CASE II. If the Course found by Dead Reckoning be more than three Points, or thirty-three Degrees, and Lfs than five Peints, or fifty-fix Degrees. RULE. With the diff. of lat. and dep. by account, find the diftance; with this diftauce, and diff. of lat. by obfervation, find another departure. Take half the fum of this dep. and dep. by account, for the true dep. with which, and the diff. of lat. by obfervation, find the diff. of longitude. EXAMPLE. Yesterday at noon we were in lat. 52° 40′ N. and are this noon in lat. 54° 22' N. having by account made 84 miles of northing, and 6 miles of wefting; required the true difference of longitude? To the diff. of lat. 84, and dep. 76, the diftance is 113 miles, and the courfe 42°. To dift. 113, and diff. of lat. between the two observations 102, the dep. is 49,5; then 76 added to 49,5 is 125,5, half of which is 62,7, the true dep. To dep. 62,7, and diff. of lat. by obfervation 102, the course is 31°, and with the courfe 31° and the meridional diff. of lat. between the two obfervations 171, I find the diff. of long. is 103 miles. - CASE III. If the Courfe by Dead Reckoning be more than five Points, or fifty-fix Degrees. RULE. With the diff. of lat. and departure by account find the diftance; then with this dift. and diff. of lat. by obfervation find the diff, of long. EXAMPLE. Yesterday at noon we were in lat. 38° 52′ N. to-day at noon we are in lat. 40° 15′ N. and by account have made 68 miles northing, and 112 miles of wefting; required the true diff. of longitude? With the diff. of latitude 68, and departure 112, I find the dif tance 131 miles, and to diftance 131, and difference of latitude by obfervation 86, the courfe is 49, nearly; with this courfe, and the meridional difference of latitude between the two observations 111, the difference of longitude is 128 miles. The reafon of the above rule is plain, if we confider, that when a fhip fails near the meridian, it will require a fenfible error in the course, to make any confiderable error in the difference of latitude; which can hardly happen if proper care is taken at the helm; and therefore it is most likely that the error is in the distance run; but when the courte is near the middle of the quadrant, or between 3 and 5 points from the meridian, it is then probable the error may be in both course and distance; and when the courfe is more than five points from the meridian, it is then most likely the error is in the course, as it will require a great error in the distance to make any confiderable one in the difference of latitude. NOTE. As the true place of a fhip depends upon her latitude and longitude being truly afcertained, I have fet thefe down only, the reft being of lefs confequence to the mariner. To correct for feveral Days. By help of the three preceding rules, the longitude may always be corrected for a fingle day, but if an obfervation has been wanted for one or more days, then mark the latitude and longitude at laft obfervation, or if this be your firft obfervation fince leaving the land, mark the latitude and longitude of the land you left; this is the only latitude and longitude you can call certain; all the following part of the reckoning muft undergo a correction, which is made as follows: Take the northings, fouthings, caftings, and weftings, that you have made fince your laft obfervation; or, if this be your first obfervation, then for every day from your leaving the land, minding not to leave out the difference of latitude and departure of the day you correct on, and bring them into the Traverfe Table, by which you will have the whole difference of latitude and departure by account fince the laft obfervation; and with that fame difference of latitude and departure find the course by dead reckoning; then observe which of the foregoing cafes that course falls under, and correct by the rule for that cafe. But when an observation has been wanting for feveral days, then mark the latitude and longitude you were in at your laft obfervation, or on leaving the land as before, and then you may correct with a greater degree of certainty, efpecially in high latitudes, by the following rules: CASE I. Reckoning from the laft certain latitude and longitude. When the course given by the meridional difference of latitude and difference of longitude by account, taken as difference of latitude and departure, is lefs than three points, or 33 degrees. RULE. To the meridian difference of latitude and difference of longitude by account (taken as difference of latitude and departure, as fhewn in Mercator's Sailing), find a courfe; with this courfe, and the meridian difference of latitude by obfervation, find a cor refponding departure, which will be the correct difference of longitude. EXAMPLE I. Having failed three days ago from latitude 49° 57' N. and got no obfervation till this day at noon, and find I am in latitude 45° 23' N. and by dead reckoning I am in 45° 12' N. having differed my longitude 173 miles; required my difference of longitude? Y 2 Lat. To meridian difference of latitude by account 423, and difference of longitude by account 173, the courfe is 22° 15'. Then with the course 22° 15, and meridional difference of latitude between the observations 407, I find the difference of longitude is 167 miles. CASE II. When the course given by the meridional difference of latitude and difference of longitude by account (taken as before) is greater than three points, and lefs than five points. RULE. To the meridian difference of latitude and difference of longitude by account, taken as difference of latitude and departure, find a distance; with this distance, and meridian difference of latitude by obfervation, find a correfponding departure; half the fum of this departure, and the difference of longitude by account, is the correct difference of the longitude. EXAMPLE II. Three days ago we were in latitude 45° 23' N. and have fince that time failed between fouth and weft, have, by dead reckoning altered our latitude 94 miles, and our longitude 147 miles; but by an observation this day, we find we are in latitude 43° 34'; required the correct difference of longitude? M. Parts. Lat. failed from 45° 23' N. I 34 M. Parts, 3063 Lat. failed from 45° 23' N. 1 49 Mer. diff. of lat. by account. 132 Mer, diff. by obfervation, 3063 2919 153 With the meridian difference of latitude by acc. 132, and difference of longitude by acc. 147, I find the distance 198, and course 48°. Then with the diftance 198, and meridian difference of la titude by obfervation 153, the dep. is 125; now 125 added to 147 is 272, and half this fum, viz. 136, is the correct diff of longitude. CASE III. When the courfe given by the meridian difference of latitude and difference of longitude by account (taken as before) is more than five points, or 56 degrees. RULE. To the meridian difference of latitude and difference of longitude by account, taken as difference of latitude and departure, find a diftance. To this diftance and meridian difference of latitude by obfervation, find a correfponding departure, this departure will be the correct difference of longitude. EXAMPLE III. Two days ago I was in latitude 43° 34' N. and have fince then made by account 50 miles by fouthing, and 256 miles difference of longitude weft, but find by observation that I am in 42° 30′N.; what is my true difference of longitude? Lat. failed from Lat, by account M. Parts.1 43° 34' N. 2910 Lat. failed from 43° 34′ 50 1 04 M. Parts. 69 Mer. diff. of lat. by obser. 2910 2822 88 Mer diff. of lat. by account Then to meridian difference of latitude by account 69, and diff. of longitude by account 256 (taken as difference of latitude and departure), the distance is 265, and courfe 75 degrees. And to distance 265, and difference of latitude 88 (the meridian difference of latitude by obfervation), the departure is 250, which is the correct difference of longitude. Here we have given, at fome length, the different methods of correcting the dead reckoning by an obfervation, which are readily done by the Table of Difference of Latitude and Departure, The fhip's way is generally greater than the diftance given by the log, and it is always fafeft to have the reckoning a head cf the fhip, that the mariner may be looking out for land, and not make it before he is aware of it. When a great fea fets after the fhip, it is common to allow one mile over for every ten given by the log, for the heave of the sea; but if the fea be athwart or against her, her diftance must be less than that given by the log. The error in the fhip's reckoning is frequently attributed to unknown currents; for by various caufes, yet undetermined, there are many counter motions of the water in the open feas, as well as thofe obferved near the fhores, where the motions may be tolerably well accounted for. Some of the obferved currents in the great feas may perhaps be owing to the tides following the moon, and to the libratory motion the waters may have thereby, and the unfettled fetting and drift of thefe currents may poffibly depend on the change in the moon's declination. However, it is well known from obfervations, that the trade-winds occafion a confiderable current within their limits, particularly within the Torrid Zone, where the motion is perpetually towards the weft, at the rate of eight or ten miles a day, but at the extremities of the trade-winds, or near the latitudes of 30° N. or S. it is likely that the currents are con pounded of the faid western motion, and of one towards the equator; therefore all fhips failing within thefe limits should allow a courfe each day for this current, NOTE. When the difference of latitude by account is lefs than the difference of latitude by obfervation, the fhip is a-head of the reckoning, but if lefs, the reckoning is a-head of the ship. When the mariner is dubious of his account of longitude, he generally runs into the latitude of the intended port, and then fails E. or W. if there be fea room, according as it is fituated, and keeps a good look-out for the land. The method I have chosen to introduce the young mariner intɔ. the most capital part of navigation is, by fhewing him firft how to work a few separate days' works, independent of each other, and then proceed to a continued Journal from London to Madeira and Teneriffe, in which will be inferted most of the occurrences that commonly happen at fea or in harbour. I have seen many young navigators, who have been taught the principles of Navigation on fhore, very deficient in keeping a journal at fea; and therefore must request the teacher not to omit putting the pupils over the following Journal, which will render them ready at working a days' work at fea, and confirm in their memory thofe rules they have been over. |