CYC 



CYC 



tna, flowering in November and Decem- 

 ber. Vide Willd. Sufi. Cnum A. 



CYCLIDIUM, in natural history, a ge- 

 nus of Vcrmcs Infusoria. Worm invisible 

 to the naked eye, very simple, pellucid, 

 flat, orbicular, or oval. There are se- 

 ven species. C. bulla; orbicular, transpa- 

 rent ; in infusions of hay ; pellucid, white, 

 with the edges a little darker; motion 

 slow and circular. C. niilium ; ellipti- 

 cal, transparent ; in vegetable infusions ; 

 pellucid, crystalline, membranaceous, 

 with' a line through the whole length. 



CYCLOID, in geometry, a curve of the 

 transcendental kind, called also the tro- 

 choid. It is generated in the following 

 manner: if the circle CDH (Plate III. 

 Miscel. fig. 15.) roll on the given straight 

 line A B, so that all the parts of the cir- 

 cumference be applied to it one after 

 another, the point C that touched the line 

 A B in A, by a motion thus compounded 

 of a circular and rectilinear motion, will 

 describe the curve A C E B, called the 

 cycloid, the properties of which are these: 

 1. If on the axis E F be described the 

 generating circle E G F, meeting the ordi- 

 naie C K m G, the ordinate will be equal 

 to the sum of the arc E G and its right 

 sine G K ; that is, C K will be equal to 

 E G + G K. 2. The line C H parallel to 

 the chord E Gis a tangent to the cycloid 

 in C. 3. The arc of the cycloid E L is 

 double of the chord E M, of the corre- 

 sponding arc of the generating circle 

 E M F : hence the semi-cycloid E L B is 

 equal to twice the diameter of the gene- 

 rating circle E F ; and the whole cycloid 

 A C E IJ is quadruple of the diameter E F. 

 4. It E R be parallel to the base A B, and 

 C K parallel to the axis of the cycloid E F, 

 the space E C R, bounded by the arc of the 

 cycloid EC, and the lines "ER and R C, 

 shall be equal to the circle area E G K : 

 hence it follows, if A T, perpendicular to 

 the base A B, meet E R in T, the space 

 E T A C E will be equal to the semi-circle 

 E G F : and since A F is equal to the semi- 

 circumference EGF, the rectangle EFAT, 

 being the rectangle of the diameter and 

 semi-circumference, will be equal to four 

 times the semi-circle EGF; and there- 

 fore the area E C A F E will be equal to 

 three times the area of the generating 

 semi-circle EGF. Again, if you draw the 

 line E A, the area intercepted betwixt the 

 cycloid E C A, and the straight line E A, 

 will be equal to the semi-circle EGF; 

 for the area E C A FE is equal to three 

 times EGF, and the triangle E A F = 

 A F X i K F. the rectangle of the semi- 

 circle and radius, and consequently equal 



to 2 E G F ; therefore their difference, the 

 area E C A E, is equal to E G F. 5. Take 

 E b = O K, draw 6 Z parallel to the base, 

 meeting the generating circle in X, and 

 the cycloid in Z, and join C Z, F X ; then 

 shall the area C Z E C be equal to the sum 

 of the triangles G F K and b F X. Hene 

 an infinite number of segments of the cy- 

 cloid may be assigned, that are perfectly 

 quadrable. 



For example, if the ordinate C K be 

 supposed to cut the axis in the middle of 

 the radius O E, then K and b coincide ; 

 and the area E C K becomes in that case 

 equal to the triangle G K F, and E b Z be- 

 comes equal to F b X, and these triangles 

 themselves become equal. 



This is the curve on which the doc- 

 trine of pendulums and time-measuring 

 instruments in a great measure depend; 

 Mr. Huygens having demonstrated, that 

 from whatever point or height a heavy 

 body oscillating on a fixed centre begins 

 to descend, while it continues to move 

 in a cycloid, the time of its falls or oscilla- 

 tions will be equal to each other. It is 

 likewise demonstrable, that it is the 

 curve of quickest descent, i, e. a body 

 falling in it from any given point above, 

 to another not exactly under it, will come 

 to tliis point in a less time than in any 

 other curve passing through those two 

 points. 



CYCLOPAEDIA, or ENCYCLOPAEDIA, de- 

 notes the circle or compass of arts and 

 sciences. 



CYCLOPTERUS, the nicker, in natural 

 history, a genus of fishes of the order 

 Cartilaginei. Generic character : head 

 obtuse ; tongue short and thick ; teeth 

 in the jaws ; body short, thick, and with- 

 out scales ; ventral fins united into an 

 oval concavity, forming an instrument of 

 adhesion. There are ten species, of 

 which the principal is C. lumpus, the 

 lump-sucker. The shape of this fish is 

 very similar to that of the bream, and it 

 sometimes grows to the weight of seven 

 pounds. Beneath the pectoral fins it 

 possesses an oval aperture, surrounded 

 with a soft muscular substance, ed^ed 

 with small thready appendages, which 

 act as so many claspers. By th:s appara- 

 tus the sucker is enabled to adhere with 

 extreme tenacity to any substance, and 

 in several cases it has been found impos- 

 sible to make it quit its hold, but by the 

 application of a force which has lacerated 

 and destroyed it. M. Pennant mentions 

 that one of these fishes, soon after being 

 caught, was flung into a pail of water con- 

 taining several gallons, and attached itself 



