any, and he was in consequence relieved
from duty. An inquiry subsequently held resulted in de Cissey's favour
(1881). He died on the 15th of June 1882 at Paris.

CISSOID (from the Gr. [Greek: kissos], ivy, and [Greek: eidos], form), a
curve invented by the Greek mathematician Diocles about 180 B.C., for
the purpose of constructing two mean proportionals between two given
lines, and in order to solve the problem of duplicating the cube. It was
further investigated by John Wallis, Christiaan Huygens (who determined
the length of any arc in 1657), and Pierre de Fermat (who evaluated the
area between the curve and its asymptote in 1661). It is constructed in
the following manner. Let APB be a semicircle, BT the tangent at B, and
APT a line cutting the circle in P and BT at T; take a point Q on AT so
that AQ always equals PT; then the locus of Q is the cissoid. Sir Isaac
Newton devised the following mechanical construction. Take a rod LMN
bent at right angles at M, such that MN = AB; let the leg LM always pass
through a fixed point O on AB produced such that OA = CA, where C is the
middle point of AB, and cause N to travel along the line perpendicular
to AB at C; then the midpoint of MN traces the cissoid. The curve is
symmetrical about the axis of x, and consists of two infinite branches
asymptotic to the line BT and forming a cusp at the origin. The
cartesian equation, when A is the origin and AB = 2a, is y squared(2a - x) =
x cubed; the polar equation is r = 2a sin [theta] tan [theta]. The cissoid is
the first positive pedal of the parabola y squared + 8ax = 0 for the vertex,
and the inverse of the parabola y squared = 8ax, the vertex being the centre of
inversion, and the semi-latus rectum the constant of inversion. The area
between the curve and its asymptote is 3[pi]a squared, i.e. three times the
area of the generating circle.

The term cissoid has been given in modern times to curves generated in
similar manner from other figures than the circle, and the form
described above is distinguished as the cissoid of Diocles.

[Illustration]

A _cissoid angle_ is the angle included between the concave sides of two
intersecting curves; the convex sides include the _sistroid angle_.

See John Wallis, _Collected Works_, vol. i.; T.H. Eagles, _Plane
Curves_ (1885).

CIS-SUTLEJ STATES, the southern portion of the Punjab, India. The name,
now obsolete, came into use in 1809, when the Sikh chiefs south of the