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IOWA ACADEMY OF SCIENCE Vol. XXIV, 1917 
by some source of intermittent and approximately instantaneous 
illumination of constant frequency B. The dots, or stroboscopic 
figures, will have a frequency past an imaginary fixed line cross- 
ing the moving row, of A=v/D 0 . At any given single illumina- 
tion a dot is seen stationary, as a camera snapshot would show 
it, and as it is impressed on the retina, and its location is say 
the point If at the next illumination, or some succeeding 
illumination not too far removed, there is some other dot at P 2 , 
the two dots will be interpreted by the eye as the same if this 
condition holds, 
displacement Pi to P 2 =As, (1) 
where a s is sufficiently small with the given experimental con- 
ditions. The apparently identical dot revealed to the eye at the 
two separate illuminations, and at succeeding illuminations in a 
similar way, may be called a simple stroboscopic image. If the 
illumination has a high enough frequency so that retinal lag 
bridges over the time interval 1/B, the image will per- 
sist in the field of vision. The single apparent displacement 
As is not restricted to the time interval 1/B; if m is a whole 
number having a maximum value suitable to the experimental 
conditions as may be accomplished in each m illuminations. 
Thus may be written, 
AS=m-AS, (2) 
where a S is the apparent displacement of a simple image in time 
m/B, that is the time between two successive illuminations for 
that image alone. More generally, 
As=v /B -n /m - Do , (3) 
where n/m is a fraction at lowest terms. Since v, D 0 , B, are all 
taken constant we have for the stroboscopic velocity, 
v 8 = As • B = v - n/ m * Do B . (4) 
The number per second of actual appearances of the component 
dot figures making up a single image is B/m, and this may 
be called the frequency of the simple image. The period of the 
image is then m/B. The distance between simple images is 
D=D 0 /m. Substituting in (4) the value of v in terms of A, 
v s = (A - n / m * B) Do . (5) 
which may be called the characteristic equation of stroboscopic 
velocity. 
