442 



BELL SYSTEM TECHNICAL JOURNAL 



These tests, while they exhibited the most important characteristic 

 predicted, did not give any other check on the validity of the mathe- 

 matical results because the systems differed so greatly from that 

 assumed by Mr. Hartley. To obtain simple results in the theoretical 

 discussion it was found necessary to make some severely restricting 

 assumptions. The mechanical system was assumed rigid except to 

 motion at frequencies near the resonant frequency. Similarly the 

 electrical system was assumed to have infinite impedance to all fre- 

 quency components except that impressed and the difference frequency 

 between the impressed and the mechanical. Thus the only currents 

 and velocities present were of the frequencies (in radians per second), 

 a!„i (mechanical), coj = co^ — Wm (difference). 03g (impressed). 



^ijm^ 



ANALYZERS 



■^"^KRT- 



TT 



# 



CRYSTAL 

 IMPEDANCE 

 ELEMENT 



Fig. 1 — Circuit diagram. 



Under ordinary conditions a non-linear system, such as this one, 

 involving two frequency components (co^ and co^) would have, as 

 modulation products, currents and velocities of all the possible com- 

 bination frequencies (rcod + ^Wm, r, 5 = 0, ±1, ±2, •••)• There 

 would be dissipation of energy at each of these frequencies. These 

 components (other than the three of interest) are the ones which must 

 be suppressed if the system is to be a good approximation to the 

 assumed one. 



In order to satisfy the above conditions the circuit of Fig. 1 was con- 

 structed. ^ The use of the parallel system instead of a simple series 

 circuit had several advantages. The forces on the tuning fork were 

 so balanced that any constant displacement was avoided. Since the 

 tuning fork had a very sharp resonance ^ the mechanical system was 



*The tuning fork with condenser plates was designed by Mr. \V. A. Marrison. 

 ' The damping effect of the air was avoided by operating the fork in a vacuum. 



