STROBOSCOPIC VELOCITIES IN THE TONOSCOPE. 



H. R. FOSSLER and L. E. DODD 

 The characteristic equation for stroboscopio velocity is 



v^ =- (A-n/,n- Bj D^ (i) 



(see Proc. Iowa Acad. Sci., Vol. XXIV, 1917, p. 222), where Vg 

 is the stroboseopic velO'City, A the frequency of the stroboscopic 

 fig-ures, B the frequency of illumination, n/m a fraction at lowest 

 terms, and D,, the distance of separation of the stroboscopic 

 figures. Eq. (1) may be rewritten, 



v^ =r v—n/rn' D^ B 



where v is the velocity of the stroboscopic screen. For the ton- 

 oscope, 



v^=^2 ^r (i-n/m- B/N) {2) 



where r is radius of drum, and N is total number of dots around 

 drum in a oiven row. Let f be the number per second of simple 

 images in a given row passing the tonoscope scale. Then, 



where D is distance of separation of simple images. Now 

 D=D.j/m (loc. cit.). Thus, 



v^=fD^ /r,i = f/m • 2 '^ r/N, (3) 



for tonoscope. Equating (2) and (3), 



f=mN-nB, (4) 



an equation that may be regarded as of the form y=mx-|-B. 

 Although f is a frequency rather than a velocity, eq. (4) will be 

 used as a special form to test eq. (1), because of the linear rela- 

 tion, land f will be referred to in this paper as the stroboscopic 

 velocity. The value of v^ is readily found from the value of f 

 by means of eq. (3). 



Eq. (4) contains two independent varial>les, N and B. Two 

 sets of curves are drawn, with N and B respectively constant, 

 and with some of the unlimited number of possible values of 

 n/m. For these two cases (4) is put into the respective forms: 



/= (m)N -{- i—nB), {5a) 



S^= {—n)B+ (mN). {5b) 



