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BELL SYSTEM TECHNICAL JOURNAL 



Since the resonant frequency of the plated crystal was measured, it was the 

 zero potential elastic constant that was determined. These crystals were 

 lightly plated with aluminum and it had been previously shown that the 

 added plating would affect the frequency by considerably less than 0.1 per 

 cent. The crystal orientations, their dimensions, the frequency constants 

 and the values of 5^2- are shown by Table I. 



These measured variations satisfy equation (A. 20) for the variation of 

 .^22' with angle very well if we take 



^fi - 127.9 X 10^'' cmVdyne; 



sf, = -44.6 X 10"''; 



su + 2^13 = 175.8 X 10^''. 



^33 = 95.6 X 10 



(A.21) 



This gives three of the constants directly, and a relation between two more. 

 To obtain the remaining constants and to test out the hypothesis that there 

 are seven elastic constants rather than six, use has been made of measure- 

 ments made for thickness vibrating shear crystals obtained by rotating one 

 edge about the X axis. These are the A T and BT series shown by Fig. 1 .9. 

 As shown by a former paper^, the frequency of such crystals depends on 

 the edge dimensions as well as the thickness dimensions. However, as the 

 edge dimensions become large compared to the thickness dimension the 

 principal frequency approaches an asymptotic value which is taken as that 

 for the infinite plate. For the AT, BT and Y cut crystals these asymptotic 

 values have been determined to have the values shown by Table II. 



6 "Low Temperature Coefficient Quartz Crystals," B. S. T. J., Vol. XIX, pp. 74-93, 

 Jan. 1940. See Fig. 5. 



