532 



BELL SYSTEM TECHNICAL JOURNAL 



ture as the width is changed (which amounts to a change in the tuning 

 of the transverse vibration), it will be seen that the experimental 

 results are in accord with the above treatment. Fig. 14 shows the 

 temperature coefficient of the two frequencies of a crystal plate at 

 58° C. as its width is progressively reduced in the neighborhood of 

 the 5th harmonic of the transverse vibration. These curves show how 

 the temperature coefficients change sign in this region. The dotted 

 sections of the curves are extrapolated, for owing to the rapid reduction 

 in activity once a coupled frequency acquires a negative coefficient, 



S 80 



^5 



o:z 



li. u 



uj O 

 Q-_I 

 5-1 



1^1 



40 



UJ 



19.10 

 WIDTH 



Fig. 14 — The change of temperature coefficient of a parallel cut crystal at 58° C. 

 as the width is progressively reduced in the region where the fifth harmonic of the 

 vibration in the direction of the width coincides with the frequency of the vibration 

 in the direction of the thickness. 



data on the crystal plate used as an oscillator are difficult to obtain 

 in this region. 



Returning to the experimentally determined curve of frequency 

 versus temperature for a parallel cut crystal plate shown in Fig. 11, 

 this can also be explained with the aid of the above analysis. Referring 

 to Fig. 12, if it be assumed that at 20° C. the crystal is oscillating 

 with a frequency yl, this is in the region where this particular frequency 

 has a positive temperature coefficient. As the temperature increases 

 the frequency increases in the direction of B, passing through a 



