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Updated: May 18, 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.
Wollaston had made a drawing of the orbit and its elements; but, having left it in town, he described the lines so accurately without naming them, that I remarked at once, "That is the curtate or perihelion distance," which pleased him greatly, as it showed how accurate his description was.
A. When the wheel of a coach rolls along the ground, any point of its periphery describes in the air a curve which is termed a cycloid; any point within the periphery traces a prolate or protracted cycloid, and any point exterior to the periphery traces a curtate or contracted cycloid the prolate cycloid partaking more of the nature of a straight line, and the curtate cycloid more of the nature of a circle.
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