224 
IOWA ACADEMY OF SCIENCE Vol. XXIV, 1917 
A from row to row is unity, or may be two in the tonodeik. The 
rows are arranged as in Scripture’s disc in ascending values 
of A ; the order of ascent in these two instruments is from left 
to right, corresponding to pitches on the piano keyboard. Be- 
cause a considerable number of the rows have frequencies near 
that of the row with zero stroboscopic velocity (for a given 
value of B), the stroboscopic response is not confined to the one 
row, but includes others on either side of it. The stationary row 
is located in the central part of this region of response. The 
responding rows to the right of the stationary row have strobo- 
scopic velocities in one direction that increase from row to row. 
The same is true for responding rows at its left except that the 
stroboscopic velocity is in the opposite direction. This type of 
symmetrical response facilitates the location of the stationary 
row, or the one that is nearest stationary. Equation (5) is to be 
applied to each row of stroboscopic figures. The illumination 
frequency B is by suitable devices equal to the frequency of a 
sounded tone of definite pitch. With the values of A for the 
different rows as nearly constant as possible, depending on the 
constancy of drive of the stroboscopic screen in the form of drum 
or disc, the pitch of a tone can be found from the known fre- 
quencies A, or vice versa, if the frequency B is known, as it is 
with a calibrated tuning fork, the velocity of the screen can be 
found. If the lowest frequency row has an A value equal to 
the frequency of say C below middle C, then, except in the case 
of a bass voice at a pitch below that, the value of n is to be 
taken as unity, and the values of m as 1, 2, 3, depending on the 
value of m in the expression for the distance between simple 
images, D=D 0 /m. The total number of rows on the screen in- 
cludes hut an octave of musical scale, obviously all that is neces- 
sary. 
To find the range of response we note that D 0 — 2 7r r/N, where r 
is the radius of the reentrant circle of dots, and N the number 
of dots in the circle. If the screen rotates once per second then 
N=A. by (4), . 
v s = v-n /m * 2 7T r/ N • B (9) 
For the stationary row, 
N = No = n/m • 2 r B/v, (10) 
whence, for a row of stroboscopic velocity v s , 
N = v/ (v-v s ) • No 
( 11 ) 
