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BELL SYSTEM TECHNICAL JOURNAL 



"This produces an electrical effect which, for great distances from the molecule, 

 is calculated by the same formula as the magnetic effect of an infinitesimal bar 

 magnet whose magnetic moment is numerically equal to the product of the quantity 

 of electricity of a single atom into the sum of the diminutions of the two distances 

 between the atoms of the two pairs under consideration. Hence, denoting by N 

 the number of crystalline molecules per unit bulk of the crystal; by h the radius of 

 the circle of each crystalline molecule; by 9 the quantity of electricity of each of the 

 six atoms or double atoms, whether positive or negative; by B the change of direc- 

 tion of each of the two diameters through atoms which experience change of direc- 

 tion; and by m the electric moment developed per unit volume of the crystal, by 

 the strain which we have been considering and which is shown in Fig. 1 .5B ; we have 



M = Nqibe COS 30° = iV^Nbqe 



(1.1)" 



Kelvin's model shows some of the symmetry properties of quartz. The 

 axis marked X is the X or electrical axis of the crystal. The Z or optic axis 

 is normal to the plane of the paper. The F or mechanical axis is the axis 



00 





(A) 



Fig. 1.6 — Longitudinal and shear strains applied to a quartz molecule 



along which the stress is applied. It is obvious that if we rotate the direc- 

 tion of the applied stress by 120°, a similar separation of charges at right 

 angles to the stress will occur. There are then three electrical axes and three 

 mechanical axes so that the optic axis can be regarded as an axis of threefold 

 symmetry for the crystal. 



As can be shown from an extension of Kelvin's model there are two other 

 types of stresses that will produce a charge separation normal to the axis. 

 Suppose that we stress the crystal along the X or electrical axis as shown by 

 Fig. 1.6A. Applying the same reasoning as before, we see that the apex 

 molecules are separated farther apart without changing the separation 

 between the other molecules. This results in a separation of the centers 

 of gravity of the positive and negative charges, with the negative charges 

 moving toward the left and the positive charges moving toward the right. 

 The separation is still along the electric axis, but is in the opposite direction j 



