104 



KNOW^LEDGE ♦ 



[March 1, 1887 



pursue, for it crosses the meridians (or north and south 

 lines) on his chart at precisely the angle at which the 

 course he is to steer should be inclined to the north and 

 south line through the ship. He can measure the angle on 

 his map at once, without any construction for correcting 

 it in any way ; and then he can direct his course on the 

 sea accordingly by the compass in the customary way, 

 making only the usual correction for the deviation of the 

 needle. 



But now, suppose our skip23er wishes to use some chart 

 for great circle sailing. If he takes liis usual sailing charts, 

 he can only obtain the great circle coarse by a complicated 

 construction, the actual curve which in a Mercator's chart 

 re|)resents a great circle course on the earth belonging to a 

 class of curves whose properties can only be treated by the 

 higher mathematics. Sir George Airy calculated a table, 

 long ago, which was intended to facilitate the construction 

 of approximate great circle courses on Mercator's charts ; 

 but to the use of this table the same objections apply as 

 to the use of Towson's tables for calculating the whole 

 course. 



Is there, however, no form of chart by which the great 

 circle course may be drawn, as in Mercator's charts the 

 seaman draws the rhumb course, as a straight line ? There 

 is the Onomonic Projection, by which this maybe done; 

 and if the seaman could turn to a gnomonic map containing 

 his port of departure — or his position at any given moment 

 — and his haven, all he would have to do in order to deter- 

 mine his proper track would be to draw a straight line from 

 one ])oint to the other. 



But there are two very serious objections to the use of 

 gnomonic charts. In the first place no gnomonic chart can 

 conveniently show more than a small portion of the surface 

 of the globe — for the scale increases enormously as the dis- 

 tance from the centre of the map increases. How enormous 

 the scale becomes, far beyond the limits to which many 

 projections can be carried, will be inferred from this, that 

 to show a hemisphere on this projection a sheet of infinite 

 size would be required. (Charts of infinite size are not 

 approved of on board ship ; they would be inconvenient 

 even on the Great Eastern.) But apart from this objec- 

 tion, which is in reality fatal against the projection, there is 

 another, which would sufiice to make the course drawn on 

 s, gnomonic chart unmeaning and therefore useless to the 

 seaman. All the angles at which the course is marked so 

 simply on a gnomonic map are diflerent from the real 

 corresponding angles on the globe itself. For the shapes 

 of ail the spaces on a gnomonic chart are distorted, in 

 varying degree, according to their distance from the centre 

 of the chart. Since the essential object of a seaman's chart 

 is to show him his bearings, this objection is altogether 

 decisive, and accordingly gnomonic maps have not come into 

 use for nautical purposes. 



There is, however, another projection which, so far as I 

 have learned, has never yet been used by seamen, which 

 possesses advantages as great in relation to modern nautical 

 requirements as Mercator's projection presented for the 

 comparatively rough requirements of Mercator's time — or 

 even for much later times when, according to Commander 

 IMaury, a seaman shaped his course from England to Boston 

 so roughly as to be well content if he fetched up at New 

 York instead. According to the plan which I thus pro- 

 pose for a nautical chart, which may either bo used alone or 

 in conjunction with a Mercator's chart, a chart can con- 

 veniently show the whole globe except either the Arctic or 

 the Antarctic regions, according as the south pole or the 

 north pole is made the centre of the map. The great circle 

 course from any one point to any other point appears as the 

 arc of a circle, the only feature in which the projection is 



less simple with reference to great circle sailing than 

 Mercator's is for ihumb courses. (Though indeed a geo- 

 metrician might be disposed to say that in this lespect the 

 proposed charts have the advantage, since in a geometrical 

 sense it is much easier to describe a circle correctly than a 

 straight line.) However, this is saying little until it is 

 shown further how this circular arc is to be drawn. For 

 instance, quite a complicated construction might be necessary 

 to determine the centre and the size of the circle required. 

 Here, then, is the construction, so simple that a schoolboy 

 often could deal with it correctly. Describe a circle through 

 the ship's place, the desired haven, and the antipodes of 

 either jioint on the chart ; this may be done without the 

 trouble of any construction, simply by feeling about with a 

 pair of compasses till the light centre and opening are foun<l. 

 But if construction bo preferred, then the simple method 

 given in Euclid, Book IV., for circumscribing a given 

 triangle may be employed. This, however, is really useless, 

 seeing that in twenty seconds the trial method will give all 

 that is wanted, whereas construction may require perhaps a 

 couple of minutes for an unpractised hand, or a minute or 

 half a minute for one which is skilful in such work. 



But the chief advantage of this new nautical chart has 

 still to be mentioned. In regard to bearings, it has pre- 

 cisely the same qualities as Mercator's chart. All bearings 

 are correctly presented ; or, in other words, the circular arc, 

 pencilled from point to point, cuts all the meridians at 

 exactly the right angle, that at which the seaman's course 

 must intersect the north and south lines on the globe when 

 he is pursuing the shortest or great circle course. 



It may be asked, however, how the new chait will lend 

 itself to composite sailing, which, as we have seen, is often 

 a necessity. It does so perfectly. The problem is to describe 

 a circular arc which shall pass through the seaman's place, 

 port, or haven, and .shall touch a given parallel of latitude. 

 All parallels of latitude are concentric circles on the chart. 

 Suppose the parallel to be touched is that of 50° south lati- 

 tude ; then all that is necessary is to describe a cii'cle on the 

 chart, which shall pass through the seaman's place or haven, 

 and touch on the inside the circle representing 50° south lati- 

 tude, while it touches on the outside the circle representing 50° 

 north latitude. Nothing can be easier, because the last two 

 conditions manifestly determine the size of the required 

 circle. For any one who will draw two concentric circles on 

 a plane will find that to touch the outer one on the inside, 

 and the inner one on the outside, a circle must have a radius 

 midway in length between the radii of the two circles. The 

 centre of the required circular arc lies on a given latitude 

 parallel in the chart ; and it need hardly be said that to 

 describe an arc of given radius through a given point, and 

 having its centre on a given arc, is child's play. 



The drawing of the great circle coui'se, or the composite 

 course, as may be required, is the work of .a minute or two 

 at the outside. The interpretation of every point of the 

 course thus determined is precisely the same as in a Merca- 

 tor's chart. If the seaman has been beaten oflf his track, he 

 can describe the shortest course from his new position as 

 readily as he could describe the rhumb coui'se on a ^lerca- 

 tor's chart and interpret it as simply. 



I venture then to express with confidence my belief that 

 the new gi-eat circle .sailing charts may serve the same j)ur- 

 pose for seamen that ISIercator's chai-t served in former 

 times — saving much time, considerable expense, and many 

 lives. For further information I may say with Mrs. 

 Clrudden, " see small handbills " — that is to say, consider 

 the pamphlet accompanying the charts as issued by ]\lr. 

 Stanford. 



