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

in longitude of two places is considerable, great circle sailing fails to save much distance; and, on the other hand, when the difference of longitude is very great, this sailing cannot be adopted, and thus the sailing withholds its chief advantage in practice when its value in theory is greatest. Thus, in an Australian voyage, we should save more distance than in any other; but from the nature of great circle sailing, it is for that purpose impracticable, since it would lead the ship directly across the south pole.

This I found to be the most formidable obstacle seven years ago, when I attempted to devise means of bringing great circle sailing into general use. For the purpose of removing this difficulty, I endeavoured to solve this problem :-If it be undesirable for the mariner to approach the pole nearer than any given latitude, how can he sail by the shortest route without violating this restriction? This problem I solved by the invention of a new sailing, which I call "composite sailing."

To explain its nature, and demonstrate the fact of its being a complete solution of this problem, we will have recourse again to the principle of the carpenter's chalk line. This line we have found to give us the shortest track, subject to restrictions. It gives us, absolutely, the shortest track over a plane; but on the surface of a globe, restricted by the rotundity of the surface, it describes the arc of a great circle, that being the shortest track over such a surface. In composite sailing we have a second restriction, not altogether a physical one, but rather a prudential one-we ought not to go nearer the pole than a given latitude. Let us, in the artificial globe, substitute a physical restriction for the real prudential one, by having the parallel raised above the surface. Now the string, when subject to tension, describes that which we call the "composite track." It is the sailing made by Australian ships that have made rapid passages, and is frequently denominated great circle sailing.

I have been charged with something like presumption in laying claim to the honour of being the inventor of a sailing. During the past summer, this matter was the subject of a correspondence with Lieutenant Maury. I may perhaps be allowed first to observe that my remarks, which induced this correspondence, were made in consequence of having read this paragraph in a Liverpool newspaper, headed "Lieutenant Maury's Great Circle Route to Australia," which is nothing more than a description of a voyage similar to those already accomplished by Boyce, Forbes, and others; and I now feel thankful to Mr. Rankin for having given me the opportunity to establish for Godfrey, Boyce, Forbes, and others, the honour

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due to them, which would otherwise have been claimed by some of the captains of the American clippers; and, if I am entitled to any honour as being the inventor of composite sailing, and had then failed to establish my claim, it might hereafter have been assigned to Lieutenant Maury. The following paragraph is extracted from that gentleman's own book, published but last year, in which, after referring to the rapid voyages which might be accomplished by this route, he concludes by adding" This opinion may be rash, or the expression of it may seem like a boast;" so that he fully implies that he claimed the originality of the idea for himself. I will now, with your permission, read that part of my letter to Lieutenant Maury which that gentleman omitted to read at the Town Hall :

In a late edition of your sailing directions, you have given instructions for making a speedy passage to Australia and back, and these have been reprinted in Liverpool as your great circle route. This route is, however, that which, in my work before alluded to, is termed ' composite sailing,' great circle sailing being inapplicable to such voyages. This sailing was original with myself. The name was never employed in navigation till the admiralty published it in the work of which I was the author. When first my ideas of the subject were submitted to men of science, the principle on which this sailing was founded was condemned as being incorrect. For years I had to combat with those who contended that this sailing was a fallacy, and, in demonstrating its accuracy, I received most valuable assistance from my friend Mr. Rae, who displayed much mathematical ability in establishing the fact of the truth of the principles on which composite sailing is founded. In May, 1850, I delivered a lecture on this subject at the Society of Arts. I had then thought that it was fully established; but after this I had letters from gentlemen who stand high as mathematicians, written under the impression that I was in error. At length the truth of its principles was established, and it has taken its stand in most new works as a 'sailing,' and now, because I have said this is my proposal and not yours, your friend Captain M'Kay, of the 'Sovereign of the Seas,' has stated that 'composite sailing' does not possess sufficient originality to entitle me to the honour of its being considered as an invention, because it is but a simple modification of the principles of great circle sailing as known for three or four centuries-old as the hills.' If so simple, how came it to pass that I had so much difficulty to convince my brother mathematicians of its truthfulness? It is simple, no doubt in practice, for the courses are taken out from my tables by inspection; but, certainly, my having furnished the means for the navigator to