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    "chunk_id": "1911:caussin de perceval:bdf97a3fe0de",
    "title": "CAUSSIN DE PERCEVAL",
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    "verified_text": "caussin de perceval, armand-pierre (1795-1871), french orientalist, was born in paris on the 13th of january 1795. his father, jean jacques antoine caussin de perceval (1759-1835), was professor of arabic in the college de france. in 1814 he went to constantinople as a student interpreter, and afterwards travelled in asiatic turkey, spending a year with the maronites in the lebanon, and finally becoming dragoman at aleppo. returning to paris, he became professor of vulgar arabic in the school of living oriental languages in 1821, and also professor of arabic in the college de france in 1833. in 1849 he was elected to the academy of inscriptions. he died at paris during the siege on the 15th of january 1871. caussin de perceval published (1828) a useful _grammaire arabe vulgaire_, which passed through several editions (4th ed., 1858), and edited and enlarged elie bocthor's[1] _dictionnaire francais-arabe_ (2 vols., 1828; 3rd ed., 1864); but his great reputation rests almost entirely on one book, the _essai sur l'histoire des arabes avant l'islamisme, pendant l'epoque de mahomet_ (3 vols., 1847-1849), in which the native traditions as to the early history of the arabs, down to the death of mahommed and the complete subjection of all the tribes to islam, are brought together with wonderful industry and set forth with much learning and lucidity. one of the principal ms. sources used is the great _kitab al-aghani_ (book of songs) of abu faraj, which has since been published (20 vols., boulak, 1868) in egypt; but no publication of texts can 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 the caustic is an epicycloid in which the radius of the fixed circle is twice that of the rolling circle (fig. 2). the geometrical method is also applicable when it is required to determine the caustic after any number of reflections at a spherical surface of rays, which are either parallel or diverge from a point on the circumference. in both cases the curves are epicycloids; in the first case the radii of the rolling and the fixed circles are a(2n - 1)/4n and a/2n, and in the second, an/(2n + 1) and a/(2n + 1), where a is the radius of the mirror and n the number of reflections. [illustration: fig. 1. c = a] [illustration: fig. 2. c = [oo]] [illustration: fig. 3. c = (1/3)a] the cartesian equation to the caustic produced by reflection at a circle of rays diverging from any point was obtained by joseph louis lagrange; it may be expressed in the form {(4c^2 - a^2)(x^2 + y^2) - 2a^2 cx - a^2 c^2 }^3 = = 27a^4 c^2 y^2 (x^2 + y^2 - c^2)^2, where a is the radius of the reflecting circle, and c the distance of the luminous point from the centre of the circle. the polar form is {(u + p) cos 1/2[theta]}^2/3 + {(u - p) sin 1/2[theta]}^2/3 = (2k)^2/3, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. when c = a or = [oo] the curve reduces to the cardioid or the two cusped epicycloid previously discussed. other forms are shown in figs. 3, 4, 5, 6. these curves were traced by the rev. hammet holditch (_quart. jour. math._ vol. i.). [illustration: fig. 4. c = 1/2a] [illustration: fig. 5. c > a] _secondary caustics_ are orthotomic curves having the reflected or refracted rays as normals, and consequently the proper caustic curve, being the envelope of the normals, is their evolute. it is usually the case that the secondary caustic is easier to determine than the caustic, and hence, when determined, it affords a ready means for deducing the primary caustic. it may be shown by geometrical considerations that the secondary caustic is a curve similar to the first positive pedal of the reflecting curve, of twice the linear dimensions, with respect to the luminous point. for a circle, when the rays emanate from any point, the secondary caustic is a limacon, and hence the primary caustic is the evolute of this curve. [illustration: fig. 6. a > c > 1/2a] caustics 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.",
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