should be permitted to act as pilot to any vessel unless he can produce a certificate of competency granted to him by properly constituted authority. We are not sanguine enough to expect that our views will be at once carried into effect, but we take the opportunity of reiterating opinions which have been before expressed in this journal, feeling sure that the time will come when they will be acted upon.

MERCATOR'S CHART.

ITS HISTORY, USE AND ABUSE.

(Continued from page 291, April No., 1883.)

T has been shown that on Mercator's chart the shortest distance between two places appears as a straight line, but that the rhumb oblique to the meridians, and cutting them at equal angles is really

a curve continually approaching the pole. It may, however, be shown experimentally on a terrestrial globe, by stretching a piece of thread evenly between, the same two places, that the shortest distance is not a straight line, but part of a circle, and in order to arrive at either place from the other by such a route, the direction (or course) must be constantly varying-unless indeed both places are on the equator, or on the same meridian, in which case the track by the great circle and the rhumb coincide. The fundamental theorem of what the old navigators usually called "globular" sailing is therefore this-the arc of a great circle joining two points on the surface of a sphere is the shortest distance between them; and on no other than on a great circle course does the ship steer for her port as if it were in sight.

All the computations in great circle sailing are effected through the methods of spherical trigonometry. Into these it is not intended to enter, but it may be well to indicate a few of the principal terms connected therewith. The equator, which is a great circle, bisects every other great circle on the carth's surface, and there must

necessarily be two points in every such circle equidistant from the equator and at the same time furthest removed from it; each of these points is called vertex; and the latitude of vertea, which is the highest latitude attained in sailing on a great circle, is the nearest approach to the elevated pole. The meridian cutting the great circle at the vertex is the meridian of verter; and the longitude of or from vertex is the arc of the equator intercepted between the meridian of any place and the meridian of vertex. The angle of position, which is the first great circle course from a place, is the angle at the place between the plane of its meridian. and the plane of the great circle; and the distance is the length of the arc of the great circle expressed in nautical miles.

The following diagram may be taken as showing the difference between the great circle and the rhumb line as delineated on Mercator's projection. Here, as is always the case, the rhumb (or loxodromic spiral) between A and B is a straight line, and the arc

of the circle is a curve (dotted line with V as vertex), indicating an apparently greater distance between the two places. A ship sailing on a great circle between two places on the same side of the equator is always in a higher latitude than if she had sailed on the rhumb line, and both tracks coincide at their extremities.

In the clear language of RAPER, "the course on the rhumb line, from one of two places to the other, is exactly the opposite of the course to that place from the other; while on the great circle these courses are very different. The ship, while on the rhumb line, is always changing the direction of her head with respect to her port, for which she never steers exactly until it is in sight, because this track cuts all the meridians at the same angle, and the meridians themselves are not parallel to each other. But on a

great circle she steers directly for her port, while, as the angle made by her track with the meridians is perpetually varying, the direction of her head appears by the compass to be continually changing. The great circle track, accordingly, is the only one on which the ship nears her port by the whole amount of distance which she makes good from instant to instant."

The great circle and the rhumb line differ most widely from each other in high latitudes and between places on nearly the same parallels. When the two places are on opposite sides of the equator, the great circle and the rhumb line intersect each other, and the difference between them is not so perceptible.

Steamers being to a certain extent independent of winds and currents can take a great circle route which is impossible to sailing ships, but the latter may often shorten the distance when adverse winds are encountered, by taking a course anywhere between the great circle and the rhumb line. When the places are widely separated, as in high southern latitudes, a great circle course is impossible to steamer and sailing ship alike, but advantage may be taken of a composite route, formed by sailing partly on a great circle and partly on a parallel.

Towson's" Tables to Facilitate the Practice of Great Circle Sailing" obviate the necessity of computation; and are equally useful, with or without the index chart. GODFRAY'S chart on the gnomonic projection shows the great circle course as a straight line, and the points for transfer to Mercator's chart can readily be taken off it. Where neither is at hand the navigator can speedily determine the practicability of the great circle route by Sir G. B. AIRY'S method for sweeping an arc of a circle, on Mercator's chart, which approaches very nearly to the correct projection of a Great Circle on one side of the Equator: the sweep of the arc is accomplished by attending to the following precepts adapted to the table which accompanies them.

Rule-1. Join the two places by a straight line. Find its middle. Draw thence a perpendicular to that line on the side next the Equator, and, if necessary, continue it beyond the Equator.

2. With the middle latitude (between the two places) enter the following table, and take out the corresponding parallel.

3. The centre of the required sweep will be the intersection of this parallel with the perpendicular.

Facility in delineating the great circle on the chart has this advantage; when, from adverse winds or other causes, a vessel has to deviate from the track, the great circle may, at any moment, be struck off anew, such that it shall pass through the actual position and the port to which the vessel is bound.

When, thirty years ago, the clipper ships were making their rapid voyages to Australia and New Zealand on the composite route, great circle sailing was spoken of as a novelty; it was, in fact, only a resuscitation of a neglected branch of navigationneglected owing to the apparent convenience of Mercator's chart. Navigators before, and for some time subsequent to, Mercator's day preferred great circle to rhumb, sailing. Probably few of our readers have heard of "The Seaman's Secrets," by John Davis, a second edition of which was published early in the 17th century (1607). The following extract shows at once the estimation in which great circle sailing was held by the old navigators, and the quaint diction in which they expressed themselves.

What is the great Circle nauigation?

Great Circle nauigation is the chiefest of all the 3 kindes of sayling, in whom all the other are contained, and by them this kinde of sayling is performed, continuing a Corse by the shortest

T

distance betweene places, not limited to any one Corse, either horizontall or paradoxall, but by it those Corses are ordered to the full perfection of this rare practise, whose benefites in long voiages are to great purpose, ordering & disposing all horizontall trauerses to a perfect conclusion; for there are many changes of horizontall and paradoxall Corses in the execution of this practise, so that vpon the shifting of a wind, when that

it may seeme that you are forced to an inconuenient

Corse by the skill of great Circle sayling, that Corse shall be found the shortest and onely proper motion to perfourme your voiage. And also when with fauourable windes the Pylote shall shape a Corse by his Chart or Compass paradoxall, as the best meane to attaine his porte, he shal by this kinde of sayling finde a better and shorter Corse, and by sufficient demonstration prooue the same, so that without this knowledge I see not how Corses may be ordered to their best aduantage; therefore sith by it perfection of sayling is largely vnderstood, & the error likewise most substantially controled, it may of right chalenge the chiefest place among the practises Gubernautick. The particularities whereof, if I should by an orderly methode labour to expresse, it would be a discourse ouer large for this place, and as I thinke troublesome if the premises be not well vnderstood.

The conception of a variation chart is not of recent date; the cosmographer Alonzo de Santa Cruz, from very imperfect observations, constructed such a chart in 1530. More than a hundred years later the astronomer, Edmund Halley, undertook, at the expense of the government of the day, three voyages into the Atlantic for the verification of certain physical data, the result of which was the production of a general variation chart on which the points where the navigator had found the same amount of variation were connected by curved lines. Towards the end of the last and the beginning of the present century, William Mountaine, F.R.S., constructed, from more than 50,000 actual observations made in different parts of the world, a variation chart which was sold by Messrs. Mount and Page at their nautical warehouse on Tower Hill. During the present century charts giving various