cyclo branch i ans

pl. [CYCLO BRANCH I ATA.] The same as CYCLO BRANCH I AT A (q. v.). ç-clo-brăn-chi-a-ta, s. pl. [Gr. kyklos = a cir cle, and branghia = gills.] [BRANCHLE.] Zool.: The name given by M. De Blainville to changes which require eleven there. he an order of Gasteropodous what he considerer i zed by the circular arrangement of the branchise. It contains two families, about to run through their cucire Lonen years or there of Venus. = kw cyclogen the Chiton ide and the Patellide. The order Cyclo- branch i at a is not universally adopted. Mr. S. P. Woodward, F. G. S., ., arranged the Chiton ide (Chitons) and Patellide (Limpets), as the thir- teenth and fifteenth families of the cla Gaster opoda, Mr. Milne-Edwards' order Prosobranch i at a and the section B Holostomata (Sea Snails). The fourteenth family-that standing between the two already mentioned-is the Dentaliade (Tooth shells). IMG:content-1683.png:[blocks in formation] eides circular, kyklos =a circle, and eidos =form.] A. As adjective : 1. Ord. Lang. Of the form of a circle. 2. Zool. & Palæont .: Pertaining to a cycloid scale or to the fishes which have this dermal covering. [CYCLOID SCALE, CYCLOIDEI.] B. As substantive : Geom.: The curve which is produced when a circle rolls forward on a straight line. A familiar example of it is a carriage-wheel moving along a smooth road. If a mark be made at any point on the circumference of a wheel, it will describe a series of cycloids. The curved figure thus produced is not, as the etymology suggests, "of the form of a circle;" were it so, then the point of the circumfer- ence commencing its revolution at a given spot on the road would, when that revolution was com pleted, return to that spot again. It does not so re- turn; but when, having completed its revolution, it afresh touches the road, it is at an advanced point in it compared with the c spot at which it came into con IMG:content-1684.png:[blocks in formation] tact with it before. Let ABE be a circle-say a carriage-wheel-revolving around its center, and at the same time moving forward along the straight line or road CD, from c to D. Let B, the highest point in the circumference of the circle, be also the point the movements of which it is desired to trace, then, during the time that takes to move from B to E, a portion of the wheel exactly equal to the same B E will have measured its length upon the ground, and the wheel will have moved that distance horizontally forward. If EF be drawn parallel to CD, then the straight line EF will be the arc BE. The whole arc CAD is four times the diameter of the circle by which it was generated. The area contained by the chord CAD and the straight line CD is three times the area of the circle ABE. If the cycloid be supposed to be reversed, and be now not a mathematical abstraction but a real material curve, then a weight placed at any point of it will take the same time to descend from any part of it to the lowest point. Moreover, it will descend more swiftly than it will in any other curve. The cycloid is a transcendental curve, since its equation cannot be expre ed in common algebraic terms. Cycloids are of different kinds. That now described is the common cycloid. Others are the There is also a curve called the Epicycloid, and prolate or inflected cycloid, and the cycloid. another the Hypocycloid (q. v.). "A man may form to himself the notion of a parabola or a cycloid from the mathematical definition of those figures."-Reid: Inquiry into the Human Mind. IMG:content-1685.png:[blocks in formation] IMG:content-1686.png:[blocks in formation]