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The Early History of Great Circle Sailing

Published online by Cambridge University Press:  01 July 1976

H. Cotter
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Extract

The least spherical distance between two points on the surface of a sphere is that along the minor arc of the great circle on which the two points lie. It is an easy matter to demonstrate this using a cord stretched between two points on a small globe; noting that the circle whose plane coincides with that of the cord contains the centre of the sphere and that it is, therefore, a great circle. It is a little more difficult to prove the fact analytically. The practice of sailing along the shortest route on an ocean passage—sometimes known as ‘orthodromic’ as opposed to rhumbline or ‘loxodromic’ sailing—would require the course to be continually changed (except, of course, in cases in which the rhumb-line and great circle arc coincide). This would clearly be impossible; the term ‘approximate great circle sailing’ is sometimes used to describe the techniques of following a great circle route as closely as practicable.

Type
Research Article
Information
The Journal of Navigation , Volume 29 , Issue 3 , July 1976 , pp. 254 - 262
Copyright
Copyright © The Royal Institute of Navigation 1976

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References

NOTES AND REFERENCES

1 Gerard Mercator (1512–1594) constructed his world map (Nova et aucta oibis terrae descriptio ad usum navigantium emervidate accommodatd) in 1569. This remarkable map, based on what is now known as a conventional cylindrical orthomorphic projection, was published in atlas form comprising 24 sheets. We have no direct evidence of how Mercator constructed this map: careful measurements of the spacing of the projected parallels of latitude manifest errors of a magnitude which indicate that he could not have used trigonometrical tables (although they were available at the time) as the basis of construction.

2 Vide Cotter, C. H., (1972). Navigational globes: ancient and modern. This Journal, 25, 345.Google Scholar

3 Cortes, M., (1561). The Arte of Navigation, London. (Translation by Eden, R. of Cortes, M. (1551) Breve compendio de la sphera y de la arte de navegar.)Google Scholar

4 Taylor, E. G. R., and Richey, M. W., (1962). The Geometrical Seaman, London.Google Scholar

5 Gerard Mercator produced his first terrestrial globe in 1541. This was of a sufficiently large scale for it to have been suitable for navigation.

6 Bourne, W., (1574). A Regiment for the Sea, London.Google Scholar (Vide Taylor, E. G. R. (1963) A Regiment for the Sea and other writings on Navigation by William Bourne. Hakluyt Society publication No. CXXI. Cambridge.)Google Scholar

7 Bourne, W., (1571). An Almanacke and Prognostication for three years … now newly added vnto my Rulles of Nauigation, London.Google Scholar (Vide Taylor, E. G. R. (1963) op. cit.)

8 Davis, J., (1595). The Seamans Secrets, London.Google Scholar

9 Taylor, E. G. R., (1954). The Mathematical Practitioners of Tudor and Stuart England, Cambridge.Google Scholar

10 ‘Horizontal’ sailing applied to the defective technique of sailing by means of the plane chart which made no allowance for the convergence of the meridians. Davis defined ‘paradoxall’ sailing thus: ‘Paradoxal Navigation, demonstrateth the true motion of the ship upon any corse assigned … neither circular nor strait, but concurred or winding … therefore called paradoxal, because it is beyond opinion that such lines should be described by plain horizontal motion … ’

11 Norwood, R., (1631). Trigonometric: Or, The Doctrine of Triangles: Divided into two Bookes: The first shewing the mensuration of Right-Lined Triangles: The second of Spherical …, London.Google Scholar

12 The difficulties of computing spherical triangles—the essence of great circle sailing problems—before the invention of trigonometrical tables of sines, decimal arithmetic and logarithms, were such that it is almost impossible for a present-day navigator to comprehend them.

13 Vide Waters, D. W., (1958). The Art of Navigation in England in Elizabethan and Early Stuart Times, London, pp. 447—456.Google Scholar

14 Norwood, R., (1637). The Sea-mans Practice Containing a Frndamentall Probleme in Navigation, experimentally verified …, London.Google Scholar

15 Sturmy, S., (1669). The Mariner's Magazine or Sturmy's Mathematical and Practical Arts, London.Google Scholar

16 Atkinson, J., (1765). Epitome of the Art of Navigation (revised and Corrected by Wm. Mountaine), London.Google Scholar

17 Vide Cotter, C. H., (1966). The Astronomical and Mathematical Foundations of Geography, London.Google Scholar

18 Anon. (1860). Great Circle or Tangent Sailing The English Cyclopaedia, conducted by Charles Knight, London.Google ScholarPubMed

19 Raper, H., (1840). The Practice of Navigation and Nautical Astronomy, London.Google Scholar

20 Vide Cotter, C. H., (1973). Henry Raper's spherical traverse table. This Journal, 26, 240–244.Google Scholar

21 Towson, J. T., (1848). Tables to Facilitate the Practice of Great Circle Sailing, London.Google Scholar

22 Maury, M. F., (1855). The Physical Geography of the Sea, London.CrossRefGoogle Scholar