514 IOWA ACADEMY OP SCIENCE Vol. XXVI, 1919 



the individual members of a given row do not coincide with those 

 of other rows. This mutual displacement of the stationary strobo- 

 scopic rows will be present where the several illumination frequencies 

 do not catch the stroboscopic figures in the same phase, and the na- 

 ture of the relative displacements depends on these relative phases. 

 (If some of the illumination frequencies are in phase while others 

 are not, the character of the effect is a combination of the two just 

 described.) 



In the second case, where a fixed value of B is taken, it may be 

 imagined that several of the possible unlimited number of rows of 

 dots on the drum are superposed to form a single resultant row. 

 Mathematically at least, as many stationary stroboscopic effects will 

 be produced as there are rows of dots superposed to form the one 

 composite row of stroboscopic figures. The resultant stroboscopic 

 effect thus produced by a single illumination frequency will be of 

 ihe same general nature and have the same two general characters 

 as in the first case. Here, however, it will be a question of the single 

 illumination frequency catching the different rows of dots all in 

 either the same or different phases. (If some of the dot frecpiencies 

 are in phase while the others are not, the character of the effect is 

 a combination of these two general characters, as in the first case.)* 



In either of the two cases, Vg for each of the component strobo- 

 scopic effects may have a plus or a minus as well as a zero value. 

 Thus, taking say any two of the component effects, ° they may have 

 the same positive, or negative, or different positive, or negative, 

 velocities. Or one of the pair may have a positive and the other a 

 negative velocity. Thus, where more than two component effects 

 are present the resultant is the complex appearance of a number of 

 rows moving through each other at different rates and in the same 

 or both directions. 



But a complex stroboscopic appearance is mathematically possible 

 by a single illumination frequency acting upon a single row of dots 

 on the drum. Thus, with reference to the f and B curves (loc. cit.), 

 for a fixed value of B there are an unlimited number of f values 

 possible, as is seen from the intersections of the line B=-constant. 

 with the velocity curves. These f values will in general be both 

 positive and negative, and depending not only on the particular 

 value of B but also on the value of N for which the set of curves 



*A third possible case may be iimagined, a composite of the two just de- 

 scribed, where there are several illumination frequencies acting- upon sev- 

 eral different rows of d.ots that are superposed to form a single complex row. 



'■By "component effect" is here meant an indivi.diual row of simple strobo- 

 scopic images due to a given row of dots (g:iven value of N) and a given fre- 

 quency of illumination. 



