SUPERPOSED STROBOSCOPIC VELOCITIES 



L. E. DODD 



The curves plotted from the stroboscopic velocity equation/ v^= 

 (A — n/m.B)D^, (1) and from the derived form," f=mN — nB, (2) 

 show that from a given frequency of the stroboscopic figures there 

 is an unlimited number of illumination frequencies that will give 

 the stationary stroboscopic condition, and conversely, for a given 

 value of the illumination frequency there is an unlimited 

 number of frequencies of the stroboscopic figures that will make 

 Vg equal to zero. 



To restate the matter in more definite form and to fix ideas in the 

 remarks that follow, reference will be made specifically to the tono- 

 scope drum." By eq. (2) above, for a given row of dots on the 

 drum (definite value of N) there is an unlimited number of illumi- 

 nation frequencies that can produce the stationary condition 

 (f=0), and conversely, for a given illumination frequency there 

 is an unlimited number of rows on the drum (supposed of infinite 

 extent) capable of reacting to that illumination frequency with a 

 stationary stroboscopic response. 



In the first case, where a fixed value of A (or N) is taken, it may 

 be imagined that several of the unlimited number of illumination 

 frequencies possible are operating at the same time. Mathemat- 

 ically at least, each of these T-equencies will produce its own station- 

 ary efifect, with the simple images caused by it alone having as their 

 distance of separation the quantity Do/m. If m=l for all of these 

 several frequencies simultaneously present then the resultant effect 

 wid have one of two general characters. The first general character 

 will show the appearance produced by one of the illumination fre- 

 quencies alone, with the exception of a greater intensity of the sim- 

 ple images, and will be due to the several illumination frequencies 

 all catching the stroboscopic figures in the same phase. (A definite 

 "phase" in the sense here used is indicated by a fixed point near 

 the surface of the drum, such as a point on the tonoscope scale.) 

 The second general character will show the appearance of several 

 rows of stationary simple stroboscopic images superposed so that 



iproc. Iowa Acad. Sci., XXIV, p. 222, 1917. 

 =Proc. Iowa Acad. Sci., XXV.. p. 49, 1918. 

 'Proc. Iowa Acad. Sci., XXIV, pp. 223-224, 1917. 

 33 



