524 



BELL SYSTEM TECHNICAL JOURNAL 



There are now two possible combinations depending upon which 

 circuit or group of circuits is kept fixed while the other is varied. 

 If the case in which the second group of circuits is kept fixed be 

 examined first, it will be seen that as the frequency of circuit No. 1 

 is varied it will come into tune successively with each of the circuits 

 of the second group. The result will be a series of coupling curves 

 with the characteristic reaction illustrated by Fig. 6 repeated at each 

 coincident point. If it be assumed that the coupling decreases as 

 the order of the harmonic increases, then the magnitude of the re- 

 action also decreases. This is illustrated by Fig. 8, which shows the 

 coupling curves of such a system plotted in terms of the equivalent 

 electrical wave-length. 



Fig. 7. 



Returning to the crystal plate, if the vibration in the direction of 

 the thickness be identified with circuit No. 1 while the width vibration 

 and its harmonics be identified with circuit group No. 2, then Fig. 8 

 should represent what happens to the crystal wave-length as the 

 thickness is reduced. Comparing Figs. 4 and 8, it is seen that this is 

 true in a restricted region but that the wave-lengths which depend 

 upon the width vibration do not continue much beyond the coupling 

 region in the experimental curves. This is to be expected, for these 

 wave-lengths which depend upon a harmonic of a vibration transverse 

 to the applied field are more difficult to excite than the fundamental 

 in the direction of the field. This particular point is discussed further 

 in connection with temperature coefficients. 



If now the case be examined in which the tuning of the second 

 group of circuits is varied, it will be seen that the coupling curves 



