GREAT CIRCLK (HI TANGENT SA1LIM.. 



GREAT CIRCLE OR TANGENT SAILING. iJ4 



MOMtnr preparation for tbow whose 

 admit of the sides of a triangle on the do 



voyage* wen no ihort ai t< 

 t triangle on the globe bring for ordinary purposes 

 Considered M straight lines: bat the teaching of spherics to the 

 navigator failing into dutne (by tome ratnordinary misconceptions) 

 great circle Railing gradually became neglected, until for many yean 

 it wan omitted in the staixUrd worki on navigation altogether. Even 

 the attempt of Dr. Kelly, the mathematical examiner at the Trinity 

 House nearly 60 yean unce, to renew the study of spheric pro- 

 jection, resulted in failure. Thui, while the aea officers of other 

 nation* are well prepared in that which forma not only the basis 

 of great circle Railing, but of nautical astronomy, the energetic and 

 intelligent mariuera of England, although programing in all ele, were 

 doomed for a time to wade in the punuit of principles through 

 work* which M regarda theory are somewhat too elaborate, and with 

 respect to the rules of spheric construction are quite inadequate, for 

 the mere navigator. 



Such was pre-eminently the state of thing!) when the late skilful 

 and lamented Lieutenant Henry Raper, R.N., produced his ' Practice 

 of Navigation,' which forms the present text book of the Royal Naval 

 service, and of the higher classon of merchant navigator*. But even 

 in this admirable work the doctrine of spheric construction has been 

 omitted as evidently forming no supposed essential in a sea officer's 

 training. 



The name of Raper must however be conspicuous as the regenerator 

 of great circle sailing. In his work he gives excellent formula;, but the 

 use of logarithms arising from rulei not underttood by the uninitiated 

 entails an effort of memory which is injuriously allowed to supplant 

 the satisfaction which a conscious knowledge of principles would so 

 unceasingly furnish. Notwithstanding this, Raper's solution of the 

 "wearisome problem" of the great circle is eminently concise and 

 practical, and for those who are content with spheric calculation, 

 nothing more can be desired. 



8pon_ after Raper's work appeared, Mr. J. T. Towsou, examiner in 

 navigation at Liverpool, devised a set of tables, by means of which, 

 and an ingeniously contrived diagram called a " linear index," together 

 with the aid of dividers and scales, he so greatly simplified the matter 

 as naturally to affect the commerce of the country, inasmuch as voyages 

 which formerly occupied nearly 150 days were principally by means of 

 great circle sailing, and, together with improvements in ship-building 

 [CUIVKB], performed in about 70 to 80 days. Hence the subject has 

 become one of large pecuniary moment ; and it must here in justice to 

 Mr. Towson be stated, that he generously presented to the Admiralty 

 {* public use the tables which had been constructed by him through 

 years of very great labour. He has subsequently been enabled to 

 further facilitate the question by adding to his tables, in 1854, a column 

 containing the means of ascertaining at once the distance between a 

 ship and her destined port. 



Various attempts have been lately made to supersede these tables : 

 one of these deserves particular mention, not only from the elegance of 

 the means employed, but from its leaving so little to be desired, 

 although that little was important. It 'occurred to the Rev. Hugh 

 Godfray, M.A., and to a merchant captain, Mr. Bergen, at about the 

 same period, that a chart constructed on the gnomonic projection 

 [GltOMoxio PROJECTION] would at once show the great circle track by 

 laying any straight edge along the two given places : this certainly 

 shf >wa ( the track with great accuracy ; but here again the aid of a second 

 diagram, formed, too, by curves which convey at sight no elucidation of 

 principles, was required in finding the " course and distance." 



I '"pillar errors exist on this question which are worthy of special 

 notice. Navigators are accustomed to use charts constructed on 

 Mercator's projection, wherein all bearings are taken as straight lines, 

 ami these straight lines cross all the meridians at the same angle, and 

 therefore offer a convenient mode of sailing and a ready means of find- 

 tag a course and distance ; but from reasons already given, as explained 

 in applying a thread to a globe, the same error in actual distance must 

 exist on M creator's charts, where the parallels are represented as straight 

 lines, as are found on the surface of the globe itself; for a parallel of 

 latitude in neither case exhibits the nearest track between two places 

 lying on it : therefore, if we wish to show on a Mercator's chart the 

 nearest distance between such two place*, it can only be represented by 

 a curve, and as a mathematical line is that which is the nearest distance 

 between two points, those who forget that the straight line- 

 Mercator's chart are, to answer a specific purpose, themselves actually 

 AbtoriioM, are liable to doubt the soundnew of the principle of great 

 circle tracks. 



Ami, again, a multitude of navigators at this day deny the possibility 

 of sailing on a great circle curve, because, say they, such would require 

 a continual change of course. As well may it be said that, because of 

 the tliHicultii* attending the qxiadrature of the circle, the use of the 

 in onlinary mathematical computations is fallacious. This 

 widely existing misapprehension would at once be demolished were 

 this method of navigation called "tangent sailing ;" such it really is ; 

 and the change of name was first proposed to the astronomer-royal in 

 1867 by Mr. Haxby : for it is the pectilar property of great circle soiling 

 that, in contradistinction to Mercator's, no two meridians are crossed 

 at the same angle. All that need be done, therefore, by a navigator is, 

 to sail at near to kit yrtat circle track <u convenient, and each Kparatt 

 course will be a lanyent to hit tract; and the shorter those tangent 



courses can be made the more will the duration of a voyage be dimi- 

 nished. But where a method is used, the principles of which are little 

 understood (for the terms lat. of vertex, long, of vertex, fto., suggest a 

 difficulty to the untrained student), a ship standing too long on one 

 course is liable to be found hundreds of miles northward or southward 

 of her desired position ; and this' will be found generally to arise from 

 the captain's using too frequently during the passage the same latitude 

 of vertex with which he started, and ON We& lie miniated kit counn 

 for Ike voyage before Itann;/ England. The following figure will illus- 

 trate this. It is the memorable and unexaggerated track of a celebrated 

 clipper across the Atlantic to England in the autumn of 1866, one of 

 the then shortest passages on record. 



In the above it will be seen that on the ship's being found at c (at 

 some distance from the dotted great circle A F between the two places), 

 she was, to save calculation, hauled up for the great circle track, instead 

 of being navigated on a newly-found track, and with, of course, a newly- 

 found " latitude of vertex " in the tables used ; while, on arriving at , 

 whither a heavy swell and &.K. wind had driven her, the captain aban- 

 doned his former track, and, prudently forming another, as at E r, 

 completed his brilliant passage upon it with credit. 



From this it appears that facilities were wanted whereby to further 

 simplify the finding of a great circle course and distance ; and as the 

 astronomer-royal, the Trinity Board, and the Local Marine Board of 

 London, and the highest authorities, approve of the use of the 

 " spherograph " as the readiest and most intelligible means of navi- 

 gating on a great circle, a case in illustration of its applicability is 

 given below. 



If we take two hemispheres on the stereographic projection, each 

 having the usual meridians and parallels drawn thereon, and attach 

 them so that they revolve concentrically, the upper one being made of 

 some transparent material, we have the powerful patented instru- 

 ment called the " spherograph." Its use in spheric navigation is as 

 follows : suppose a ship to be in latitude 60" N., and bound to a 

 port which is in lat. 10 N. and 60 difference of longitude westerly. 

 The fijure 2 will show the problem as tet by the spherograph, in which 

 the dotted lines ore supposed to be teen through the upper sphere. 

 The only manipulation required was the moving the under pole P to 

 the ship's latitude, EQ being the equator. Then PD would evidently 

 be the difference of latitude, and D x the difference of longitude, while 

 p x would give at once the great circlet rack, and the angle x p D would 

 show at once the course to be sailed; and counting the dotted parallels 

 of the under nphere which cross P x, we evidently read off the number 

 of degrees in the distance between p and x, which multiplied by 60 

 gives the nearest distance in geographical miles. Hence the course 

 x p D (measured at 90 from the angular point I'), or at c B, would be 

 about 724 (or S. 724 W., because the diff. of lat. and diff. of long, are 

 southerly and westerly by question), and the distance x P = about 684 

 x 60 = 8810 miles. 



Fig. J. 





Suppose, in addition , the ship, when next able to ascertain her p. 

 was found to be in latitude 40 (instead of 60), and having only 30 of 

 ongitude to make. We should now, as in fig. 8, set the under i 

 10* north latitude and (omitting all unnecessary lines for the cake of 



