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Updated: May 24, 2025
The action of a paddle wheel in the water resembles in this respect that of the wheel of a carriage running along the ground: that point in the radius of the paddle of which the rotative speed is just equal to the velocity of the vessel will describe a cycloid; points nearer the centre, prolate cycloids, and points further from the centre, curtate cycloids.
Thereupon followed the epicycloids, curves which as the cycloid is generated by a point upon the circumference of a circle rolled along a straight line are generated by a similar point when the path of the circle becomes any curve whatever. Caustic curves, spirals without number, succeeded, of which but one shall claim our notice, the logarithmic spiral, first fully discussed by James Bernouilli.
The length of the arc described does not signify, as the times of vibration will be the same, whether the arc be the fourth or the four hundredth of a circle, or at least they will be nearly so, and would be so exactly, if the curve described were a portion of a cycloid.
At the mention of dead-lights, the meaning of which he did not understand, the poor governor's heart died within him: he shivered with despair, his recollection forsaking him, he fell upon his knees in the bed, and, fixing his eyes upon the book which was in his hand, began to pronounce aloud with great fervour, "The time of a complete oscillation in the cycloid, is to the time in which a body would fall through the axis of the cycloid DV, as the circumference of a circle to its diameter."
To quote Pascal again, I see no objection, at this stage, to defining the process by the curve which that geometrician studied under the name of roulette or cycloid, the curve traced by a point in the circumference of a wheel when the carriage is advancing in a straight line: this point turns like the wheel, though it advances like the carriage.
But to speak of the author of the ‘Provincial Letters,’ of the problems on the Cycloid, and finally of the ‘Pensées,’ as if his intellect had suffered from his conversion, is to use words without meaning.
With the aid of a system of tangents of which I first showed him the rule and the method of construction, my artist has obtained the ordinary cycloid, followed by the interior and the exterior epicycloid and, lastly, the same curves both lengthened and shortened. His drawings are admirable Spider's webs, encircling the cunning curve in their net.
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.
Owen was an accomplished lecturer; but one's attention to him depended on two things a primary interest in the subject, and some elementary acquaintance with it. If, for example, his subject were the comparative anatomy of the cycloid and ganoid fishes, the difference in their scales was scarcely of vital importance to one's general culture.
My uncle Toby understood the nature of a parabola as well as any man in England but was not quite such a master of the cycloid; he talked however about it every day the bridge went not forwards. We'll ask somebody about it, cried my uncle Toby to Trim. When Trim came in and told my father, that Dr.
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