EVOLUTION OF QUARTZ CRYSTAL CLOCK 573 



surface and coupled effects. Since, for a given shape, the volume increases 

 with Hnear dimension in greater porportion than the surface area, it can be 

 inferred that surface phenomena would affect a large resonator less than a 

 smaller one. 



This is also a reason for employing a stubby shape, in order that the volume 

 of crystal may bear as large a ratio as possible to its surface area. From 

 this standpoint alone a sphere would be ideal but for other reasons, chiefly 

 concerned with the temperature coefficient, it would be unsuitable. It is 

 probable that a polished prolate spheroid, properly oriented with respect to 

 the erystal axes, would satisfy both conditions. Such a resonator could 

 be supported by a pair of wires, serving also as electrical leads from metal- 

 plated electrodes, using techniques already well established. 



Crystal resonators as now used in many of the most stable oscillators have 

 been constructed to withstand severe mechanical shock while in operation. 

 It is likely that a slight improvement in frequency stability might be ob- 

 tained by relaxing a Uttle on the mechanical stability of the present support. 

 Where the greatest accuracy of rate is desired, such as in national standards 

 laboratories and in astronomical observatories, it should be possible to 

 provide suitable mountings for crystal resonators having more delicate 

 supports than those required in mobile equipment. The GT crystal illus- 

 trated in Fig. 21 is mounted on eight supporting wires for applications 

 requiring great mechanical stability, and at the same time remains one of the 

 most stable frequency controlling resonators t\^r produced. It would be 

 reasonable to expect a Httle improvement in frequency stability at the 

 expense of some mechanical stability if four supports were used instead of 

 eight. 



There is a good possibility also that some improvement could be obtained 

 by reducing the electrical coupling to the crystal. At present, the plates 

 are usually provided with plated metal electrodes which cover the entire 

 large surface areas. Some increased stability in frequency might be expected 

 by the use of relatively smaller electrodes covering only the central part of 

 the resonator where the amplitude of vibration is small. At least two 

 advantages might be expected from such a modification. One is that the 

 loading effect is least near the node for vibration, another is that any loose- 

 ness of material, or elastic hysteresis, would be least troublesome where the 

 motion is least. Of course, it is chiefly the variations in such effects that 

 concern us. One would expect, however, that if such effects exist at all they 

 might be minimized by the use of smaller electrodes. 



These particular effects may be eliminated completely, of course, by the 

 use of isolated electrodes spaced from the crystal — but at the expense of 

 other possible variations related to changes in electrode spacing. There is 



