82 



BELL SYSTEM TECHNICAL JOURNAL 



An investigation of how far beyond Fq the new method of equal- 

 ization could be employed disclosed certain limitations. In general an 

 increase in frequency range, either by shortening the string or by elec- 

 trical equalization, reduces the sensitivity, with the result that more 

 current must be passed through the string to secure the desired de- 

 flection. Since the heating of the string increases with the square of 

 the current a limit of improvement is ultimately reached. With 

 electrical equalization this limit has been found to be in the neighbor- 

 hood of 2.5Fo. A peculiar action of the string in the neighborhood 

 of 3Fo, described below, would also place an obstacle in the way of 

 equalizing the galvanometer much beyond 2.5 Fo, were the limit not 

 already set by the heating. 



When a current remote from 3Fo is applied to a string, the deflection 

 is found to be practically proportional to current for all values within 

 the normal range. When a frequency near 3Fo is applied, however, 

 the deflection is linear for very small deflections, but at a certain 

 critical value becomes non-linear — increasing very rapidly to from 

 two to three times its previous value. Beyond this point the deflection 

 again becomes linear with current. As the current is decreased, the 

 deflection decreases linearly to approximately the critical value and 

 then decreases abruptly. It does not follow the curve of increasing 

 current, however, but actually forms a hysteresis loop. The phenom- 

 enon is shown in Fig. 8. With a frequency of 2000 cycles the deflection 



20.25 

 < 



if) 0.15 



Z 0.10 



6 8 10 12 14 16 



R. M.S. CURRENT IN MILLIAMPERES 



Fig. 8 — Deflection-current characteristics for strings tuned to 3000 cycles for 

 frequencies near and remote from ZF<i. 



is practically linear with current for all values, but for a frequency of 

 9100 cycles, approximately 3Fo, the hysteresis loop occurs. This dis- 

 continuity is greatest at 3/^o but is detectable at frequencies several 



