UM 



NAVIGATION. 



f PLANE SA 



Without logarithm*. 



dep. diff. lat X tan. course. 



tan. course, 33 46' . . -06682 



diff. lat 82, reversed . '-> 



53466 

 ISM 



departure - 54792 miles. 



4. A ship from lat 50 13' N., while sailing on a course 

 between south and east, a distance of 98 miles, makes 

 82 miles of departure : What course did she keep, and 

 what latitude did she arrive at 1 



1. To find the count. 



By logarithms. 



As dist -98 . . .-1-9912 

 :dep. -82. . . . 1'9138 

 : : rad. . . . .10 



; sin. course, 56 48' . . 9-9220 

 Without logarithms. 



82 41 

 sin. course dep. -s- dist 55 ^a 



J 



n. 66" 48" . . -8367 

 Hence the course is S. 56 48' E. 



2. To find the diff. lot. 



By logarithms. 



As rad. . . . - 10 



: COB. course, 66 48' . . 

 : :dist - 98 . . . . 1-9912 



: diff. lat = 63 66 



Without logarithms, 

 diff. lat. = dist X cos. course. 

 cos. coarse, 56 48 . -6476 

 dist - 98, reversed . 89 



49284 

 4381 



1-7290 



diff. lat. = 53-665 miles - 54' 

 And 50 13' N. 64' N. = 49 Iff N., the lat in. 



5. Yesterday at noon we were in lat 38 32' N. ; and 

 this day at noon we were in lat 36 66' N. We have run 

 on a single course between 8. and E., at OJ knots an 

 )i< in r : required our course and departure. 



Lat from 38 32" N. 24, number of hours. 



Lat in SO 3 60 N. 6} 



Diff. lat, 1 30 N. - 96 miles 



120 

 12 



1 32 miles, the distance. 

 1. To find the course. 

 By logarithms. 



Asdist - 132 . . . 2-1206 

 : diff. lat - 90 . , . 1-9823 



: : rad 10 



cot. course, 43 W . . 9-8617 



Without logarithm*. 



oft fl 

 cos. course - diff. lat -i- dist = "",-7? 



I - J 11 



11)8 



oo. course, 43 20 1 . . -7273 

 ,'. the course is 8. 43 20 E. - 8.E. 6. 8. J E. nearly. 



2. TujitU the dtpartun. 

 By logarithms. 



As rad. 10 



: sin. course, 43" 20* . . '.' s:'.r.r, 



:: dist - 132 ... i: r-'<-. 



: dop. - 90-68 . . . i '.'.;i 



.*. departure 90 58 mile* E. 



Without logarithms. 



dep. sin. course X dist. 

 sin. course, 43 20" . . '0802 

 dist. 132, reversed . . . -.'! 



6869 



2059 

 137 



departure = 90 58 miles E. 



The foregoing examples have all been solved by com- 

 putation. As remarked at page 1053, the same results, 

 though with not precisely the same amount of accuracy, 

 maybe obtained by inspection of the Traverse Table. 

 There is also a third method of proceeding, much prac- 

 tised by seamen, though less accurate still, by which the 

 required conclusions may be reached : it is the method 

 of construction.* A circle is described, and the north 

 and south line, or the horizontal meridian, is drawn 

 through its centre ; then, from a scale of chords, con- 

 structed agreeably to the radius used, which radius is of 

 course the chord of 60 on the scale, the chord of the 

 course is pricked off in its proper direction from the N. 

 or S. extremity of the meridional diameter ; from the 

 same extremity, a line is then drawn through the point of 

 the circumference before marked : this is the line of dis- 

 tance, or hypotenu*al line, and the line already drawn 

 through the centre is the line of difference of latitude : 

 whichever of these is given is now to be measured off 

 from any scale of equal parts, and the right-angled tri- 

 angle is then to be completed by introducing the third 

 side, which, measured from the same scale, will give the 

 length sought. 



In this illustration, the course and one of the sides in- 

 cluding it, are supposed to be given ; but if the course be 

 unknown, and any two of the sides of the triangle 

 given, the mode of proceeding is readily suggested from 

 that above : in all cases we have two parts of a right- 

 angled triangle given to construct the triangle a simple 

 geometrical problem. The unmeasured parts are then to 

 be measured, the angle of the course from the scale of 

 chords, and the sides from the scale of equal parts 

 already employed. We shall conclude this article with 

 a few examples for the exercise of the learner : he will 

 not forget that the given courses are always understood 

 to be the true courses, that is, the compass courses cor- 

 rected for variation, local deviation, and leeway. The 

 means by which the variation of the compass is ascer- 

 tained cannot be considered hero, as the subject belongs 

 to Nautical Astronomy. (See next Chapter.) 



Examples for Exercise* in Single Courses. 



1. A ship from latitude 48 40' N. sails N.E. by N. 290 

 miles. Required the departure made and the latitude in. 



Ans. Departure, 104 '4 miles E. Latitude in, 52 4(1 N. 



2. A ship from latitude 49 30' N. sails N.W. by N. 

 103 miles. Required her departure and the latitude in. 



Ans. Departure, 57 2 miles W. Latitude in, 50 56' N. 



3. A ship from latitude 47 20' N., sails on a course 

 between N. and E. a distance of 98 miles, and :irri\ 



lat. 48 42' N. Required the course steered and tin 

 parturo made. 



Ans. Course, N. 33" 12 1 E. Departure, 53 7 miles E. 



'4. A ship sails S.E. E. from latitude 15 55' S. till 



There U alto* fourth method by OI-!<TIR' SCJII.K which It i> not 

 worth while to dwell upon. Any mechanical operation with scale and 

 compaMca U necessarily affected with Inaccuracy ; and an < 

 the Traverse Table require! leaa time, and furnishes truer results, It in 

 always to be preferred next to computation. 



