334 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



torsion generating pure shear waves. These waves may be modified by 

 the environment around the crystal (vacuum, gas, liquid, solid) and 

 react back. Thereby a mechanical I'esistance, Rm , and a mechanical 

 reactance, X m , are imposed on the electrical properties of the crystal 

 element in the circuit. This connection comes out as: 



ARe = KiRm 



A/= -K,Xm, 



where ARe is the increase m measured electrical resistance of the crystal 

 element in the medium compared to in vacuum (or practically in dry 

 air or nitrogen). The decrease in resonant frequency of the crystal ele- 

 ment under these conditions is A/. Thus Ki and K2 are electromechanical 

 constants, which fundamentally may be calculated from the dimensions 

 and piezoelectric constants of the crystals. Now, in simple, Newtonian 

 liquids, 



Rm = Xm = 'Virfrfp 



Thus, by carefully measuring ARe (or A/) on a liquid of accurately 

 known density p and viscosity 17, at a given frequency /, and a given 

 temperature, the constants Ki and K2 may be evaluated without as- 

 sumptions and approximations of deriving them. Their constancy will 

 then reflect the electromechanical stability of the system. Their be- 

 haviour under various conditions will be illustrated below. One further 

 point is that when a liquid or solution does exhibit shear rigidity, or, in 

 other words, if the single large molecules in a dilute solution are able 

 to store energy, then Rm > Xm ■ Hence, in this case, the observed 

 quantities ARe , and especially A/ require particular precision. 



In this regard, typical magnitudes of change of /r between dry air 

 and pure cyclohexane, at various temperatures, appear in Fig. 10. 

 Questions often arise as to the arbitrariness of suspension of the radi- 

 ating crystal, by the fine supporting and lead wires. The effects with 

 the plain wires, in the solid curves of Fig. 10, are somewhat, but not 

 radically, changed when a metal bead is put on, heavily loading vibra- 

 tions in the wires, as shown by the dashed curves. In Fig. 11, a some- 

 what larger influence of the loaded support wires is shown for the Re 

 values, but both curves, by their smoothness and shape over a tem- 

 perature range where the thermal expansion and other elastic constants 

 of the metal support wires are quite different from those of the quartz 

 crystal, affirm reliability of mounting and electromechanical coupling. 



Fig. 10 shows, even for an 80-kc crystal, that A/ for an organic liquid 



