84 Mr. E. F. Northrup on the Specific Inductive 



Here D is trie total distance between either pair of large 

 plates. The variation in the value obtained for K when d s 

 varies from its true value is the error. Call the error E. 

 Then 



Be*," ^-d(D-d,r ' ' ' ■ l ; 

 from (10) 



d^di 



a -K(D-d 3 y 



Substitute this value of d in (11), and we obtain 



E= rf 3 (D-rf 3 ) (12) 



The error is least when c)E = 0. Differentiating (12) we 

 obtain 



3E = 



-KD(K-2rf 3 )dd 3 



which, put =0, gives 



<?3=5 (13) 



This says that a variation of d 3 from its true value produces 

 the minimum error in the value deduced for K when the 

 plate N is halfway between the two large plates A and 0. 

 To have the plate in this position the following relations 

 must hold : — 





d 3 = 



A D d + di 



d *~ 2 ~ 2 



and from (9) 

 Whence we obtain 





a 





D 



d\ 7 

 £ + <*, 





2 



2 ' 



This result, of course, can only be of value when K is 

 approximately known. 



