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VIII.—On Knots

Published online by Cambridge University Press:  14 March 2016

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Extract

The following paper contains, in a compact form, the substance of several somewhat bulky communications laid before the Society during the present session. The gist of each of these separate papers will be easily seen from the abstracts given in the Proceedings. These contain, in fact, many things which I have not reproduced in this digest. Nothing of any importance has been added since the papers were read, but the contents have been very much simplified by the adoption of a different order of arrangement; and long passages of the earlier papers have been displaced in favour of short general statements from the later ones. With the exception of the portion which deals with the main question raised, this paper is fragmentary in the extreme. Want of leisure or press of other work may justly be pleaded as one cause; but there is more than that. The subject is a very much more difficult and intricate one than at first sight one is inclined to think, and I feel that I have not succeeded in catching the key-note. When that is found, the various results here given will no doubt appear in their real connection with one another, perhaps even as immediate consequences of a thoroughly adequate conception of the question.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 28 , Issue 1 , 1877 , pp. 145 - 190
Copyright
Copyright © Royal Society of Edinburgh 1876

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References

page 146 note * Proc. R. S. E. 1875–6 (p. 59).

page 146 note † Göttinger Studien, 1847.

page 147 note * “Messenger of Mathematics” January. 1877.

page 147 note † Higher multiple points may, of course, occur, but an infinitesimal change of position of the luminous point, or of the relative dimensions of the coils of the knot, will remove these by splitting them into a number of double points, so that we need not consider them.

page 159 note * 1877, p. 338, and p. 382.

page 165 note * Proc. R. S. E. 1877, p. 310 (footnote), and p. 325.

page 165 note † Some further illustrations of this will be found in the abstract of my paper on “Links” Proc. R. S. E. 1877, p. 321.

page 179 note * Electrodynamics and Magnetism, §§ 5-8, Quarterly Math. Journal, 1859.

page 180 note * Werke, Göttingen, 1867, v. p. 605.

page 190 note * Proceedings, R. S. E., May 7th, 1877.

page 190 note † Mathematische Annalen, IX. 478 Google Scholar.

page 190 note ‡ I Professor Fischer has just shown me an enlarged copy of Boeddicker's pamphlet above mentioned. Twenty pages are now added, mainly referring to the connection of knots with Riemann's surfaces, and the title is altered to Erweiterung der Gauss'schen Theorie der Verschlingungen. Stuttgart, 1876.