28
NAVIGATION.
steered and the variation given, viz. Let your face be turned to-wards the point of the compass upon which the ship is steered; andif the variation be easterly, count the quantity of it from the coursesteered towards the right hand; but if westerly, towards the lefthand; and the course thus found is the true course steered. Thus,suppose the course steered is N6E, and the variation one pointeasterly; then the true course steered will be NNE; also suppose,the course steered is NE6E, and the variation one point westerly;then, in this case, the true course will be NE ; and so of others.Hence, by knowing the lee-way variation, and course steered, wemay thence find the ship’s true course; but if there be a currentunder foot, then that must be tried, and proper allowances madefor it, as has been shewn in the section concerning Currents, fromthence to find the true course.
VI. After making all the proper allowances for finding the ship’strue course, and making as just an estimate of the distance as wecan ; yet by reason of the many accidents that attend a ship in aday’s running, such as different rates of sailing between the timesof heaving the log; the want of due care at the helm by not keep-ing her steady, but suffering her to yaw and fall off; suddenstorms, when no account can be kept, &c. the latitude by accountfrequently differs from the latitude by observation : and when thathappens, it is evident there must be some error in the reckoning;to discover which, and where it lies, and also how to correct thereckoning, you may observe the following rules :
Rule 1. If the ship sail near the meridian, or within 2 or 2-| pointsthereof; then if the latitude by account disagrees with the latitudeby observation, it is most likely that the error lies in the distancerun ; for it is plain, that it.will require a very sensible error in thecourse to make any considerable error in the difference of lati-tude, which cannot well happen if due care be taken at the helm,and proper allowances be made for the lee-way, variation, and cur-rents. Consequently, if the course be pretty near the truth, andthe error in the distance run regularly through the whole, we may,from the latitude obtained by observation, correct the distanceand departure by account, by the following analogies, viz. As filedifference of latitude by account is to the true difference of lati-tude, So is the departure by account to the true departure, Andso is the direct distance by account to the true direct distance.The reason of this is plain : for let AB, fig. 17, denote the meri-dian ol'the ship at A, and suppose the ship sails upon the rhumbAE near the meridian, till by account she is found in C, and con-sequently her difference of latitude by account is AB ; but by ob-servation she is found in the parallel ED, and so her true differ-ence of latitude is AD, her true distance AE, and her true de-parture DE ; then, since the triangles ABC, ADE, are similar, itwill be AB : AD :: BC : DE, and AB : AD :: AC : AE.
Exump. Suppose a ship from lat. 45° 20' N. after having sailedupon several courses near the meridian for twentv-four hours, herdifference of latitude is computed to be upon the whole 95 milessoutherly, and her departure 34 miles easterly ; but by observationshe is found to be in lat. 43° 10' N. and consequently her true dif-ference of latitude is 130 miles southerly: then for the true depar-ture it will be, As the difference of latitude by account 95 is to thetrue difference of latitude 130, so is the departure by account 34to the true departure 46'52, and so is the distance by account 100’9to the true distance 138.
Rule 2. If the courses are for the most part near the parallel ofE. and W. and the direct course be within five and a half or sixpoints of the meridian ; then if the latitude by account differs fromthe observed latitude, it is most probable that the error lies in thecourse or distance, or perhaps both; for in this case it is evidentthe departure by account will be very nearly true ; and thence bythe help of this, and the true diff. of latitude, may the true courseand direct distance be readily found by Case 4of Plane Sailing.
Examp. Suppose a ship from lat. 43° 50' N. after having sailedupon.several courses near the parallel of E. and W. for twenty-four hours, is found by dead reckoning to be in lat. 42° 45' N.and to have made 160 miles of westing ; hut bv good observationthe ship is found to be in lat. 41° 35' N. Required the truecourse and distance sailed' With the true difference of lat. 75miles, and departure 160 miles, we shall find by Case 4 of PlaneSailing, the true course to be S. 64° 53'W. and the direct dis-tance 176-7 miles.
Rule 3. If the courses are for the most part near the middle of the j-■uiadrant, and the direct course within two and six points of the |
meridian, then the error may be in the course, or in the distance,or in both, which will cause an error both in the difference of thelatitude and departure; to correct which, having found the truedifference of latitude by observation, with this, and the direct dis-tance by dead reckoning, find a new departure (by Case 3 of PlaneSailing): then half the sum of this departure, and that by deadreckoning, will be nearly equal to the true departure ; and conse-quently with this, and the true difference of latitude, we may (byCase 4 of Plane Sailing) find the true course, and distance.
Examp. Suppose a ship from lat. 44° 38' N. sails between S. andE. upon several courses near the middle of the quadrant, fortwenty-four hours, and is then found by dead reckoning to be inlat. 42° 15' N. and to have made of easting 136 miles; but by ob-servation she is found to be in lat. 42° 4' N. Required her truecourse and distance ? With the true difference of latitude 154 miles,and the direct distance by dead reckoning 197'4, you will find (byCase 3 of Plane Sailing) the new departure to be 123 4 and half thesum of this and the departure by dead reckoning will be 123-7, thetrue departure ; then with this, and the true difference of latitude,you will find (by Case 4 of Plane Sailing) the true course to beS. 39° 0 'E. and the direct distance 198-2 miles.
VII. In keeping a ship’s reckoning at sea, the common methodis to take from the log-board the several courses and distancessailed bv the ship last twenty-hours, and to transfer these togetherwith the most remarkable occurrences into the log-book ; intowhich also are inserted the courses corrected, and the difference oflatitude and difference of longitude made good upon each ; thenthe whole day’s work being finished in the log-book, if the lati-tude by account agree with the latitude by observation, the ship’splace will be truly determined ; if not, then the reckoning mustbe corrected according to the preceding rules, and placed in thejournal. The form of the log-book and journal, with an exampleof a davs’ work, are here subjoined. To express the days ofthe week, they commonly use the characters by which the sunand planets are expressed, viz. © denotes Sunday, ]) Monday,$ Tuesday, $ Wednesday, If. Thursday, Friday, 1? Satur-day.
It is to be observed that the journal or sea-reckoning is a regularaccount written every day in a book (fit for that purpose) and stat-ing the course, distance, difference of latitude, and departure theship has made, what latitude and longitude she is in; and alsothe wind, weather, with all accidents and occurrences that marhappen. For this purpose there must be provided a folio-book oftwo, three, or four, quires of large paper, ruled like the log-board,with five columns, taking up about halt the breadth of each page.The five columns may be marked or noted at the head of eachcolumn with letters to denote the hours, knots, fathoms, courses,which have been steered, and winds, which have blown that day',&c. In the first column (marked at the upper end with IT) writedown the hours of the day; that is for common voyages, 2, 4, 6,8, 10, 12, and 2, 4, 6, 8, 10, and 12: but for an East India voy-age, 1, 2, 3, &c. to 12 at midnight; then 1, 2, 3, &c. to 12 atnoon. And thus far is the book fitted, and prepared to copy offthe log-board. Under these five columns let there be ruled seve-ral short columns, which may take up the whole breadth of eachpage of the book. These are intended to note the courses, distances,&c. made good in the preceding twenty-four hours. Every dayat noon, write in the five columns the same which is written on thelog-board, which contain the ship’s courses steered, distances runby the log, what winds have blown, wlval sails handed, and when.In the vacant space of the right hand of these five columns (whichtakes up more than half the breadth of the book) express the trans-actions of that day, as winds, weather, currents, setting of the sea,handing of sails, meeting or parting with ships, death of men, va-riation of the compass, and all other accidents and occurrenceswhatsoever. Then correct the several courses, by allowing forleeway, currents, and variation, according to the nature of them;and bring them into one course by the rules above given for re-solving a traverse, by which you will find the ship’s distance, dif-ference of latitude, and departure from the meridian; which setdown in columns bearing those titles; then by the Mercalor’ssadingfind the latitude and longitude the ship is in, which also enter in co-lumns with their proper titles’, then if the observed latitude differsfrom the latitude by account, (he corrections are to be made asabove directed, and thus will the day’s work be completed: th«following specimen will furnish an idea of this subject -.