The exoskeleton is sometimes absent but generally consists of overlapping cycloid or ctenoid scales.
There are two principal types of Teleostean scales, the cycloidand ctenoid.
Covered with rounded scales shaped like the cycloid scales of Teleosteans as in Amia.
In the Gymnophiona the integument bears small cycloid scales arranged in rings which are equal in number to the vertebrae.
The rounded scales of Amia and of many fossil ganoids such as Holoptychius are shaped like cycloid scales, but differ from them in being more or less coated with enamel.
In all the Scyphophori the body is oblong, covered with cycloid scales, the head is naked, there are no barbels, and the small mouth is at the end of a long snout.
The scales are alwayscycloid and are usually large.
The scales are chiefly cycloid and the fins are without true spines.
The scales, if present, are cycloidor replaced by bony plates.
In Dasyscopelus the scales are spinescent, but in most of the genera, as in Myctophum, the scales are cycloid and caducous, falling at the touch.
The Archæomænidæ differ from Pholidophoridæ in having cycloid scales.
In this group the body is robust with large scales, ctenoid in Ctenothrissa, cycloid in Aulolepis.
In Batrachoides, a South American genus, the body is covered with cycloid scales.
The diamond-shaped enameled scales disappear, giving place to cycloid scales, which gradually become thin and membranous in structure.
The Trichonontidæ, with wide gill-openings and cycloid scales, are also related to the Callionymidæ.
The steep descents form cycloid curves, that flatten at their bases, and over which the ferruginous stratum of mould atop projects like a cornice.
In the line of descent the placoid scale preceded the ganoid, which in turn was followed by the cycloidand lastly by the ctenoid scale.
The fishes that are mostly attacked are of the soft-rayed species, having cycloid scales, the spiny-rayed species with ctenoid scales being most nearly immune from their attacks.
The tail is diphycercal in all, ending in a long point, and the body is covered with cycloid scales.
Ganoid scales are thickened and covered with bony enamel, much like that seen in teeth, otherwise essentially like cycloid scales.
Ctenoid scales have a comb-edge of fine prickles or cilia; cycloid scales have the edges smooth.
In general, however, the more primitive representatives of the typical fishes, those with abdominal ventrals and without spines in the fins, have cycloid or smooth scales.
Sometimes, as in the eel, the cycloid scales may be reduced to mere rudiments buried in the skin.
In all the Dipnoans the trunk is covered with imbricated cycloid scales and no bony plates, although sometimes the scales are firm and enameled.
The cycloid has been called by Montucla, the Helen of geometers.
The cycloid is the curve described by a point in a circle, while it makes one revolution along a horizontal base, as in the case of a carriage wheel.
Cycloid and ctenoid scales are those of ordinary fishes, and are precisely alike, except that the hinder, or attached, end of the latter is split into a comblike fringe.
Many of the species are covered with bony plates, or with ganoid scales; others have cycloid scales.
In other Teleostomes the scales are as a rule thin, rounded and overlapping--the so-called cycloid type (fig.
The distinctions between cycloid and ctenoid scales, between placoid and ganoid fishes, are vague, and can hardly be maintained.
Chasles, in his History, says that the cycloid interweaves itself with all the great discoveries of the seventeenth century.
Limiting the conditions to the simple fall in a vacuum, the only case which was at first considered, it is easily found that the required curve must be a reversed cycloid with a horizontal base, and with its origin at the highest point.
The cycloid is the simplest member of the class of curves known as roulettes.
His enquiries into evolutes enabled him to prove that the evolute of a cycloid was an equal cycloid, and by utilizing this property he constructed the isochronal pendulum generally known as the cycloidal pendulum.
The mechanical properties of the cycloid were investigated by Christiaan Huygens, who proved the curve to be tautochronous.
The method by which the cycloid is generated shows that it consists of an infinite number of cusps placed along the fixed line and separated by a constant distance equal to the circumference of the rolling circle.
The name cycloid is usually restricted to the portion between two consecutive cusps (fig.
No mention of the cycloid has been found in writings prior to the 15th century.
A famous period in the history of the cycloid is marked by a bitter controversy which sprang up between Descartes and Roberval.
Pascal is said to have written his treatise on the cycloid from a religious motive.
He is said to have worked out the formula for the cycloid curve while watching the path described by flies that had lighted on the wheels of his carriage, and were carried forward and around by them.
However, for a short distance near the bottom, the circle so nearly coincides with the cycloid that a pendulum swinging in the usual circular path is, for small arcs, isochronous for practical purposes.
Huygens proposed to apply his discovery to clocks, and since the evolute of a cycloid is an equal cycloid, he suggested the use of a flexible pendulum swinging between cycloidal cheeks.
It is impossible to mill out even a convex cycloid or epicycloid, by the means and in the manner above described.
The outer curve H L, evidently, could be milled out by the cutter, whose centre travels in the cycloid C A; it resembles the cycloid somewhat in form, and presents no remarkable features.
It will be seen, then, that if the centre of the cutter travel in the cycloid A C, its edge will cut away the part G E D, leaving the template of the form O G I.
Is a Cycloid with its equal Sides A B, A C, and pendulous Body E, oscillating therein.
Pascal’s labours on the cycloid may be said to bring to a close his scientific career.
Pascal’s discoveries as to the cycloid belong to a later period of his life, after he had long forsaken the scientific studies which engrossed him at this time, and had become an inmate of Port Royal.
Since the evolute of a cycloidis an equal cycloid the object is attained by means of two metal cheeks, having the form of the evolute near the cusp, on which the string wraps itself alternately as the pendulum swings.
It may be noticed that if the scales of x and t be properly adjusted, the curve of positions in the present problem is the portion of a cycloid extending from a vertex to a cusp.
In the case of a particle oscillating under gravity on a smooth cycloid from rest at the cusp the hodograph is a circle through the pole, described with constant velocity.
