Electric Strength of Solid Dielectrics. 



131 



If, as there is reason to believe, the inverse square law 

 holds at atomic distances, and, further, polarization is a 

 separation of opposite charges of magnitude e by a distance 

 x, the forces are, d being the distance between centres, 



(2) 



{(<*-! 



1 



2 + 



1 



2xf T (2d-2x) 2 T (3d-2x) 2 



+ 



} (6) 



{1 1 "| 



(d+2x) 2 + (zd-\-2xy + (3rf + 25.r) 2 + ~' $ C 7 ) 



U) *>A ™d + 2x 0»75 d- 2x 1 



w * \{2~25d 2 + 'dxd+4:x*y/ 2 (2-25<2 2 -3^+4# 2 ) 3 ' 2 J 



f 0-86^+ 2 j; 0-86^-2a; \ 



+ \_{3d?+ t d'4:6xd+4:a; 2 ) s >' 2 '~ (3d*-3-46a>d + 4# 2 ) 3 / 2 J 

 and so on. ... (8) 



The sum of these may be written ce 2 jd 2 , where c is a 



function of -% shown graphically in fig. 2 calculated up to 

 42 elements. The influence on any one is not a restoring 



Fig. 2. 



X 



l '2 -3 -4- -5 2L 



4 

 6 



8 

 10 



12 

 14- 

 16 



force but one increasing x , that is in effect increasing the 

 field. The change of this force of interattraction with dis- 

 placement is given above for various ratios of xjd. 



K2 



d. 





0-10 



-062 



0-20 



-2\10 



0-25 



-3*50 



0-40 



-13-30 



O-50 



— GO 





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