538 On the Tones produced by Rotating Tuning-forks. 



the straight line produced by a blow perpendicular to one of the 

 faces of the rods. On setting the rod in rotation, this straight 

 line by no means remained at rest; on the contrary, figures were 

 produced which I was surprised to find were alike for all the 

 rods, though their width and thickness bore the most varied pro- 

 portions to each other, but which depended on the rate of rota- 

 tion. On turning slowly, figures like fig. 1 were produced, 

 which, as the speed was raised, passed into figs. 2, 3, and lastly 

 into fig. 4, the last being composed of two concentric luminous 

 circles upon a less brightly illuminated ground. Intermediate 



Fig. 1. Fig. 2. Fig. 3. Fig. 4. 



rates of rotation gave figures formed by lines w T hich did not re- 

 turn into themselves, and which therefore had a less sharply 

 marked appearance. All these figures arise in the following 

 manner : — If the plane of vibration of a rod remained constant, 

 its vibrations would have a smaller amplitude in the direction 

 of its greatest thickness, and a larger amplitude in that of its 

 least thickness. Hence we should see a stationary streak of 

 light, in which the turning points a, b, c, and d (fig. 5), Fig. 5. 

 where the knob is momentarily at rest, would appear mm 

 brightest. Such freedom of motion is, however, only 

 partially possible in the case of the firmly fixed pris- IjM 

 matic rod; and consequently the figure turns round, 

 more slowly than the rod, but quickly enough to produce 

 the appearance shown in fig. 4. The more slowly the gggg 

 rod rotates, in comparison with its number of vibrations, 

 the oftener does its shifting principal plane of vibration cross its 

 original position of equilibrium during one revolution ; and thus 

 are produced knotted or looped figures, among which figs. 3, 2, 

 1, and others, with still more loops, are the only ones which 

 stand out with special distinctness, in consequence of their being 

 formed by lines returning into themselves. Their form is con- 

 sequently quite independent of the ratio between the width and 

 thickness of the rods; but figures with many loops are less rea- 

 dily formed in proportion as the rod vibrates more slowly. The 

 figures which a rod which is not vibrating at right angles to one 

 of its faces exhibits on rotation are compounded of these and 

 the well-known kaleidophonic figures. 

 Erlangen, June 1866. 



