Paper, 'Preliminary notice on the diameters of plane cubics' by John James Walker

Description

Walker writes: 'A diameter is the locus of mean points of a system of parallel chords, which may be called “its” chords; but through any point pass two chords, which have that as mean point. Considering the points then on a given diameter, its own chords through those points are all parallel to the polar of its own mean point with respect to the “centroid”, which polar is itself a double chord; the other system of chords touch a parabola, which is touched by the diameter itself at its own mean point; viz, for that point the diameter is itself the chord of the second system; and the connector of that point with the centre of the “centroid” is a diameter of the parabola. To every diameter of the cubic corresponding to a parabola, the envelope of all these parabolas is a quartic curve; while the double chords, which are otherwise distinguished as those having their mean points on the “centroid”, envelope a second cuspidal quartic.' He presents a series of differential equations.

Annotations in pencil and ink.

Subject: Mathematics

Received 21 April 1887. Read 5 May 1887.

A version of this paper was published in volume 42 of the Proceedings of the Royal Society as 'On the diameters of plane cubics. preliminary notice'.

Reference number

PP/10/43

Earliest possible date

1887

Physical description

Ink and graphite pencil on paper

Page extent

3 pages

Format

Manuscript