♦ KNOWLEDGE ♦ 



199 



DCABTER OF THE SOUTHERN CHART On the Same Projection (and on the 

 same scale), showing fourteen iUu-stratiTe great circle tracks in the >orth 

 Atlantic, obtained by the same method. [L and K mark the points where 

 the steamships from Queenstown and from Bordeaux respectively cross tbe 

 Newfoundland Bank.] 



HOW TO USE THE CHART 



I To find the great circle course between two places, A and B. 

 Describe a circle through A, B, and a the ant.pode of A (or 



through A, B, and h the antipode of B) ; it will pass through h (or a) 

 and be the t/reat circle required. 



II To tiiid the rcnSra or highest latitude reached. 

 A straight line through the pole and the centre of ABba cuts this 



great circle in t/ir /riff /test latitude point required. 



III To find the bearing at any point of the course. 

 The course cuts the Meridians at angles shoirinff t/ie true hearing 



IV To find the composite course between A and B, touching lat. I. 

 With radius equal to half the distance, across pole on chart 



between north-latitude I and south-latitude /, describe arcs through 

 A and B touching lat.Z; these arcs, and part of lat. paraUel (0 

 between them, make up t/ie composite course reqmred. 



V To find the great-circle distance between A and B. 

 Find « the pole of the great circle course (90° in lat. from vertex), 



and centres D and F of great circles through A^^ and Bp; then tJu- 

 great circle course A B contaiM as many degrees as t/iere are m t/io 

 supplemeut of DpF, eac/i degree containing GO geograp/acal ''"te. 



Note.— If a ship is driven from her course, as from L to 0, the 

 great circle course from C (as CA) is found by I. 

 Example. 



To find T., the great circle course ; II., its rertc.x ; III., the hearing 

 (at an,/ point); IV., the comjwsite courte (lat. .50); and V the rfj^- 

 tance ;' from Cape Town A (antipode «), to MeUmirne B (antipode b). 



I. Find C, the centre of circle through A, B, a, b, and describe, 

 round C, t/ie required great circle course AVB. 



II TbroughP.C, draw PCdV, giving the w'rfra.V. 



III. Draw compass-card N-E-W-S about 0,NS meridional, then 

 OT tangent to course, shows the bearing at 0. 



Note.— Angle EOT = angle NOC. 



IV. Bisect w' Gat- 50 N & S) in G ; about P describe arc cGc ; 

 with radius Gt- and centre on fc', desc. arcs AH, BK ; AHVJiB is 

 the reqmred composite course. . t • i 



T Take p on PV, 90'' from V ; find D, the centre of a circle 

 throucrh A,p, and a ; and F, the centre of a circle through B,/», and 

 b- AVB contains as manq degrees as t/ie supplement of t/ieaTii^lc 

 DpF By measurement with a protractor, AVB contains 92^', cor- 

 responding to 5,565 geog. miles. True distance 5,5GGi geog. mUes 

 (587 geog. miles less than Mercator's course). 



CHARTS FOR GREAT CIRCLE SAILING.* 



SHOWING AT ON'CE THE GREAT CIRCLE TRACK, THE 

 COMPASS BEARING AT EACH POINT, AND THE DIS- 

 TANCE ; ALSO THE "COMPOSITE COURSE" TOUCHING 

 ANT GIVEN LATITUDE. 



By Richahd A. Phoctor. 



5S1HE shortest distance between any two points 

 on a globe is the lesser are of the great 

 circle passing through them (a great circle 

 on a sphere being one whose plane passes 

 through the sphere's centre). But the sea- 

 man, in passing from port to port on the 

 earth, generally follows what is called a 

 rhumb lim — such a track that he has the same compass 

 course (apart from magnetic variation) throughout his jour- 

 ney. Mercator's projection, on ^\hich the charts of the 

 world in our books of geography are drawn (I mean thoi-e 

 charts which show the whole world), was invented to help 

 the sailor in marking his true rhumb course from port to 

 port, this course being shown in Mercator's charts as a 

 straight line. In long journeys, however, especially such as 

 are made hi the southern hemisphere, the rhumb course is 

 far longer than tlie gi-eat circle course. For instance, frora 

 Cape Town to ISIelbourne the course on a rhumb line is 587 

 miles longer than the course on the arc of a great circle. 

 Even in such a journey as from Queenstown to New York 

 (where, however, the great circle track is broken by the 

 Newfoundland shores, and two arcs have to be combined) 

 there is a considerable saving of distance in following the 

 great circle route. Moreover, for sailing vessels tacking 

 against adverse winds the saving is far gi-eater. In tacking 

 along a rhumb course, sailing as close to the wind as she 

 can, a .^ailing vessel is often actually increasing her distance 

 from her haven. In passing from the English Channel to 

 New York, on a rhumb course, against adverse winds, a 

 sailing vessel tacks over 7,360 miles ; but taking the great 

 cu-cle course, the distance traversed in all her tacks would 

 be only 6.490 miles, a saving of 870 miles, or five or six 

 days' sailing for a craft of medium speed I On some of the 

 long South Sea journeys, where the difference in miles be- 

 tween the rhumb course and the great circle course may be 

 seven or eight hundred miles, the actual difference of dis- 

 tance traversed in tacking against adverse winds would 

 amount to two or three thousand miles ! 



My present object is to show how charts may be made 

 which will be as convenient for great circle sailing as Mer- 

 cator's charts are for sailing on a rhumb line. 



Two difliculties have checked the extension of the sy.stem 

 of <n-eat circle sailing. In the first place, a process of calcu- 

 lation has to be gone through to determine even the proper 

 frst course for great circle sailing, that is, the bearing at 

 the port of departure; and a fresh ftilculatiou has to be 

 made for a succession of points— usually taken five degiees 

 in longitude apart— along the gi-eat cu-cle course. Secondly, 

 it often happens that the true great circle course would 

 carry a ship into inconveniently high latitudes. 



To meet the first difiiculty, various methods have been 

 from time to time suggested for obtaining graphically the 

 gi-eat circle course. Sii- George Airy invented a most 

 ingenious but unfortunately a complicated construction 

 for drawing the great circle course on a Mercator's chait. 

 Mr. Hush Godfrav, the author of the Cambridge text-book 

 on the Lunar Theoi v, suggested the use of the gnomonic 

 projection, where the" great circle course is represented by a 

 straight line, just as the rhumb course is rep resented on a 



* This article is mainly a reprint from the Scientific American, 

 from whose pages the illustrations have been reduced. 



