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pole. The parallel of 48° of latitude is but two-thirds the diameter of a great circle, and the parallel of 60° is only one-half the size; and it is on these parallels that the mariner steers his ship, when his port is east or west of his ship, if he adopts any other system of navigation than that of great circle sailing. If he sails north or south, he sails on the arc of a great circle, whatever system he employs, because the meridians, or north and south lines, are great circles dividing the earth's surface into equal parts. Also the mariner who sails east or west on the equator, sails on the arc of a great circle, the equator being a great circle; but, in all other cases the mariner who sails by Mercator's chart takes his ship by a circuitous route. If he does not sail in the direction of one of the cardinal points, he sails on what is technically called a rhumb line; which on the chart is represented as a straight line, but on the globe is a spiral, making endless revolutions round the poles. Thus Mercator's sailing conducts the ship by a circuitous route, as compared with great circle sailing. It was adopted on account of its simplicity, and not on the supposition that it conducted the vessel by as short a route as great circle sailing did. By Mercator's sailing a ship may be navigated by one course throughout the voyage. For instance, if the ship and her port be both in the latitude of 50° north, and the port west of the ship, she could then reach her port by sailing a due west course throughout the voyage. But not so by great circle sailing; she would then have, if in north latitude, first to steer north of the west, and constantly vary her course to the left, till at length she would reach her port by a south-westerly course. This fact requires explanation; the ordinary mariner cannot be made to comprehend how it is possible that, by varying his course continually, he will reach his port by a shorter track than by sailing one course all the voyage. It is generally supposed, if the place A be west of B, that B must be east of A. This would be the case if this earth were a plane, but it cannot be so on the surface of the globe. East or west are local or relative terms; they have no existence in space, but refer only to the locality in which we are situated. If I say that A is west of me, I imply that the position of A is at right angles to the meridian, or north and south line of the place in which I am situate. Now if all the meridians were parallel to each other, then a line at right angles to one would be at right angles to all. And the meridians of all places are represented by parallel lines on the chart; and so it is that, by referring to the chart, it appears that if A be to the west of B, then B must be the east of A. But on the globe, the meridians, or north and south lines, meet at both poles in angles varying with the latitude and the difference of longitude; conse

quently, a direct line which cuts one meridian at any angle cannot cut any other meridian at the same angle. Now, supposing that either of the audience and myself were at equal distance from the North Pole, the pole between us, and in sight of each other, we should then be both north of each other, because each would be situated in the direction in which the North Pole was situated. Thus it must be when the principles of great circle sailing are admitted; but, according to Mercator's principles, we should be east and west of each other, being both on the same parallel, which on the chart is represented as a straight line, running east and west. Then, we find that the great circle course is the direction we see any object-the course the crow flies; it is the real direction of the object, if in sight; it is the direction in which is situate the base of a mountain, when we discern its summit in that position. It is also the position of any place at which a heavenly body is vertical, at the time in which that heavenly body is seen from any other place. For instance, the island of St. Salvador, or Cat Island, has, at a certain hour of the sidereal day, a star, called Alpha Arietis, nearly vertical, or overhead. Liverpool has also another star, called Beta Draconis, nearly vertical, at a certain time of each sidereal day. Now the position in which we, at these times, see these stars is the real position of the place over which it is vertical at the time. If, then, we sail from Liverpool for St. Salvador, we should see Alpha Arietis bearing west; as we proceeded on our voyage, its position with regard to the ship's place would veer round to the south, till at length we reached our port at last by a course S.W. by S. During the whole of this voyage, we should see the vertical star of St. Salvador right before us; and the vertical star of Liverpool right astern; and in returning, by great circle sailing, we should observe the vertical star of Liverpool right a-head, and the vertical star of St. Salvador right astern; so that it is evident that though we were obliged, in adopting great circle sailing, to alter continually our course by compass, still we sailed directly from one port to the other. Not so, however, if we adopted Mercator's sailing. We should then start from Liverpool, with the position of the vertical star of St. Salvador to the right 28°. The difference between the position of our port and our course would daily decrease, until we arrived at our destination. Thus, again, we find that, by Mercator's sailing, we sail one course by compass throughout the voyage; but, by great circle sailing, we constantly vary our course; still it is by great circle sailing we steer directly to our port, while by Mercator's sailing we arrive at our destination by a circuitous route.

It was not from the want of a conviction of the advantages connected with great circle sailing that, till of late, it had been so rarely used by practical men, but from the tedious length and embarrassing nature of calculations requisite to determine the series of ever-changing courses which a vessel must pursue, in order to follow the track of a great circle.

In order to obviate this evil, I invented and computed a set of tables, in 1847, which the British Admiralty did me the honour to publish, by means of which the finding of these courses in succession is reduced to an affair of inspection. By this means I have had the honour of introducing great circle sailing into general use; from which circumstance it has been assumed by some, erroneously, that I have laid claim to the invention of great circle sailing, and this supposed assumption of mine has been apparently confirmed by the fact of my laying claim to the honour of being the originator of composite sailing, which is often denominated great circle sailing, and to which we shall hereafter refer. In order to clear myself from the charge of assuming the honour of being the inventor of great circle sailing, with which I have been frequently taunted, I will read from one of the most extensively-circulated works ("Weale's Rudimentary Treatise") a quotation from a lecture delivered by myself to the Society of Arts :

"From a communication by Mr. Towson to the Society of Arts, in May, 1850, it appears that, in 1495, Sebastian Cabot projected a voyage across the Atlantic on this principle, with a view to the discovery of a north-west passage to India. In 1537, in the first treatise on Navigation, the system was treated of by Numez. In 1561, Cortez, and after him Coignet and Zamaramo, advocated the adoption of great circle sailing."

From these observations it will be evident that I am not chargeable with the desire to claim the unmerited honour of being the inventor of great circle sailing.

Before we advance further in the investigation of the subject, it will be necessary to make a few remarks on the nature of Mercator's sailing. In order that the sphere should be drawn on a plane, it is necessary to distort the surface. Those regions towards the pole have to be distended for this purpose. In thus distorting the earth's surface, the shortest route is made to appear as circuitous; and the circuitous route, by a parallel of latitude, is represented by a straight line. If two places do not differ in longitude more than 30 or 40 degrees, the error of Mercator's chart is not very perceptible. In crossing the Atlantic, it differs from the great circle route not more than 100 miles in practice;

consequently, whilst navigation did not extend much beyond the Atlantic, and was confined principally to regions in which the track is required to be modified, on account of winds, the disadvantage of using Mercator's sailing was not practically experienced. But the length of our voyages have since been greatly extended; more than two hundred vessels from this port alone have, in the last year, sailed on a voyage to circumnavigate the earth. The Pacific is now oftener crossed than the Atlantic was in the time of Mercator and Wright, so that ten times the amount of saving can be now effected in the length of the voyage. From Liverpool to New York, scarcely a hundred miles can be saved; whilst, in a voyage from Panama to Shanghai, a saving of 1200 miles is effected.

But this is not all the advantage to be derived from a knowledge of the principles of great circle sailing in the Pacific. Previously to 1847, the route proposed for steamers, between the west coast of America and China, was from Panama, coaling at the Sandwich Islands-a distance of about 9,500 miles, against 5,000 by the route known by the name of Lieutenant Maury's track. By the chart, the Panama route appears the better; but, on examining the globe, the error of the chart is made apparent. We need not, however, select as our illustration a track in which our American friends are more interested than ourselves. There is a route which might be daily traversed by Liverpool sailing ships, which, as a case of great circle sailing, may be adduced as an example of its value. Many ships that take out freights of deals, slate, or bricks to Australia, call, on the homeward voyage, at the Chincha Islands for a cargo of guano. The route usually taken is by the north of New Zealand-the most direct, as appears by the chart, but not so if we consult the globe. The distance by the great circle is nearly 1,000 miles less. But this is not the only advantage. The great circle takes the ship into regions in which the winds are more favourable, and, in other respects, more advantageous for navigation. (See plate No. 1.)

A friend of mine was speaking of great circle sailing, a few days since, when he remarked that he did not much value it, because the mariner should consult the winds, and be rather guided by them, than be induced to adopt the great circle route in shortening his distance. I agree with him that the greatest value should be attached to favourable winds. No practical man would advocate the adoption of any route without considering the winds that prevail in the region through which he is required to navigate; but I contend, that, with all the knowledge of the winds that I hope may hereafter result from the system introduced by Lieutenant Maury, still the mariner could not avail himself

of the advantage of such knowledge, if ignorant of the principles of great circle sailing. Where is the mariner, whose knowledge of this earth is derived from a chart of Mercator's projection, who would ever think of sailing to the southward so high as the 54th parallel, in order to reach the Chincha Islands? For the sake of favourable winds, the passage through Cook's Strait was proposed, but never would it have been suggested to enter the regions of the westerly trades, except by one who understood the principles of great circle sailing.

But I will now refer to another example, to prove the necessity of a knowledge of this earth as a globe, in order to avail ourselves practically of any acquaintance with the nature of the winds that prevail in various. regions of the ocean. Great circle sailing does not effect so much saving of distance under some circumstances as under others. If we have the equator between the ship and her port, a considerable saving in distance cannot be effected: thus, in a voyage between Panama and Australia, the difference between Mercator's track and the great circle route is only 170 miles, if it were practical. But New Zealand comes in the great circle track, so that there are three routes from which the mariner can make his choice, neither differing more than 100 miles from the other; they are the rhumb, or Mercator's track, the great circle route by the north of New Zealand, and the great circle by the south of New Zealand. These routes, separate from each other 2,000 miles and upwards, have winds of a very different character prevailing. I was consulted as to the best route a steamer might take in sailing from Panama to Australia and back. Had I known no more of the earth's surface than that which I derived from Mercator's chart, I should have had the difficult problem to solve of balancing winds against distance. But the knowledge of the earth's true surface made the question easy of solution. I find by the south of New Zealand the most favourable winds that blow for a voyage from Australia to Panama. From Panama to Australia, by the great circle, north of New Zealand, we get as favourable winds as by the rhumb track; and, although we save only 70 miles of distance, we avoid the innumerable dangers which lie in the Mercator's track, in which we should have been entangled in the Low Archipelago, in Dangerous Archipelagoominous name-amongst coral reefs without number, atolls, lagoon islands, innumerable rocks, and unknown islands. This perhaps forms the most striking illustration of the value of great circle sailing, in giving us the choice of more than one route. (See plate No. 1.)

There was, however, one objection that existed some years since to the value of great circle sailing. It was said that, unless the distance

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