# Volltext: Helmholtz's treatise on physiological optics. Volume 2. Edited by James P. C. Southall. Translated from the 3rd German edition (2)

184, 185.]
§22. Duration of the Sensation of Light
219
figures seen in the mirror appear to execute the movement, which they are
intended to represent, although each of them stays at the same place on the
disc.
If the apertures are designated by numbers, so that the eye looks first
through number one, then, as the disc turns, through number two, etc.; and
if also the diagrams along the radii drawn to these apertures are designated
by the same numbers; then when the spectator looks through aperture No. 1,
he will see in the mirror the image of diagram No. 1 opposite the image of his
eye. As the disc turns, aperture No. 1 goes past his eye, and for the time
being the image in the mirror is completely hidden by the dark disc, until
aperture No. 2 arrives in front of his eye, and then he sees an image again.
But now diagram No. 2 is there instead of diagram No. 1, that is, on the
radius drawn to the eye. Then there is darkness again until aperture No. 3
comes in front of the eye, and diagram No. 3 appears at the same place where
the other two diagrams were just before. If all the diagrams were exactly
alike, the spectator would get a series of separate but equal visual impressions;
and if they were repeated fast enough, they would fuse into a prolonged
sensation of an object at rest. But if each diagram is a little different from
the preceding one, the separate impressions will be fused also in the image
of an object; which, however, seems to be continually changing in the way
that the images succeed one another.
When the number of diagrams is not the same as the number of apertures,
the diagrams appear to be moving forwards or backwards. Suppose there are
n apertures and m diagrams, the numbers n and m, however, not being very
different; and that at first one of the diagrams is located on the radius directed
towards the observer’s eye opposite one of the apertures. When the disc is
2?r
turned through the arc —, the next aperture arrives in front of the eye. But
n
the distance of the second diagram from the radius above mentioned is equal
/2tt 2tt\
to an arc I —--j. Now if this arc is small enough so that the second
\n m /
diagram is nearer the place, where the first diagram was first seen, than any
other diagram now visible, this second digram now in sight will be identified
with the first one that was seen before; and the impression is that the first
diagram has been seen to traverse the corresponding arc. Usually, m is
taken equal to (n+1) or (ft—1). In the former case, the diagrams advance
with the motion of the disc, and in the latter case the movement is in the
opposite direction.
The narrower the apertures in the larger disc, the less of the images will
be seen; but the fainter they will be too. Uchatius1 constructed an apparatus
for projecting the images on a screen. A useful application of the stroboscopic
disc was made by J. Müller2 for exhibiting the phenomena of wave motion.
The daedalion of W. G. Horner is a similar affair, except that the holes
are on the surface of a hollow cylinder, and the figures partly on the inner
surface (preferably transparent), and partly on the base.
In the devices described so far the figures and apertures revolve with the
same angular velocity. We obtain another set of phenomena when the
angular velocities are different.
One of the simplest contrivances of this kind is the top (Fig. 44) made by
J. B. Dancer of Manchester, when a second disc is attached to the upper part
of the axle, as in Fig. 49. This disc has holes in it of different shapes; and a
piece of string is tied to the edge, as shown in the cut. Owing to the friction
1 Sitzungsberichte der k. k. Akad. zu Wien. X. 482.
2 Poggendorffs Ann. LXVII. 271.

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