CAT 



CAT 



These curves are generated after the 

 following* manner. If there be an infinite 

 number of rays, as A B, A C, A D, &c. 

 (plate Miscellanies, fig 1 . 6.) proceeding 

 from the radiating- point A, and reflect- 

 ed at any given curb B D H, so that the 

 angles of incidence be still equal to 

 those of reflection ; then the curve B E 

 G, to which the reflected rays B I, C E, 

 D F, &c. are tangents continually, as in 

 the points I, E, F, is called the catacaus- 

 tic curve. 



If the reflected I B be produced to K, 

 so that A B = B K, and the curve K L be 

 the evolute of the catacaustic B E G, be- 

 ginning at the point K ; then the portion 

 of the catacaustic BE = AC ABx 

 C E B I continually. Or if any two in- 

 cident rays, as A B, A C be taken, that 

 portion of the caustic that is evolved 

 while the ray A B approaches to a coin- 

 cidence with A C, is equal to the differ- 

 ence of those incident rays x the differ- 

 ence of the reflected rays. When the 

 given curve is a geometrical one, the 

 catacaustic will be so too, and always 

 rectifiable. The catacaustic of a circle is 

 a cycloid, formed by the revolution of 

 a circle along a circle. Thus, A B D, 

 fig. 7, being a semicircle exposed to 

 parallel rays ; then those rays which fair 

 ntur the axis C B will be reflected to F, 

 the middle point of B C ; and those which 

 fall at A, as they touch the curve only, 

 will not be reflected at all ; but any inter- 

 mediate ray H I will be reflected to a 

 point K, somewhere between A and F. 

 And since every different incident ray 

 will have a different focal point, there- 

 fore, those various focal points will form 

 a curve line A E F in one quadrant, and 

 F G D in the other, being the cycloid 

 above-mentioned. And this figure may 

 be beautifully exhibited experimentally 

 by exposing the inside of a smooth bowl, 

 or glass, to the sun beams, or strong can- 

 dle light ; for then this curve A E F G D 

 will appear plainly delineated on any 

 white surface placed horizontally within 

 the same, or on the surface of milk con- 

 tained in the bowl. The caustic of the 

 common semi-cycloid, when the rays are 

 parallel to the axis, is also a common cy- 

 cloid, described by the revolution of a 

 circle upon the same base. The caustic 

 of the logarithmic spiral is the same curve, 

 only set in a different position. 



CATACHRESIS, in rhetoric, a trope 

 which borrows the name of one thing to 

 express another. Thus Milton, describ- 

 ing Raphael's descent from the empyreal 

 heaven to paradise, say?, 



" Down thither, prone in flight, 



He speeds, and thro' the vast ethereal 

 sky 



Sails between worlds and worlds." 



CATACOMB, a grotto or subterrane- 

 ous place of burial for the dead. 



The term is particularly used in Italy, 

 for a vast assemblage of subterraneous 

 sepulchres, three leagues from Rome, in 

 the Via Appia, supposed to be the sepul- 

 chres of the ancients. Others imagine 

 these catacombs to be the cells wherein 

 the primitive Christians hid themselves. 

 Each catacomb is three feet broad, and 

 eight or ten high, running in form of an 

 alley or gallery, and communicating with 

 one another. 



Mr. Monro, in the Philosophical Trans- 

 actions, gives it as his opinion, that the 

 catacombs were the burial places of the 

 first RomanSj before the practice of burn- 

 ing the dead was introduced ; and that 

 they were dug in consequence of these 

 opinions, that shades hate the light, and 

 love to hover about the place where their 

 bodies were laid. 



CAT ACOUSTIC S,an appellation given 

 to the doctrine of reflected sounds. See 

 ACOUSTICS. 



CATALOGUE, a list or .enumera- 

 tion of the names of several books, men, 

 or other things, according to a certain 

 order. 



CATALOGUE of the stars, is a list of the 

 fixed stars, disposed in their several con- 

 stellations with the longitudes and lati- 

 tudes of each. 



The most renowned composers of 

 these catalogues are, 1. Ptolemy, who 

 added his own observations to those of 

 Hipparchus Rhodius, about the year of 

 Christ 880. 2. Ulugh Beigh made a cata- 

 logue of the fixed stars in 1437. S.Tycho 

 Brahe determined the places of 777 stars 

 for the year 1600. 4. William, Landgrave 

 of Hesse, with his mathematicians, deter- 

 mined the places of 400 fixed stars. 5. 

 In the year 1667, Dr. Halley, in the island 

 of St. Helena, observed 350, not visible in 

 ourhorison. And 6. J. Hevelius, adding 

 his own observations to those of the an- 

 cients, and of Dr. Halley, made a cata- 

 logue of 1888. But the last and greatest 

 is the Britannic catalogue, a performance 

 the most perfect of its kind, compiled 

 from the observations of the accurate 

 Mr. Flamstead, who, with all the talents 

 and apparatus requisite for such an un- 

 dertaking, devoted himself to that w ork 

 for a long series of years. It contains 

 2934 stars. 



In 1782, M. Bode, member of the Royal 



