PARALLEL SAILING.] 



NAVIGATION. 



1057 



Examples. 



1. A ship from latitude 53 D 36' N. longitude 10= 18' 

 E., sails due west 236 miles : required the longitude in. 



To find the diff. long. 

 By logarithms. 



As cos. lat., 53 36' . . .-97734 



: radius . .10 



: : distance =236 . . 2 3729 



: diff. long. = 397 7 . 2-59D5 



Without logarithms. 



diff. long. =dist. -;- cos. lat. 

 cos. 53 36'= -5,9,3,4)236 (3977 

 17802 



6798 

 5341 



457 

 415 



42 

 42 



Hence the diff. long, is 3977 miles=398 miles nearly. 



Reducing this to degrees, 

 60)398 



diff. long. = 

 long, left . 



long, in . 



6 e 38' E. 

 1018'W. 



. ) The difference to be taken, 

 . ) as the longitudes are E. 



340'E. 



and \V. 



2. A ship from latitude 32 N-, sails due east till her 

 difference of longitude is found to be 384 miles : what 

 distance has she run ? 



To find the distance. 

 By logarithms. 



As radins . 



: cos. lat., 32 

 ; : diff. long =384. 



-10 



, 9 9284 



. 2-5843 



distance = 325-6 



25127 



Without logarithms. 



Dist.=diff. long. X cos. lat. 



cos. 32 =-8480 

 384 reversed, 483 



2.VI 4 



678 



34 



825-6 



Hence the distance run is 325-6 miles. 



3. From two ports in latitude 32 W N., distant 256 

 miles, measured on the parallel, two ships sail directly 

 north, till they come to the latitude 44 30* N. : how 

 many miles, measured on the parallel arrived at, are 

 they apart ? 



This question is to bo worked by using the pro- 

 portion (A). 



By logarithms. 



As cos. lat. from, 32 20' Arith. Comp. -0732 



: cos. lat. in, 44 30' ... 9'8532 



:: first dist. = 206 . . . 2-4082 



: seed. dit. = 21G-l 



VOL. I. 



. 2 3346 



Without logarithms. 



D'=D cos. L'-=-cos. L 

 cos. L'= cos. 44, 30'= '7133 

 D =256, reversed, 652 



14266 



3567 



428 



cos. L=cos. 32 20',= -8,4,5,0)182 61(216 1 



1690 



1361 

 845 



516 

 607 



9 



Hence, measured on the parallel of 44 30' X., the 

 ships are 216 miles apart. Their least distance apart is 

 the arc of the great circle from one to the other ; because 

 an arc of a great circle of the sphere is the shortest dis- 

 tance between its extremities. 



4. A ship from latitude 42 54' S., longitude 9 16' W., 

 sails due west 196 miles : required her longitude in. 



Ans. 13 44' W. 



5. A ship has sailed due east for 3 days on the 

 parallel of 43 28'; her rate of sailing has been, on the 

 average, 5 knots an hour. What difference of longitude 

 has she made ? Ans. 8 16' E. 



6. A ship from longitude 81* 36' W. sails due west 

 810 miles, and is then found by observation to be in 

 longitude 91 5ff W. : on what parallel has she sailed 1 



Ans. The parallel of 59 41'. 



7. In what parallel of latitude is the length of a degree 

 only one-third the length of a degree at the equator I 



Ans. Lat. 70 S^. 



8. Two ships in latitude 47 54' N., but separated by 

 9 35' of longitude, both sail directly south 836 miles, 

 and at the same rate : how many miles were they apart 

 at starting, and how many after running the 836 miles 1 



Ans. First distance, 385 miles ; second distance, 477 

 miles. 



9. If two ships in latitude 44 30" N., and distant 

 from each other 216 miles, were both to sail, at the same 

 rate, directly south until their distance on the parallel 

 arrived at, became 256 miles, what latitude would they 

 be in ? Aus. 32 17' N. 



10. If a ship sail due east 126 miles, from the North 

 Cape in latitude 71 10' N., and then due north, till she 

 reaches latitude 73 26' N., how far must she sail west to 

 reach the meridian from which she started 1 



Ans. 111'3 miles. 



MIDDLE LATITUDE SAILING. It has already been 

 sufficiently seen that the principal object of plane sailing 

 is to determine the difference of latitude made by a ship 

 sailing upon an oblique rhumb. This sailing gives us no 

 information respecting the change made in the ship's 

 longitude ; but if the rhumb sailed upon, instead of 

 being oblique to the meridians crossed by it, cuts them 

 all at right angles, as in parallel sailing, then, as just 

 shown, the difference of longitude made may be accurately 

 ascertained. Except in this particular case, the de- 

 termination of the change of longitude made by a ship in 

 sailing from one place to another, is a problem the strict 

 solution of which is by no means easy. Independently 

 of astronomical observations, there are two modes of 

 proceeding : one is called Middle Latitude Sailing, and 

 can be regarded only aa a close approximation to the 

 truth, unless a certain correction, hereafter given, be 

 applied to it.* The. other is called Mercator's Sailing, 



In the year 1805, Mr. Workman published, under the sanction of the 

 then Astronomer Royal, Dr. Maskelyne, a small and very useful table for 

 correcting the errors of middle latitude sailing. The table is even now 

 scarcely so well known as it ought to be ; and as it removes the only 

 objection to this mode of finding the difference of longitude, we have 

 inserted it, a little abridged, at the end of these remarks on mid. lat. 

 sailing, and would strongly recommend it to the notice of the practical 

 navigator. (Sec page 1U60). 



61 



