380 Mr. E. Edser. An Extension of 



of restitution F l called into play by the rotation fa will be equal 

 to dwjdhu where hi = -fa. Thus 



The first term represents the force acting on an atom of the mole- 

 cule whose subscript is unity, when that molecule alone is displaced ; 

 the succeeding terms represent the force on the same atom, due to 

 the displacement of the remaining molecules throughout the medium. 

 A number of relations, similar to those given by Maxwell,* may be 

 deduced, but require no further notice here. 



Let the conducting surfaces, each of area A, and separated by a 

 distance D, be charged by means of a battery to a constant potential 

 difference V. Let t , fa, fa. . . . be the molecular rotations produced. 

 If, when electrical equilibrium has been acquired, the molecular 

 rotations are further increased by dfa, d0 2 , dfa. . . . , the increment of 

 electrical energy supplied by the battery will be equal to A . Vdl. 

 Further, writing V = PD, we obtain for this energy E, the equivalent 

 expressions 



E = AD . Pdl! = P27(/ sin dfa 



where 2 indicates summation for the whole of the molecules through- 

 out the medium. Since, on releasing the molecules, the above amount 

 of electrical energy will be returned to the battery (the resistance of 

 leads being considered negligible), we must have 



sin n dfa = 22d0 {a0 + b nl fa + b nz fa + ---- 

 Since the dfa's are arbitrary, 

 Ply sin. 6i dfa = 



Hence F! = Pq sin 0i. Consequently the couple acting on a polar- 

 ized molecule will be equal to that due to a field P. Further, if P 

 = 4*7rff, it is easily seen that 



2 



a^ = 4 TTff . q sin lt 



Similar reasoning will apply when the inter-atomic separations 

 are considered. Consequently the total electrical field contributed 

 by the molecules throughout the medium is numerically equal to 

 4jrli, and acts in a direction opposed to P, the result formerly 

 obtained.] 



* ' Treatise,' vol. 1, chap. 3, 87, 88. 



