FOR FACILITATING GREAT-CIRCLE SAILING. 'Jl7S 



It may perhaps excite surprise that so obvious a solution should not have presented itself 

 before, especially as this projection had already been applied to celestial maps, and even, as I 

 have since learnt, to terrestrial maps on a small scale* — maps, however, intended only for the 

 study of the geography of the globe, and not at all adapted to the wants of the mariner, — 

 they were not charts, and there was no provision made for the determination of the course 

 from one point to another. On Mercator's charts the Rhumb course is the angle made by the 

 track with the meridian, and is seen at once by drawing a parallel through the nearest 

 compass-rose, of which several are always traced on the chart ; but this is not the case with 

 charts on the Central Projection : a N.E. course, for instance, will not bisect the angle 

 between the north and the east although these are at right angles to one another when the 

 Pole is the centre of projection, nor yet will the N.E. course make a constant angle with the 

 meridian lines; its value will be ever changing with the latitude, and the same will be true of 

 all other courses. 



Now in celestial or in geographical maps the courses are of no consequence, it is more 

 important that those stars or towns which are on the same great-circle should be readily 

 found. But, to the mariner who must guide himself by the compass, any chart which does 

 not at once indicate the Rhumb course is almost useless. Mercator's chart gives at once a 

 track (though not the shortest) and the course to be steered ; and these are the two elements 

 absolutely necessary, — without the track the ship might run into dangers, and without the 

 course the track cannot be followed. 



This may perhaps explain why such a simple projection as the central which satisfies one 

 of the conditions of the Great-circle Problem, and that condition the very important one of 

 indicating the direct and shortest track by merely drawing a straight line, should never have 

 been applied to charts. It does not give the series of courses to be followed, nor even the 

 first one on which to set out. 



The various methods hitherto proposed for simplifying Great-circle sailing have all been 

 directed to the determination of these courses, and where any attempt has been made at 

 drawing the track it has always been on a Mercator's chart. My own ideas at first took the 

 same direction, and I aimed at inventing some instrument which would trace the track on 

 Mercator's chart by a continuous motion ; but I gave this up as soon as it occurred to me to 

 try the central projection. By the addition of a diagram I have made this projection answer 

 all the conditions of Great-cii-cle sailing with as much, if not more, facility than Mercator's 

 chart does for sailing on a Rhumb : the track is seen a straight line, and this being drawn, 

 the various courses and the distances to be run upon each are obtained, as also the distance 

 from the ship to her destination, by a mere inspection of the diagram ; and the chart can be 

 used like an ordinary one for pricking off the ship's place day by day. 



Windward Sailing. 



I have stated before that the advantages of Great-circle sailing were not confined to 

 steamers, and that sailing vessels when beating against a head-wind might derive still more 

 benefit from it. 



• Published by the Society for the Diffusion of Useful Knowledge. 



35 — 2 



