LESSOXS IN XAVKJATIn.V. 



i.e., during tho first hour tho ship made 3 knot* and 4 for. 



longs on a compass course K.S.K. (that in, her head pointed 



i), and that she was drifting 1 !<int to loo- 



!o prosHiiro of tho wind (the wind being 

 "ii th< . she makes leeway to tho ri^ht, mid tho allow- 



made to rijht \ ipoas ooune). 



uro lasted at varying spcod for throe hours, in which 

 timr 10 knota wero made. A north course was then begun, and 

 persevered in for 12 hours at varying speeds, amounting in all 

 to 60 knots run ; and BO on. During the day five different 

 oonrsoa wero steered, or more correctly six, as while steering 

 : making .} point leeway (to loft) the wind so shifted as to 

 - sido pressure, and tho vessel ceased to make lee- 

 way : this amounted to a virtual alteration of the true course 

 jy point to tho right. But besides those courses there was a 

 constant current setting W.S.W. ^ S. (true course) at 1 knot 

 per hour during tho whole day, carrying tho ship with it. It 

 may therefore bo reckoned a3 a seventh course, distance 24 

 mi !<, and as such appears in the traverse table. Had tho 

 different courses boon run in different currents, each must have 

 boon separately corrected for currants, but in this case it is 

 unnecessary. 



The various true courses and distances are now arranged one 

 below the other in a table ruled aa below, called a traverse 

 table ; thus 



The first course is thus found from the compass course 

 (E.S.E) : One point leeway added to right gives S.E.b.E. ; 2 

 points variation to left give E.b.S.JE., equivalent to a course 

 7| points from the meridian. Under course ?i points and dis- 

 tance 10 miles, we find in the tables diff. lat. = T5 minutes, 

 departure = 9'9 miles. Insert these results in the traverse 

 table, remembering that, from the course run, the diff. lat. 

 must be reckoned southwards, and departure eastwards. If 

 the letter N. appear in the course, the diff. lat. is north ; if S., 

 it is south ; if neither, there has been no change of latitude, 

 and the ship has sailed on a parallel. If E. appear in the 

 course, the departure is eastward ; if W., then westward ; if 

 neither, then there is no departure i.e., the ship is sailing on 

 a meridian, or due north or south. Hence in the fourth course 

 tho whole distance (25 miles) is west departure, and there is no 

 diff. lat. By adding up tho heaviest column under diff. lat. 

 (N. in this case), and subtracting the other from it, we get 60'6 

 miles, the nett difference of latitude ; similarly with departure. 



If the ship started in lat. 30 N., we obtain her now latitude, 

 or " latitude in," thus 



Latitude left . . 

 Diff. lat., GO-6 miles 



30 0' N. 

 1 0-6 N. 



Latitude in ..... 31 0'6'N. 



The aggregate departure duo to the general course during 

 the day is 74 - 6 west, and the general or direct course which 

 clearly lies between west and north may be found by formula 

 (5), either by logarithms or by a table of natural sines, tan- 

 gents, etc. The latter plan is usually the least troublesome ; 



Tan. course 



- - = 1-2475 ; 

 diff. lat. 60-6 



.'. course = 51 (approximately), or N. 51 W. 

 = N.W.iW. (approximately). 



Course being known, distance may be found by (3) or (4). 



It need scarcely bo said that, by using formulae (1) and (2), 

 the " dep. and diff. lat. table " may be dispensed with, and 



trioter but unnecessary accuracy attained. Calculation bj 

 tables it called inspection, and by the formula computation. 



Sailor* have another mode of working out diff. lat, depar- 

 tore, eto., and the result* of compound omme* ris., by em* 

 struction, a means which, however suitable for illiterate men, u 

 not to bo compared with either of the others named. A circle 

 is drawn, divided by a north-and-sonth and east-and-went line. 

 Tho corrected course steered is marked by a line radiating from 

 tho centre in the appropriate direction (the circle being viewed 

 aa a skeleton compass). The number of miles run, transferred 

 by compasses from any scale of chords, is pricked on the line, 

 one compass point being at the centre. From the other point 

 a perpendicular is drawn to the north-and-south line, and the 

 part intercepted between it and tho centre represents the diff. 

 lat. in miles, while the perpendicular represent* the departure. 

 Instead of being computed, these quantities are measured by 

 compasses on tho same scale from which the distance run wag 

 taken. Unless this is done very carefully, with the best instru- 

 ments, the error on any but a very short distance may be con- 

 siderable. If the course is unknown, and other data given, 

 the triangle is constructed by the same system of measurement ; 

 indeed, this may bo called plane sailing by Geometry instead of 

 Trigonometry. In traverse sailing the several courses are 

 marked by radiating lines, but after the distance run on the 

 first course has been marked upon it by compasses, aa before, 

 a line is drawn from tho point thus reached parallel to the 

 radiating line representing the second course. On this second 

 line is marked the second distance run, and so on, until tho 

 paper contains an exact plan of tho ship's actual track. A line 

 from the centre to the hist point reached gives tho equivalent 

 course, and its length shows the direct distance run. Diff. hit. 

 and departure are then found as before. 



V. Parallel Sailing. It has been seen that the theory of 

 plane sailing stops short of giving us the longitude, which the 

 mariner needs to know as much as the 

 latitude. For this purpose plane sailing 

 must be supplemented by tho rules cither 

 of mid-latitude sailing or Mercator sail- 

 ing. To find the longitude is a matter 

 of some difficulty, except in the case cf 

 parallel sailing, or sailing due east and 

 west, already alluded to, and with which, 

 as a stepping-stone to tho others, we will 

 now deal. 



Suppose A B (Fig. 6) to be the track 

 of a ship, sailing due east a known 



number of miles. Let the meridians of A and B cut the equator 

 at x and Y. Then, 



A B and x Y being similar arcs, A B : X T : : radius B p : radius T o. 

 But radius Y o = radius B o, and B P = o Q ; 



/. = - = cos. angle o = cos. lat. of parallel A B, 



x Y BO 



since either arc or angle forms a measure of the latitude of B. 

 Now A B = distance sailed in miles, and X Y = distance Bailed 

 in minutes of longitude, i.e., "difference of longitude;" 



distance sailed , , 



= coa. lat. ; 



Fig. 6. 



difference of longitude 

 difference of longitude in minutes = 



di.-t.u.. o 



...(6) 



Pig. 7. 



DistuuL-o soiled. 



cos. hit. 



Fig. 7 shows how questions in 

 parallel sailing may be solved by a 

 right-angled triangle, constructed in 

 accordance with this formula. Any 

 two of the three things being given, 

 the other can be found ; thus, 



cos. lat. = , and dist = 



diff. long. 



COB. hit. X diff. long. 

 The perpendicular of the triangle has no significance. 



Suppose a ship in lat. 30 N., long. 25 W., sails 200 miles 

 due east ; what is her " longitude in P" 



By (6), diff. long. = ~ = 231', nearly = 3 51' ; 



.'. longitude in = 25 - 3 51' W. = 21 9* W. 

 Here we have used only the table of natural sines and cosine*. 



