574 BELL SYSTEM TECHNICAL JOURNAL 



considerable promise in such means, the end result depending upon how 

 precisely the resonator may be held in a fixed position by means that will 

 not change its resonance characteristics. Such means have, in fact, been 

 used successfully in a number of German quartz clocks such as at the 

 Physikalisch-Technische Reichsanstalt^"^, and with the Dye ring resonator 

 developed by D. W. Dye and L. Essen at the National Physical Labora- 

 tory i^s . 126^ England. 



For any given resonator and circuit a careful study would probably reveal 

 an optimum amplitude of oscillation that would yield a maximum stability 

 against residual uncontrollable variables. With the GT crystal, as used 

 currently, the maximum amplitude of motion is about 0.00006 mm. It 

 would be possible to limit the motion to a tenth or a hundredth of this value 

 if it should be found desirable. 



Further studies of the factors contributing to aging of the quartz material 

 also should produce valuable improvements. Since resonators, which ap- 

 pear to be alike in all other respects, often age at greatly different rates, some 

 being very small or substantially zero, it would seem that some reason should 

 be discoverable for such variations and some effective control established. 



There are other relatively massive shapes that should be investigated 

 further such as the ring crystal, mentioned earlier in this paper, and as 

 developed and studied by Dye and Essen^^^ ' ^^^. The ring may be excited 

 in various modes of vibration some of which are more favorable than others 

 from the standpoint of mounting. By choice of orientation relative to the 

 crystal axes, and of dimensions, certain of these can be designed to have zero 

 temperature coefficients in a restricted temperature region. 



Another shape that holds great promise because of its convenience of 

 mounting, along with the other desirable properties, is the rectangular rod 

 vibrating longitudinally in its second or higher overtone such as first de- 

 scribed by Scheibe and Adelsberger^°^. Still another possible massive 

 shape is a much thicker version of the GT crystal which would combine the 

 very favorable temperature-frequency characteristic with that of reducing 

 the ratio of surface area to volume. 



In seeking the highest possible accuracy a precise temperature control is 

 essential in all cases, even with the GT type of resonator with its wide region 

 of low- temperature coefficient. The reason for this is that the frequency of 

 oscillation depends not only on the mean temperature of the resonator but 

 also upon the temperature gradient throughout its volume. Thus, even if a 

 resonator has the same frequency exactly at different mean temperatures, 

 its frequency will vary a little while the temperature is varying from one 

 value to another. The effect of this can be reduced by enclosing the crystal 

 unit in an envelope with thermal lagging so that such variations as do exist 

 at the temperature control layer are prevented from reaching the crystal. 



