Abstract
MANY people must have noticed the curious curved appearance presented in a photograph by the spokes of a moving vehicle. It is well known that the envelope of a diameter of a circle rolling along a straight line is a cycloid of half the dimensions of the cycloid traced by a point on the circumference. The part of the moving spoke which makes the strongest impression on the photographic plate will be where it intersects the consecutive position, so that the, photograph really gives us a small piece of the envelope of each spoke. The effect may be compared to the ordinary caustics of reflection or refraction. The accompanying photograph shows, not only the curvature of the spokes, but also the cusps of the envelopes of the spokes the ends of which have touched the ground during the exposure. In the diagram, the envelopes for a circle with fourteen equidistant diameters are drawn, and the parts of the envelopes which have been put in strongly indicate the appearance that would be presented in a photograph, supposing that three spokes had touched the ground during the exposure. The spokes on the upper half of the moving wheel leave no impression on the plate, because their points of ultimate intersection lie outside the spokes themselves.
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MILNE, R. Curvature of Wheel Spokes in Photographs. Nature 67, 8 (1902). https://doi.org/10.1038/067008b0
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DOI: https://doi.org/10.1038/067008b0
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