Bauhaus-Universität Weimar

Helmholtz's treatise on physiological optics. Volume 2. Edited by James P. C. Southall. Translated from the 3rd German edition
Helmholtz, Hermann von
186, 188.] 
§22. Duration of the Sensation of Light 
and if p is a whole number, the colours will have new positions during the 
second revolution, but during the third the same positions as in the first, 
and in the fourth the same as in the second. Thus a stationary colour effect 
may be obtained, provided the top spins fast enough for the impression on the 
eye to outlast the time it takes the hole to make two revolutions. In this 
case there are (2p+l) repetitions of the same sequence of colours; but this 
sequence is not now the same as the sequence of colours on the lower disc, 
but consists of mixtures of pairs of colours that are opposite each other on the 
TTh 2 
lower disc. For instance, if p = l, that is, if -- =?:, the initial colour will 
n — m 3 
appear again for the following angles: 
0°, 240°, 480° (or 120°), 720° (or 0°), 960° (or 240°), etc., 
that is, always for 0°, 120° and 240°. On the other hand, the colour on the 
lower disc on the other half of this same diameter will appear as being midway 
between the above angles, that is, at 120°, 360° (or 0°), 600° (or 240°), etc.; 
and hence at the same three places as the other colour so as to be mixed with it. 
And, in general, when the fraction -- reduced to its lowest terms is 
equal to —, and the impression on the eye outlasts q revolutions of the lower 
disc, there will be p repetitions of a sequence of colours caused by mixing pairs 
of colours on the lower disc that are at the distance q apart. But if the impres¬ 
sion on the eye does not persist so long, the colours appear to dance to and fro. 
By varying the number, shape and size of the holes in the upper disc, of 
course very variegated kaleidoscopic patterns may be obtained in this way. 
In the case of this particular contrivance, these pictures are more variegated 
still, and the patterns are sometimes very delicate, on account of peculiar 
oscillations that take place in the upper disc. As soon as the upper disc is 
dropped in its place, the top begins to hum loudly; and if the lower disc is pure 
white, the pattern on the upper disc does not change into a system of concentric 
rings, as it would have to do if the upper disc revolved uniformly, but what is 
seen is a great number of repetitions of the form of the hole. From this it 
may be inferred that the rate of revolution of the upper disc is retarded and 
accelerated in regular alternation. These oscillations must be due to the 
friction of the upper disc against the axle. Moreover, there is another system 
of oscillations in which the centre of the upper disc moves to and fro hori¬ 
zontally; as is shown by certain peculiarities of the pattern as it appears 
against a white background. 
These phenomena are exhibited in a more orderly way by Plateau’s 
anorthoscope. Two small pulleys of different diameters, whose axles lie one 
directly behind the other in the same straight line, are driven by two endless 
cords, "both of which run around the periphery of a larger disc. The latter is 
turned by a crank. A transparent disc with a distorted diagram on it is 
fastened to one pulley, and on the other there is a black disc with one or more 
slits. When the discs are revolved, the drawing appears in its correct form. 
Letting m and n denote the number of revolutions per second made by the 
screen and the pattern, respectively, we saw that all points of the pattern that 
are at the same distance from the centre will appear in turn on an arc tra- 
versed by a point in the slit in the screen whose angular measure is 2tt — 
But in the distorted drawing on the transparent disc these points are made 
to take in the entire periphery. Suppose, therefore, that the points of the 
original object and its distorted drawing are given by polar coordinates, and 
that p denotes the radius vector drawn from the centre as pole, and w denotes


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