n deprive the _Essai_, which is now very rare, of its value as a
trustworthy guide through a tangled mass of tradition.

CAUSTIC (Gr. [Greek: kaustikos], burning), that which burns. In surgery,
the term is given to substances used to destroy living tissues and so
inhibit the action of organic poisons, as in bites, malignant disease
and gangrenous processes. Such substances are silver nitrate (lunar
caustic), the caustic alkalis (potassium and sodium hydrates), zinc
chloride, an acid solution of mercuric nitrate, and pure carbolic acid.
In mathematics, the "caustic surfaces" of a given surface are the
envelopes of the normals to the surface, or the loci of its centres of
principal curvature.

In optics, the term _caustic_ is given to the envelope of luminous rays
after reflection or refraction; in the first case the envelope is termed
a catacaustic, in the second a diacaustic. Catacaustics are to be
observed as bright curves when light is allowed to fall upon a polished
riband of steel, such as a watch-spring, placed on a table, and by
varying the form of the spring and moving the source of light, a variety
of patterns may be obtained. The investigation of caustics, being based
on the assumption of the rectilinear propagation of light, and the
validity of the experimental laws of reflection and refraction, is
essentially of a geometrical nature, and as such it attracted the
attention of the mathematicians of the 17th and succeeding centuries,
more notably John Bernoulli, G.F. de l'Hopital, E.W. Tschirnhausen and
Louis Carre.

Caustics by reflection.

The simplest case of a caustic curve is when the reflecting surface is
a circle, and the luminous rays emanate from a point on the
circumference. If in fig. 1 AQP be the reflecting circle having C as
centre, P the luminous point, and PQ any incident ray, and we join CQ
it follows, by the law of the equality of the angles of incidence and
reflection, that the reflected ray QR is such that the angles RQC and
CQP are equal; to determine the caustic, it is necessary to determine
the envelope of this line. This may be readily accomplished
geometrically or analytically, and it will be found that the envelope
is a cardioid (q.v.), i.e. an epicycloid in which the radii of the
fixed and rolling circles are equal. When the rays are parallel, the
reflecting surface remaining circular, the question can be similarly
treated, and it is found that