394 Prof. W. M. Thornton on the Polarization of 



minutes the quartz was sufficiently electrified to pick up 

 pieces o£ tissue-paper one millimetre square. 



Later observations showed that 20 minutes was not long- 

 enough to establish full polarization. The ellipsoid was 

 therefore resuspended, having now a free period of 34* 73 

 seconds. After 120 hours in a field of 0*137 electrostatic 

 unit the period was 17 seconds ; after 24 hours longer 

 in a field increased to '26$ unit, 9*72 seconds. 



Values of the dielectric constant calculated from the 

 restoring couple on an ellipsoid making small swings in an 

 alternating field of force are in close agreement with the 

 best previous determinations. The assumption made in cal- 

 culating the couple is that the polarization is taken up 

 instantaneously in any position, and the agreement shows 

 this to be justified. When, however, the field is unidirec- 

 tional the components of polarization are not the same along 

 and at right angles to the axis of the ellipsoid. It will be 

 shown subsequently that several days are, in general, required 

 to reach a steady state when the ellipsoid is allowed to stand 

 in line with the field. There is in this position no transverse 

 polarization, but if the ellipsoid is then given small swings 

 there will be one which alternates with the motion and may 

 thus be considered to be proportional to the constant obtained 

 in alternating fields. 



The ellipsoid behalves in fact as if it were in effect crystal- 

 line, and the restoring couple at unit angular displacement is 



(i^-iAe)™ w 



Where k x is the longitudinal and /c 3 the transverse suscep- 

 tibility, N and L the longitudinal and transverse reaction 

 coefficients, V the volume of the ellipsoid, and F the intensity 

 of the external field. 



This couple is equal to 47r 2 I(n 2 — ?? 2 ), where I is the 

 moment of inertia of the suspended system ; n, n , the 

 frequency of swing with and without the field. 



Hence 



Writing 



(V^xr ~ i * 2 T \VF 2 = 4tt 2 I (n 2 - n Q 2 ). . (2) 



we 



have 



4tT 2 I( > 2 — 7? .q 2 ) _k 1 _ 



VF 2 + l + Ks L.~"*' 



Kl =a/(1— Na), 

 and the dielectric constant 



— _ i+(4tt-:n> 



