NAVIGATION. 



[PABALLKL RAILIMO. 



Nort. It will save time, and ho guard against mii- 

 tako in the filling up the several columns from the Tra- 

 verse Table, if, before that table is opened, a mark be 

 j ut ..K. -::i- to each ooune, and in each of the columns 

 where the entries connected with that course are to be 

 inserted. Thus, if N. occur in the course, mark a little 

 emu against it in the N. column, near enough to the 

 runt-hand margin of tliat column to allow of room for 

 the extract from the Traverse Table ; if S. occur in the 

 ooune, put a like mark in the S. column. If E. occur, 

 mark the E. column ; and if \V. occur, mark the \\ . 

 column. Then, when the Traverse Table is consulted, 

 we shall have precluded the risk of writing the particulars 

 fr. in it in the wrong column 



2. A ship sails S.W. 6 S. 24 miles; N.N.W. 57 miles ; 

 8.E. 6 E. } E. 84 miles ; and S. 35 mile*. Required the 

 direct course aud distance. 



ADR. Course, S. 43 E. Distance, 57 miles. 



a A ship from latitude 50 13' N. has sailed the fol- 

 lowing courses, namely 



1st \Y.s.\v., :! miles. 2nd. W. 6 N., 35 miles. 

 3rd. 8. 6 E., 46 miles. 4th. S.W. 6 W., 55 miles. 5th. 

 S.S. K. 41 miles. Required the latitude in, and the 

 direct course and distance sailed. 



Ana. Lat in, 48 8' N. Course, S. 39 19' W. , or S. W. 

 6 S. J W. Distance, 102 miles. 



4. A ship from latitude 28 312' N. has run the follow- 

 ing courses, namely 



1st N.W.6N., 20 miles. 2nd. S.W., 40 miles. 3rd. 

 N.E 6 E., GO miles. 4th. S.E., 55 miles, oth. W. 6 S., 

 41 miles. 6th. E.N.E., 66 miles. Required the latitude 

 in, and the direct course and distance. 



Ana. The same latitude. Course, dueE. Distance, 



70 2 miles. 



5. From noon to noon the following courses were run, 

 namely 



1st &W. 6S., 20 miles. 2nd. W., 16 miles. 3rd. 



X.W. b W., 28 miles. 4th. S.S.E., 32 miles. 6th. 



K, 14 miles. 6th. S.W., 36 miles. What dif- 



e of latitude has the ship made, and what is her 



direct course ami distance ? 



Ans. Diff. Ut, 607 miles S. Course, S.W. Distance, 



71 7 miles. 



G. A ship sails from latitude 10 6' S., the following 

 courses, namely 



1st N.N.E., 86 miles. 2nd. N., 74 miles. 3rd. E. 

 6 N., 63 miles. 4th. N.N.W. } N., 40 miles. 6th. 

 I N.E. i N., 2L miles. Required the latitude in, and 

 direct course and distance. 



Ana. Lat. in, 6 34' S. Course, N. 23 25' E. Dis- 

 tance, 231 miles. 



7. A ship from latitude 51 30' N., running at the rate 

 o< 8 knots an hour, sails W.S.W., 3 hours; N.W., 2i 

 hours ; W., 4 hours ; S.W. 6 S., 2J hours ; and .N.WT 

 I W., 2 hours. Required her latitude in, and her direct 

 course and distance. 



Ans. Lat in, 61 30' N. Course, W. Distance, 90 7 



8. A ship from latitude 24 32' N., sails the following 

 courses, namely 



1st. S.\V. /, W., 45 miles. 2nd. E.S.E., oOmiles. 3rd. 

 8.W., 30 miles. 4th. S.E. 6 E., 60 miles. 6th S W. 6 

 8. J W., C3 miles. Required her latitude in, her de- 

 parture, and the direct course and distance. 



Ans. Lat in, 22 3' N. Departure, 0. Course, S. Dis- 

 tance, 14!) -2 miles. 



In this last example, the ship is said to have returned 

 to the meridian from which she sailed, so that her course 

 from the place arrived at to that left, is concluded to be 

 due south. In the present case, the latitude being low, 

 the error of this conclusion is practically of no conse- 

 quence ; but the balance, or aggregate of the several 

 departures made on a traverse, U not, in strictness, the 

 departure due to the direct course fact that sailors, 

 in general, are not nulli. n-ntly sensible of. We shall ad- 

 vert more at length to this matter in our introductory 

 observations to MERCATOR'S SAILING. 



PAMALLKt SAII.ISU. When a ship sails upon a parallel 

 of latitude, her distance run U then the same as her 



departure ; her difference of latitude in nothing, and her 

 difference of lougitu le may ! ied. The 



is one of parallel tailing, the theory of which may 

 tig. it. be established in the 



following in inner : 



ie diagram 



at p. 696, Chapter 

 Mil . 



letC Q represent 

 a portion of the equator 

 corresponding to the 

 portion B P of a paral- 

 lel of latitude sailed 

 over by a ship, the 

 points P Q beii 

 the same meridian. 

 Th.-n OCis the radius 

 of the equator, and 

 N B the radius of tho parallel, an 1 the difference of lon- 

 gitude of 11 and 1' will lie in. mired by tho arc C Q. 



Now, since similar arcs are to one another as the radii 

 of the circles to which they belong, we have 



N B : O : : dist. B P : diff. long. C Q. 



But N B is the geometrical cosine of the latitude C B, to 

 the radius O C ; consequently N B is equal to O C multi- 

 plied by the trigonometrical cosine of the angle QO 1' of 

 the latitude ; that is, expressing the latitude in degrees 

 and minutes, and not in linear measure, we have 



OCcos. lat. : OC : : dist. sailed : diff. long. (1) 

 .'. cos. lat. : 1 : : dist sailed : diff. long. (2) 



And it follows from this, that if tho distance between 

 any two meridians on a parallel in latitude L, be D, 

 anil the distance of the same meridians on a parallel in 

 latitude L' lie D', then alternating the proportion (1) 



cos. L : cos. L' : : D : D' . . . (A) 

 The proportion 2) evidently solves the problem- 

 Given the latitude of the parallel aud the distance s 

 on it, to find the difference of longitude ; the solution 

 being 



,._ , , ... distance Bail.nl 



difference of longitude . .. x . . (3) 



cos. latitude 



So that, as in the former cases, we may connect tho 

 three things concerned in a right-angled plane trianglo 

 Fig. 17. (Fig. 17), the base representing tho 



distance sailed, the hypotenuse, the 

 difference of longitude, and the angle 

 between the two the latitude of tho 

 parallel, because we know from tho 

 theory of tho right-angled triangle 

 that these three pails are ivlat. 

 condition (3V Any problem in parallel sailing inav, 

 therefore, always be reduced to a case of right-a 

 triangles ; and consequently may be solved, like a 

 problem in plane sailing, by inspection of tho Tra. 

 Table. We shall only have to consider the latitn 

 tho parallel as course, and tho distance as <Hjf. lit.; the 

 corresponding distance in tho Traverse Table will bo the 

 diff. long. 



It must bo observed, however, that the perpendicular 

 of our right-angled triangle merely servos to <.-. 

 gethcr tho three things here mentioned ; it has no M ;ni- 

 fication in navigation. The distance sailed on a pai 

 tho latitude of that parallel, and tho difference of longi- 

 tude between the place left aud that arrived at, :u 

 lated to one another as the three parts, notin-d al ,,ve, of 

 a right-angled triangle, the perpendicular of which 

 merely serves to complete the diagram in which thoso 

 relations are geometrically embodied. 

 The proportion (2) above, is usually expressed thus: 



cos. lat : radius : : dist. sailed : diff. long, 

 where rad. = 1 when the table of natural sinos and cosines 

 is ued ; and log. rad. 10 when tho logarithmic t-ihle is 

 used. As usual, we shall exhibit tho working by both 

 tables ; but it will be perceived, as in most of tin- com- 

 putations already given, that the former table U in 

 general to be preferred. 



