Great Circle Sailing

Zetetic Astronomy, by 'Parallax' (pseud. Samuel Birley Rowbotham), [1881], at sacred-texts.com

GREAT CIRCLE SAILING.

AMONG landsmen a great amount of misconception prevails as to what is really meant by the so-called "great circle sailing;" and notwithstanding that the subject is very imperfectly understood, the "project" or hypothesis--for it is nothing more--is often very earnestly advanced as an additional proof of the earth's rotundity. But, like all the other "proofs" which have been given, there is no necessary connection between the facts adduced and the theory sought to be proved. Although professional mariners are familiar with several modes of navigation--"parallel sailing," "plane sailing," "traverse sailing," "current sailing," "middle latitude sailing," "Mercator sailing," and "great circle sailing," the "Mercator" and "great circle" methods are now the favourites. Nearly all the above systems necessitated the sailing by, or in relation to, Rhumb-lines, or lines at right angles to the meridian lines; and whether the earth is a plane or a globe, these are not geometrically at right angles to lines of latitude, except at the equator. Hence Mercator's projection, on account of its lines of latitude and longitude being square to each other, has been almost universally employed. But previous to the general adoption of Mercator's plan, many leading navigators saw that Rhumb-line sailing upon a globe was practically a series of small circles, and conceived

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of a method very similar to that which is now called the "great circle" system. As early as 1495 Sebastian Cabot suggested the adoption of this method. It was also advocated in 1537 by Numez, and in 1561, and subsequently by Cortez, Zamarano, and others. After lying dormant for a long time, the system was revived by Mr. Towson, of Devonport, who read a paper before the Society of Arts, in May, 1850, and afterwards presented his "tables to facilitate the practice of great circle sailing," to the Lords Commissioners of the Admiralty, who "ordered them to be printed for the use of all mariners."

Many persons suppose that the words "great circle sailing" simply mean that the mariner, instead of sailing in a direct line from one place to another, on the same latitude, takes a circuitous path to the south or north of this direct line, where the degrees of longitude being smaller, the distance passed over, although apparently greater, is actually less. It is then falsely argued that as "the greatest distance round is the nearest path," the degrees of longitude must be smaller, and therefore the earth must be a globe. This is another instance of the self-deception practised by many of the advocates of rotundity. It is really painful to reflect upon the manner in which a merely fanciful hypothesis has reduced its advocates to mental prostitution. The poor dawdling creature, who vaguely wanders in search of anything or everything which will satisfy her longings, is only a type of the philosophical wanderer who seeks for, and pounces upon, whatever will prove, or only seem to prove, his one idea--his uncontrolled and often uncontrollable longing for something to confirm

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his notions, and satisfy his desire to be wise and great. The motive which actuates the greater number of modern philosophers, cannot be less or other than the love of distinction. If it were a love of truth and of human progress and welfare they would scrupulously examine the premises on which their theories are founded. But this the advocates of the earth's rotundity and motion have seldom or never done. There is no single instance recorded where even the necessity for doing so is admitted. Hence it is that whilst to question the groundwork is forbidden, they abruptly seize upon everything which gives colour to their assumptions, although in many cases neither pertinent nor logically consistent. In the case before us the contraction or convergence of the degrees of longitude beyond the equator is unproved; and again if they were convergent there could not be a single inch of gain in taking a so-called great circle course between any two places east and west of each other. Let the following experiment be tried in proof of this statement. On an artificial globe mark out a great circle path, between say Cape Town and Sydney, or Valparaiso and Cape Town. Take a strip of sheet lead, and bend it to the form of this path; and after making it straight measure its length as compared with the parallel of latitude between the places. The result will fully satisfy the experimenter that this view of great circle sailing is contrary to known geometrical principles. Strictly speaking, it is not "great circle sailing" at all which Mr. Towson and the Lords of the Admiralty have recommended. The words great circle are only used in comparison with the small circles which are described in sailing upon a Rhumb-line track.

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"The fundamental principle of this method is that axiom of spherical geometry, that the shortest distance between any two points on the surface of a sphere lies on the line of a great circle; or, in other words, of a circle passing through the centre of a sphere. But maps and charts, being flat representations of the surface of a globe, are of necessity distorted, and are only correct near the equator, the distortion increasing as the poles are approached; and hence it follows that the course which on the globe is the shortest, is on the chart made to appear very much the longest, and the reverse. This was clearly shown to be the case by the comparison on a chart and on a globe of the course between Van Dieman's Land and Voldivia, on the western coast of South America: the course, which by the chart appeared to be a straight line, when laid down upon the. globe was found to be very circuitous, whilst the line of a great circle, cutting the two points, appeared on the chart as a loop of great length." ¹

"Mercator and parallel sailing conduct the ship by a circuitous route when compared with the track of a great circle." ²

In nautical language Rhumb-line sailing, which was almost universally practised before the recent introduction of great circle sailing, consists in following parallels at right angles to the meridian lines, and as these meridian lines are supposed to be convergent, it is evident that the course of a ship so navigated is not the most direct; a great circle path is one at angles less than 90° north and

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south of the meridian. If the reader will draw a series of Rhumb-lines on a map of "the globe," he will at once see that the course is circuitous. But if he draws lines at a slight angle north in the northern, and south in the southern region, to the above-named Rhumb-lines, he will readily notice that the ship's course is more direct, and therefore the mariner adopting the so-called "great circle'' method, must of necessity save both time and distance, but only in comparison with the Rhumb-line path. It is not absolutely the shortest route; as the earth is a plane, the degrees of longitude in the south must diverge or expand, and spread out as the latitude increases; and the parallels or lines of latitude must be circles concentric with the northern centre. Hence there is in reality a still shorter path than either the Rhumb-line or the great circle course.

This will at once be evident on trying the following simple experiment. Place a light, to represent the sun, at an elevation of say two feet on the centre of a round table. Draw lines from the centre to the circumference to represent meridian lines. Mark any two places to represent Cape Town and Melbourne; now take any small object to represent a ship sailing from one of these places to the other, and, on moving it forward, keeping the light at the same altitude all the way the line of latitude or path of the ship will be seen to be an arc of a circle, which practically is a great circle route, whilst the Rhumb-line and greater route would be represented by a series of tangents to the meridian lines between the two places. The nearest route geometrically possible is the chord or

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straight line joining the ends of the arc which forms the line of latitude. Let this line or chord be drawn, and all argument will be superfluous, the proposition will be immediately self-evident.

Thus we have seen that great circle sailing is not the shortest route possible, but merely shorter than several other routes, which have been theoretically suggested and adopted; and to affirm that the results are confirmatory or demonstrative of the earth's rotundity, is in the highest degree illogical.

Footnotes

282:1 "From "A Paper on the Principles of Great Circle Sailing," by Mr. J. T. Towson, of Devonport, in the "Journal of the Society of Arts," for May, 1850.

282:2 "Treatise on Navigation," p. 50. By. J. Greenwood, Esq., of Jesus College, Cambridge. Weale, 59, High Holborn, London.