THE STROBOSCOPIC EFFECT 
225 
Let V be the maximum value of v s at which the response van- 
ishes. Then for the lower limiting row, 
N 1 = v/(v + V) * No , (12) 
and for the upper limiting row, 
N 2 = v/(v-V) • No (13) 
It follows that the range of N values for the region of response 
is 2vV/ (v 2 -V 2 ) • N 0 , and the range of N values above the sta- 
tionary row is greater than the range below that row by the 
amount 2Y 2 / (v 2 -V 2 ) • N 0 . The taking of V as constant in equa- 
tions (12} and (13) neglects any variation in that quantity with 
D 0 and supposes the dots all of equal size. In these equations 
v is the linear velocity of the drum or disc used as stroboscopic 
screen. The distribution of stroboscopic velocities in the case 
of a disc will be of a character modified from that of the drum 
because of the varying radii of the reentrant circles of figures. 
III. Mathematics of the Movies. 
In motion pictures the stroboscopic screen is in reality the 
film that is intermittently illuminated, and the stroboscopic fig- 
ures are the film images. The stroboscopic images may be re- 
garded as (projected to the movie screen where they appear mag- 
nified. The resultant moving picture as a whole is considered 
for purposes of analysis as made up of a very large number of 
small areas (method of the calculus). Each small area contains 
its own moving picture, which is treated as a simple stroboscopic 
image, with its corresponding stroboscopic figures on the film. 
Unlike the images in the case of the belt in I, the elementary 
images in the movies have a component of motion at right angles 
to the velocity of the stroboscopic screen as well as in its own 
direction. The component of motion at right angles is due to 
the manner of distribution of the component elementary figures 
on the film. 
Equations (7) and (8) are applicable if n/m is put equal to 
unity. For the component of motion at right angles to the film 
velocity the second term in (7) is zero, and the first term is re- 
placed, since there is no velocity of the film in this direction, 
15 
