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References

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  1. P. F. Gaehr, Science 68, 567 (1928).
    [CrossRef] [PubMed]
  2. R. M. Packard, Science 68, 567–568 (1928).
    [CrossRef]
  3. C. E. Ferree, Science 68, 645–646 (1928).
    [CrossRef] [PubMed]
  4. J. P. Guilford, J. Exp. Psych. 12, 259–266 (1929).
    [CrossRef]
  5. H. S. Gradle, Science 68, 404 (1928).
    [CrossRef]
  6. “J. M.,” Quarterly J. Sci. Lit. Arts 10, 282 (1821.)
  7. P. M. Roget, Phil. Trans. Roy. Soc. London,  1, 131 (1825) (cited by Helmholtz, Physiological Optics (Optical Society of America) Vol. II, p. 223).
    [CrossRef]

1929 (1)

J. P. Guilford, J. Exp. Psych. 12, 259–266 (1929).
[CrossRef]

1928 (4)

H. S. Gradle, Science 68, 404 (1928).
[CrossRef]

P. F. Gaehr, Science 68, 567 (1928).
[CrossRef] [PubMed]

R. M. Packard, Science 68, 567–568 (1928).
[CrossRef]

C. E. Ferree, Science 68, 645–646 (1928).
[CrossRef] [PubMed]

1825 (1)

P. M. Roget, Phil. Trans. Roy. Soc. London,  1, 131 (1825) (cited by Helmholtz, Physiological Optics (Optical Society of America) Vol. II, p. 223).
[CrossRef]

Ferree, C. E.

C. E. Ferree, Science 68, 645–646 (1928).
[CrossRef] [PubMed]

Gaehr, P. F.

P. F. Gaehr, Science 68, 567 (1928).
[CrossRef] [PubMed]

Gradle, H. S.

H. S. Gradle, Science 68, 404 (1928).
[CrossRef]

Guilford, J. P.

J. P. Guilford, J. Exp. Psych. 12, 259–266 (1929).
[CrossRef]

M., J.

“J. M.,” Quarterly J. Sci. Lit. Arts 10, 282 (1821.)

Packard, R. M.

R. M. Packard, Science 68, 567–568 (1928).
[CrossRef]

Roget, P. M.

P. M. Roget, Phil. Trans. Roy. Soc. London,  1, 131 (1825) (cited by Helmholtz, Physiological Optics (Optical Society of America) Vol. II, p. 223).
[CrossRef]

J. Exp. Psych. (1)

J. P. Guilford, J. Exp. Psych. 12, 259–266 (1929).
[CrossRef]

Phil. Trans. Roy. Soc. London (1)

P. M. Roget, Phil. Trans. Roy. Soc. London,  1, 131 (1825) (cited by Helmholtz, Physiological Optics (Optical Society of America) Vol. II, p. 223).
[CrossRef]

Quarterly J. Sci. Lit. Arts (1)

“J. M.,” Quarterly J. Sci. Lit. Arts 10, 282 (1821.)

Science (4)

H. S. Gradle, Science 68, 404 (1928).
[CrossRef]

P. F. Gaehr, Science 68, 567 (1928).
[CrossRef] [PubMed]

R. M. Packard, Science 68, 567–568 (1928).
[CrossRef]

C. E. Ferree, Science 68, 645–646 (1928).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

The cycloid effect. Automobile with twelve yellow wooden spokes driven past camera at forty miles per hour. Shutter speed, 1/40 sec. An example of the pattern of spoke visibility as seen by both eye and camera.

Fig. 2
Fig. 2

The cycloid effect. The cylinder base is marked out with eight white adhesive tape “spokes,” and the cylinder allowed to roll down the inclined plane. This photograph (taken with an exposure of 1/10 sec. at the time when the cylinder had reached the end of the incline) reproduces the effect approximately as the eye sees it. Diagram shows pattern of cylinder base. Motion is from right to left, with counterclockwise rotation.

Fig. 3
Fig. 3

Creation of the cycloid effect through mechanical and optical overlap. Cylinder base black, with four white spots along one radial line. Background black. Cylinder allowed to roll down inclined plane. The camera with shutter open records the trajectory of the spots: (1) The central spot describes a straight line. (2) The peripheral spot describes a cycloid. (3) The intermediate spots describe prolate cycloids. It is noted that in the upper hemisphere there is no overlap of the trajectories, whereas in the lower hemisphere these trajectories form a repetitive pattern of overlap. The loci of maximum overlap become loci of maximum brightness, and their summation forms the basis of the apparent “spokes.”

Fig. 4
Fig. 4

The cycloid effect produced mechanically by stencil replica of cylinder base. Stencil rotated through successive 1 2 arcs, along base line, and tracings made at each position. Photograph shows summation of tracings made during one-half of a complete revolution of the stencil. The loci of maximum overlap are cycloids, which give rise to the illusion of “spokes.”

Fig. 5
Fig. 5

The cycloid effect, as seen when the eye is made to move rapidly past a stationary rotating wheel. (The resultant pattern is identical with that produced when lateral and rotatory motion are combined in the cylinder itself as it rotated down the inclined plane.) When the camera, with wide open shutter, is held in the hand, and swept past the stationary rotating wheel, the same pattern of interlacing cycloids is created. This effect is probably an example of the “unexplained visual phenomenon” described by Gradle, who reported moving airplane propellor visibility “as the visual axis was turned laterally.”

Fig. 6
Fig. 6

The cycloid effect is not modified by the interposition of a stationary grid. Cylinder base marked out with eight white adhesive tape radii, and cylinder allowed to roll down inclined plane. The apparent curvature of rapidly rolling carriage wheels, when viewed through a series of slits, as described by “J.M.” in 1821, is therefore seen as an example of and anticipation of the cycloid effect.

Fig. 7
Fig. 7

The Roget effect, as seen by the eye, and as recorded by the camera with wide-open shutter. Stationary rotating wheel with four white adhesive tape radii on black background. Rotation counterclockwise. Grid composed of alternate vertical 1 4 slits and bars moved slowly from right to left between wheel and camera.

Fig. 8
Fig. 8

The Roget effect, as seen by the eye, and as recorded by the camera with wide-open shutter. Stationary rotating wheel with four white adhesive tape radii on black background. Rotation counterclockwise. Grid composed of single 1 4 vertical slit, moved slowly from left to right between wheel and camera. The pattern itself is static. The eye sees the same effect as here recorded.