A TABLE OF THE TOTAL NUMBER OF STROBOSCOP- 
IC VELOCITY CURVES FOR ANY OF THE NAT- 
URAL NUMBERS FROM 1 TO 500 INCLUSIVE 
TAKEN AS A LIMITING VALUE OF n AND m 
L E. DODD 
The stroboscopic velocity equation ^ is 
Vg = (A — n/m’B)DQ, 
where n/m is a fraction at lowest terms. Since there are as many 
stroboscopic velocity curves as there are different values of n/m 
this fraction may be referred to as the “stroboscopic parameter.’’ 
A question of importance in the study of stroboscopy is, what 
is the total number of stroboscopic velocity curves for all possible 
values of the stroboscopic parameter up to and including a given 
limit determined by the condition, 
n not greater than m not greater than p, 
where p is the limiting natural number. 
This total number, Q, of the stroboscopic velocity curves for 
each of the values of p from 1 to 500 inclusive has been calculated, 
and the Q values are given in the appended table. 
TABLE 
p 
Q 
9 
Q 
P 
Q 
1 
1 
61 
2323 
121 
8991 
2 
3 
62 
2383 
122 
9111 
3 
7 
63 
2455 
123 
9271 
4 
11 
64 
2519 
124 
9391 
5 
19 
65 
2615 
125 
9591 
6 
23 
66 
2655 
126 
' 9663 
7 
35 
67 
2787 
127 
9915 
8 
43. 
68 
2851 
128 
10043 
9 
S.5 
69 
2939 
129 
10211 
10 
63 
70 
2987 
130 
10307 
11 
' 83 
71 
3127 
131 
10567 
12 
91 
72 
3175 
132 
10647 
13 
115 
73 
3319 
133 
10863 
14 
“ 127 
74 
3391 
134 
10995 
IS 
143 
75 
3471 
135 
11139 
16 
1S9 
76 
3543. 
136 
11267 
17 
191 
77 
3663 
137 
11539 
18 
203 
78 
3711 
138 
11627 
1 See Proceedings Iowa Academy of Science, vol. 24, 1917, p. 221. 
