too fast. Here it is fuppofed that the fhip is lying too, or makes no way through the water; but if fhe is failing to or from the fun, proper allowance must be made for her run during the elapfed time. To find the apparent Time by the Sun's Altitude. Find the fhip's latitude and longitude by account, at the time of obfervation, by carrying the reckoning forward to that time. With a quadrant well adjusted, take the altitude of the fun's lower limb. E e 2 Take the difference between the femi-diameter and dip of the horizon, and add it to the obferved altitude; the fum will be the fun's apparent altitude. Take the difference between the fun's refraction and parallax in altitude, and fubtract it from the apparent altitude; the remainder will be the true altitude of the fun's centre; hence the true zenith diftance. Turn the ship's longitude into time, and either fubtract it from, or add it to, the time per watch, according as it is east or weft; the fum or difference will be the reduced or fuppofed time at the place of obfervation. Look in the Nautical Almanack, page 2 of the month, for the fun's declination on the noon immediately preceding, and the noon immediately following the reduced time, and find their differ ence. With half the reduced time take out the number (T. XVIII.) correfponding to the hours at top and minutes in the left-hand column, with which multiply the diff. of decl. cut off four figures from the right hand of the product, the remainder is the correction to be added or fubtracted according as the decl. is increafing or decreafing the refult is the decl. or reduced time at the ship; with this decl. find the polar diftance; then add together the zen. dift. co-lat. and polar dift into one fum. From half this fum fubtract the zenith distance, noting the half fum and remainder; then add together, The log. co-fecant of the comp. of the lat. The log. fine of the difference into one fum, Rejecting their Rejecting indices. Find the log. fine of half the fum of the four logarithms, which being doubled, and brought into time, as before, will give the time from the midnight before the altitude was taken. Half the fum of thefe four logarithms will give the log. co-fine of half the hour angle, which being doubled and turned into time, by allowing fifteen degrees for every hour, &c. or more briefly by the table, will give the true time, if the altitude was taken in the afternoon; but if in the forenoon, its complement to 24 hours will be the true time, reckoned from the preceding, or noon before. NOT. The refraction is found in Table VII of this book; EXAMPLE I. Suppofe, on the 7th May, 1805, at 5h. 30m. 32f P. N. per watch, in lat. 39° 54' N. and lon. 35° 30' west of Greenwich, by account, Dip account, the altitude of the fun's lower limb fhould be found to be 15° 45', the eye being 18 feet above the furface of the fea, and the true apparent time when the obfervation was made were required? Obf. alt. fun's 1.1. 15° 45′ 0′′ Semi.15'52" Diff. +0 11 48. NOTE. By turning the long. W. into time, and adding it to the time at the hip, gives the reduced time, 7 h. 52 m. 32f. and the difference of declination between the 7th and 8th of May, is 16′ 33′′ = 993′', which multiplied by 3282, a number found in T. XVIII correfponding to 3h. 56 m. 16. half the reduced time from the product; cut off four figures from the right, the remainder 5' 26" is the correction to be added to the dec. for May 7, gives the true declination at the reduced time. Or it may be worked thus: As Sois 7h. 52.32" = Το 3259 ==== Log. 2,51375 NOTE. NOTE. If the reduced time be any even part of 24, as 1, 1, , &c. take fuch aliquot part of the daily diff of decl. and apply it to the decl. of the laft noon; the fum or diff. will be the true decl. at reduced time. EXAMPLE II. Suppose that in the forenoon, or A.M. on the roth of October, 1806, in lat. 51° 30' N. and long. 52° E. the alt, of the fun's lower limb fhould be found as under, the eye being 18 feet above the furface of the sea, and the true apparent time of the day were required? H. M. 20 14 Alt. 90 20 30 3)61 3 13 33 Ditto Ioth 6 29 17 S. Lon. E. in t. 3 28 Red. T. 16 53 Ap. alt Diff. in 24 hours o 22 52 22′ 52"x,7042 gives 16 6 Diff. +0 11 59 Dec. Oct. 9, at n. 6° 6′ 25′′ 13 44 59 Tr.dec.for lon.&t.6 22 31 Refra. 3' 48" } Diff.-0 '} 3 39 |