ustics by refraction.

The simplest instance of a caustic by refraction (or diacaustic) is
when luminous rays issuing from a point are refracted at a straight
line. It may be shown geometrically that the secondary caustic, if the
second medium be less refractive than the first, is an ellipse having
the luminous point for a focus, and its centre at the foot of the
perpendicular from the luminous point to the refracting line. The
evolute of this ellipse is the caustic required. If the second medium
be more highly refractive than the first, the secondary caustic is a
hyperbola having the same focus and centre as before, and the caustic
is the evolute of this curve. When the refracting curve is a circle
and the rays emanate from any point, the locus of the secondary
caustic is a Cartesian oval, and the evolute of this curve is the
required diacaustic. These curves appear to have been first discussed
by Gergonne. For the caustic by refraction of parallel rays at a
circle reference should be made to the memoirs by Arthur Cayley.

REFERENCES.--Arthur Cayley's "Memoirs on Caustics" in the _Phil.
Trans._ for 1857, vol. 147, and 1867, vol. 157, are especially to be
consulted. Reference may also be made to R.S. Heath's _Geometrical
Optics_ and R.A. Herman's _Geometrical Optics_ (1900).

FOOTNOTE:

[1] Elie Bocthor (1784-1821) was a French orientalist of Coptic
origin. He was the author of a _Traite des conjugaisons_ written in
Arabic, and left his Dictionary in MS.

CAUTERETS, a watering-place of south-western France in the department of
Hautes-Pyrenees, 20 m. S. by W. of Lourdes by rail. Pop. (1906) 1030. It
lies in the beautiful valley of the Gave de Cauterets, and is well known
for its copious thermal springs. They are chiefly characterized by the
presence of sulphur and silicate of soda, and are used in the treatment
of diseases of the respiratory organs, rheumatism, skin diseases and
many other maladies. Their temperature varies between 75 deg. and 137
deg. F. The springs number twenty-four, and there are nine bathing
establishments. Cauterets is a centre for excursions, the Monne (8935
ft.), the Cabaliros (7655 ft.), the Pic de Chabarrou (9550 ft.), the
Vignemale (10,820 ft.), and other summits being in its neighbourhood.

CAUTIN, a province of southern Chile, bounded N. by Arauco, Malleco and
Bio-Bio, E. by Argentina, S. by Valdivia, and W. by the Pacific. I