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| Hutton, Charles Mathematical and Philosophical Dictionary 1795 | ||||||
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, one of the 48 old constellations, placed near Cepheus, not far from the north pole. The Greeks probably received this figure, as they did the rest, from the Egyptians, and in their fables added it to the family in the neighbouring part of the heavens, making her the wife of Cepheus, and mother of Andromeda. They pretend she was placed in this situation, to behold the destruction of her favourite daughter Andromeda, who is chained just by her on the shore, to be devoured; and that as a punishment for her pride and vanity in presuming to stand the comparison of beauty with the Nereids.
In the year 1572 there burst out all at once in this constellation a new star, which at first surpassed Jupiter himself in magnitude and brightness; but it diminished by degrees, till it quite disappeared at the end of 18 months. This star alarmed all the astronomers of that age, many of whom wrote dissertations upon it; among the rest Tycho Brahe, Kepler, Maurolycus, Lycetus, Gramineus, and others. Beza, the Landgrave of Hesse, Rosa, and others, wrote to prove it a comet, and the same that appeared to the Magi at the birth of Christ, and that it came to declare his second coming: these were answered by Tycho.
The stars in the constellation Cassiopeia, are in Ptolomy's catalogue 13, in Hevelius's 37, in Tycho's 46, and in Flamsteed's 55.
, a moiety of the constellation Gemini; called also Apollo. Also a star in this constellation, whose latitude, for the year 1700, according to Hevelius, was 10° 4′ 20″ north; and its longitude 16° 4′ 14″.
CASTOR and Pollux. See Gemini.
CASTOR and Pollux, in Meteorology, is a fiery meteor, which at sea appears sometimes adhering to a part of the ship, in the form of a ball, or even several balls. When one is seen alone, it is properly called Helena; but two are called Castor and Pollux, and sometimes Tyndaridæ.
By the Spaniards, Castor and Pollux are called San Elmo; by the French, St. Elme, St. Nicholas, St. Clare, St. Helene; by the Italians, Hermo; and by the Dutch, Vree Vuuren.
The meteor Castor and Pollux, it is commonly thought, denotes a cessation of the storm, and a future calm; as it is rarely seen till the tempest is nigh spent. But Helena alone portends ill weather, and denotes the severest part of the storm yet behind.
When the metcor adheres to the masts, yards, &c, it is concluded, from the air not having motion enough to dissipate this flame, that a profound calm is at hand; but if it flutter about, that it denotes a storm.
, the art, or act, of encamping an army.
, or Catacaustic Curves, in the Higher Geometry, are the species of caustic curves formed by reflection.
These curves are generated after the following manner: If there be an infinite number of rays AB, AC, AD, &c, proceeding from the radiating point A, and reflected at any given curve BCDH, so that the angles of incidence be still equal to the angles of reflection; then the curve BEG, to which the reflect- ed rays BI, CE, DF, &c, are always tangents, as at the points I, E, F, &c, is the catacaustic, or causticby-reflection. Or it is the same thing as to say, that a caustic curve is that formed by joining the points of concurrence of the several reflected rays.
Some properties of these curves are as follow. If the reflected ray IB be produced to K, so that AB = BK, and the curve KL be the evolute of the caustic BEG, beginning at the point K; then the portion of the caustic BE is , that is, the difference of the two incident rays added to the difference of the two reflected rays.
When the given curve BCD is a geometrical one, the caustic will be so too, and will always be rectifiable. The caustic of the circle, is a cycloid, or epicycloid, formed by the revolution of a circle upon a circle.
Thus, ABD being a semicircle exposed to parallel rays; then those rays which fall near the axis CB will be reflected to F, the middle point of BC; and those which fall at A, as they touch the curve only, will not be reflected at all; but any intermediate ray HI will be reflected to a point K, somewhere between A and F. And since every different incident ray will have a different focal point, therefore those various focal points will form a curve line AEF in one quadrant, and FGD 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 candle light; for then this curve AEFGD will appear plainly delineated on any white surface placed horizontally within the same, or on the surface of milk contained in the bowl.
The caustic of the common cycloid, when the rays are parallel to its axis, is also a common cycloid, described by the revolution of a circle upon the same base. The caustic of the logarithmic spiral, is the same curve.
The principal writers on the caustics, are l'Hôpital, Carré, &c. See Memoires de l'Acad, an. 1666. & 1703.