% This paper has been transcribed in Plain TeX by
% David R. Wilkins
% School of Mathematics, Trinity College, Dublin 2, Ireland
% (dwilkins@maths.tcd.ie)
%
% Trinity College, 2000.

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\centerline{\Largebf ON THE DOUBLE MODE OF GENERATION}

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\centerline{\Largebf OF AN ELLIPSOID}

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\centerline{\Largebf By}

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\centerline{\Largebf William Rowan Hamilton}

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\centerline{\largerm (Proceedings of the Royal Irish Academy,
   4 (1850), p.~173.)}

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\centerline{\largerm Edited by David R. Wilkins}

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\centerline{\largerm 2000}

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\centerline{\largeit On the Double Mode of Generation of an
Ellipsoid.}

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\centerline{{\largeit By\/}
{\largerm Sir} {\largesc William R. Hamilton.}}

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\centerline{Communicated May~22, 1848.}

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\centerline{[{\it Proceedings of the Royal Irish Academy},
vol.~4 (1850), p.~173.]}

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Sir W.~R. Hamilton communicated the following double mode of
generation of an ellipsoid, which had been suggested to him by
his quaternion formul{\ae}.

Conceive two equal spheres to {\it slide\/} within two cylinders,
in such a manner that the right line joining their centres may
remain parallel to a fixed line; then the locus of the varying
circle in which the two spheres intersect each other will be an
{\it ellipsoid}, inscribed at once in both the cylinders, so as
to touch one cylinder along one ellipse of contact, and the other
cyclinder of revolution along another such ellipse.

And the {\it same\/} ellipsoid may also be generated as the locus
of {\it another\/} varying circle, which shall be the
intersection {\it of another pair of equal spheres}, sliding
within the same pair of cylinders, but having their line of
centres constantly parallel to another fixed line.  Every
ellipsoid can be generated by the above double mode of
generation.

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