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‘On a Problem of Navigation’

Published online by Cambridge University Press:  23 November 2009

J. E. D. Williams
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Extract

I am reminded that this was the title of a paper by Professor W. M. Smart, published elsewhere in 1946, dealing with the rhumb line on the spheroid, by references in recent issues of this Journal to a paper of mine entitled ‘Loxodro-mic distances on the Terrestrial Spheroid’ which appeared in this Journal 32 years ago: the subject crops up every few years.

Type
Forum
Information
The Journal of Navigation , Volume 35 , Issue 3 , September 1982 , pp. 517 - 519
Copyright
Copyright © The Royal Institute of Navigation 1982

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References

REFRENCES

1Smart, W. M., (1946). ‘On a Problem of Navigation’, Monthly Notices of the Royal Astronomical Society, 106, 2, p. 124.CrossRefGoogle Scholar
2This Journal, 34, 247 and 35, 187.Google Scholar
3This Journal, 3, 133.Google Scholar
4This Journal, 34, 247.Google Scholar
5A pun: ‘Kremer’ meant ‘merchant’, Latin ‘mercator’, in archaic Dutch.Google Scholar
6As we would now say, the second condition is that the projection should be ‘orthomorphic’ or ‘conformal’. Conformal mapping theory was settled by Gauss around about 1830.Google Scholar
7This Journal, 9, 371.Google Scholar
8MP = √(f 1f 2) dϕ and MD (or LP) = ff 1dϕ where f 1 and f 2 are functions of latitude ϕ which are determined by the form of the Earth. It would be odd if those who tabulated the results of the first integral a century ago were unaware of the significance of the second.Google Scholar