494 BELL SYSTEM TECHNICAL JOURNAL 



also been known that oscillations may be produced in a crystal either 

 parallel to the impressed electric field or perpendicular to it, the so- 

 called longitudinal and transverse effects. There is a certain amount 

 of mechanical coupling between such different modes of vibration 

 within the crystal, more or less close, depending upon the shape, and 

 in particular depending upon the ratio of dimensions in the principal 

 directions of vibration. In view of these facts it was thought probable 

 that crystals could be produced with such coupling between the modes 

 which have inherently positive and negative coefficients that the 

 resultant temperature coefficient would be nil. 



Series of crystals of rectangular and circular shape were made to 

 test this fundamental assumption. It was found that the temperature 

 coefficient does vary with the shape of a resonator and, in particular, 

 that crystals may be proportioned so as to have a coefficient that is 

 practically nil. The relations between the temperature coefficient 



Fig. 1 — Crystals used in preliminary temperature coefficient tests. 



and the dimensions in the case of rectangular plates have been further 

 studied in detail by F. R. Lack ^ of the Bell Telephone Laboratories. 



In the first experiment performed with circular discs for this study 

 a large disc was first cut and smaller ones cut from it, after measure- 

 ment, to insure constancy of material, thickness and orientation with 

 respect to the crystal axes. The parts remaining after three sizes of 

 discs had been cut in this way, with the remainder of the slab from 

 which they were obtained, are shown in Fig. L The slab is shown in 

 the partly assembled original crystal in Fig. 2 to show the manner of 

 cutting. With such circular discs it was found that at least one 

 diameter could be found for which the temperature coefficient is very 

 small throughout the entire room temperature range. 



Low temperature coefficient crystals obtained in this way are subject 

 to the usual mounting difficulties, namely that the friction on the 

 mounting considerably increases the decrement, and by an amount 



3 "Observations on Modes of Vibrations and Temperature Coefficients of Quartz 

 Plates," by F. R. Lack, presented before the Institute of Radio Engineers, April 

 3, 1929. 



