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BELL SYSTEM TECHNICAL JOURNAL 



analyzed in the appendix and is quantitatively explained in terms of 

 the elastic constants of the crystal. On the basis of this explanation, 

 an investigation is also given in the appendix, of crystals cut at differ- 

 ent orientations, and a crystal having many advantages for filter uses 

 is derived. 



Some experimental data ^ have been taken for perpendicularly cut 

 crystals for various ratios of axes. Figure 3 shows the principal reso- 



3 4 5 6 7 



DEPTH OF OPTICAL AXES IN MILLIMETERS 



Fig. 3 — Principal resonant frequency of a perpendicularly cut crystal as a function of 



the width of the crystal. 



nant frequency (the frequency for which the electrical impedance is a 

 minimum) for a series of crystals whose mechanical axes are all 10 

 millimeters, whose electrical axes are 0.5 millimeter, and whose optical 

 axes vary from 1 to 10 millimeters. As will be observed, increasing the 

 length of the optical axis in general lowers the resonant frequency. 

 The discontinuity in the curve for the ratio hjlm = -23 is discussed in 

 detail in the appendix. 



^ The experimental data shown by Figs. 3 and 4 have been taken by Mr. C. A. 

 Bieling while the temperature coefficient curve of Fig. 5 was measured by Mr. S. C. 

 Hight. 



