The collected mathematical papers of Arthur Cayley.

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387.
NOTICES OF COMMUNICATIONS TO THE LONDON MATHEMATICAL SOCIETY.
[From the Proceedings of the London Mathematical Society, vol. iI. (1866-1869),
pp. 6-7, 25- 26, 29, 61-63, 103-104, 123-125.]
December 13, 1866. pp. 6-7.
PROF. CAYLEY exhibited and explained some geometrical drawings. Thinking that
the information might be convenient for persons wishing to make similar drawings, he
noticed that the paper used was a tinted drawing paper, made in continuous lengths
up to 24 yards, and of the breadth of about 56 inches (1); the half-breadth being
therefore sufficient for ordinary figures, and the paper being of a good quality and
taking colour very readily. Among the drawings was one of the conies through four
points forming a convex quadrangle. The plane is here divided into regions by the
lines joining each of the six pairs of points, and by the two parabolas through the
four points; and the regions being distinguished by different colours, the general form
of the conies of the system is very clearly seen. (Prof. Cayley remarked that it would
be interesting to make the figures of other systems of conies satisfying four conditions;
and in particular for the remaining elementary systems of conies, where the conies pass
through a number 3, 2, 1 or 0 of points and touch a number 1, 2, 3 or 4 of lines:
the construction of some of these figures is, however, practically a great deal more
difficult.) Other figures related to Cartesians and Bicircular Quartics. One of these
was a figure of a system of triconfocal Cartesians; and derived from this by inversion
in regard to a circle, there was a figure of a system of quadriconfocal bicircular
quartics: in the assumed position of the inverting circle, each quartic consists (like
the Cartesian which gives rise to it) of an exterior and an interior continuous curve,
and the general aspect of the figure is that of a distortion of the original figure of
the Cartesians. Another figure was that of the bicircular quartic, for which the
1 Sold at Messrs Lechertier-Barbe's, Regent Street, at 6d. per yard, or 9s. the piece.
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