STROBOSCOPIC VELOCITIES IN THE TONOSCOPE 51 



Thus the curves from (5a) have slope in and y — intercept 

 ( — nB), and those from (5b) have slope ( — n) and y — intercept 

 (mN). The values of n/m for the comparatively few curves 

 actually drawn are indicated on them. 



The meaning of cui*ves from (5a), where B is taken constant 

 for the plotting- of the curves, is that if we had a continuous 

 tonoscope drum, instead of a drum with but a single octave, 

 which included values of N from 1 to infinity, the x — intercepts 

 of the straight lines would give the values of N (=n/m*B) for 

 rows stationary by stroboseopic response for the particular value 

 of B, while the f values on the straight lines would g-ive the 

 stroboseopic velocities. For the actual tonoscope we are limited 

 to the tonoscope octave. The visible stroboseopic response for a 

 given value of B is of course limited to segments of such straight 

 line curv^es, which segments include the zero value for f. 



The meaning of cuiwes from (5b), where N is taken constant 

 for the plotting of the curves, is that for a given row (definite 

 value of N) the x — intercepts give the values of B (=m/n*N) 

 which are able to make that row stationary by stroboseopic 

 response, and the other points on the curves give the finite strob- 

 oseopic velocity in terms of f as a function of B for that row. 



For the curves from (5a), Fig. 1, B is taken equal to 160, so 

 that the value of Nq for which n/m=l/l, falls within the ton- 

 oscope octave. For any other value of B the set of curves would 

 be slipped either up or down along- the y — axis, with the axig-ular 

 relationsi remaining unchanged. The values of n/m most used 

 practically in the tonoscope are: 2/1 (bass voice), 1/1 (where 

 pitch of sounded tone lies within tonoscope octave), 1/2, 1/4 

 (soprano voice). 



Similarly, for the curves from (5b), Fig. 2, X is taken equal 

 to 120, so that the value of N^ for n/m=l/l, falls within the 

 tonoscope octave. For any other value of N the set of curves 

 is slipped either up or do^vn the y — axis, while the angular rela- 

 tions remain unchanged. 



EXPERHIEXTAL. 



Xine cases, affording five different values of n/m, viz., 1/1, 

 1/2. 1/3, 2/1, 3/2, are experimentally investigated by observa- 

 tion on the toncscope. The curves, Fig. 3, for these cases are 

 drawn from eq. (5a), and the small circles indicating points on 

 the curves give experimental values. The agTeement between 



