THE STROBOSCOPIC EFFECT 
229 
same straight line, and the curve of location is a straight line 
parallel to the y' axis. Then, 
( v s )x = 9 / 9 t (x'+h)=0 
( v s ) y = ^/ 9 t (y '+]) (24) 
( v s )z =d / 9 t (z /+ 0) =0 
By (21) v s ~ d / d t (y '+j). With the stationary condition 
9 y'/ 9 t= -&j/ ^t , (25) 
which shows that for this condition the index point has a velocity 
with respect to the moving axes equal and opposite to that of 
the screen with respect to the fixed axes. 
Similar treatment holds for the vertical component of strobo- 
scopic velocity for an elementary image in the movies, although 
the general equation (21) is applicable to them if the curve of 
location is suitably chosen. This curve may be considered as 
confined to the surface of the film, thus reducing the problem 
to one of two dimensions. The movie audience interprets the 
motions in three dimensions as they actually occurred in nature, 
and the curves of location in two dimensions on the film are 
projections of curves of location in three dimensions. 
THEORY OF THE STROBOSCOPIC EFFECT BY DIRECT REFLEC- 
TION OF LIGHT FROM VIBRATING MIRRORS. 
An examination of the values of D in the equation, D=D 0 /m, 
for the distance between simple stroboscopic images in the tono- 
deik when the stroboscopic effect is 'produced first by manometric 
flame and then by vibrating mirror, reveals that with a given 
frequency of vibration the values of D are identical in the two 
cases. This indicates that the chief determining factor in the 
effect by vibrating mirror is the intensity difference on a small 
area of the screen at the two half-period pauses. Intensity 
maxima occurring during the half-periods should, on the con- 
trary, have the effect of doubling the frequency, which would 
make the value of D by vibrating mirror equal to 1/2 D by 
manometric flame, and this is not in harmony with observed 
fact. 
The importance of the half-period pause of a vibrating light 
pencil of constant intensity is strikingly seen in photographs 
of oscillating beams where there is relative motion between the 
plane of vibration of the beam and the plate during the photo- 
graphing. Some excellent photographs of this character, taken 
with the aid of the phonodeik, are given in Professor D. C. Mil- 
ler ’s recent book, ‘ 1 Science of Musical Sounds. ’ ’ 
