THE STROBOSCOPIC EFFECT 
223 
Equation (5) shows that v s may have plus or minus values, 
or may vanish, at which time the stationary stroboscopic condi- 
tion is present. V s is positive in the direction of v positive. 
When v s =0 we have, 
A 0 /Bo = n/ m (6) 
The fraction n/m in (5) is to a limited degree independent of 
A/B, although equal to A 0 /B 0 , for the value A/B may be in- 
creased or decreased within certain limits without changing the 
value of n/m. These limits are the values at which v 8 has be- 
come so great that the moving row of simple images becomes a 
blur. Continued change will introduce a new value of n/m. 
In (5), as seen by (6), n is independent of m just as A is in- 
dependent of B. 
If in (3) v, B, and D 0 are variable, then 
1 2 t 2 
As= J" v dt - n/m * |D g dt, (7) 
t x ti 
where I), is a function of the time consistent with the observed 
As, and the time between two successive illuminations is(t 2 — — t x ). 
The average stroboscopic velocity over this time interval may be 
taken as the “instantaneous stroboscopic velocity,” and its 
value is 
v s = As/(t s — tO, (8) 
where the value of As is given by (7). In practical cases v, 
though not exactly constant, may have a fairly constant mean 
value, and equation (5) may be used to find the “mean” strobo- 
scopic velocity, provided B and D 0 are constant. 
If the factors v, D 0 , B, in (5) are variable and known func- 
tions of the time, then by special mathematical treatment of gen- 
eral application (see IV below) instantaneous values may be 
assigned to v s , • 
II. Mathematics of the Tonoscope and the Tonodeik. 
The belt illustration in I holds for the stroboscopic screen of 
the tonoscope and the tonodeik where there are a large 
number of parallel rows of figures on the same stroboscopic 
screen, each with its own value of D Q . The value of v for each row 
is of course the same, likewise B. The stroboscopic velocity given 
by (5) is the tangential value, as is the value of v substituted in 
(5), and D 0 is a length of arc. The difference in the value of 
