Potts — Rowland's JVetv Method. 105 



As in the case considered above, a coil does not act as a self- 

 induction alone but as a self-induction in parallel with a 

 capacity due to the electrostatic action of the turns of the coil 

 on one another. For this reason the above formula is not exact 

 for any actual case ; but there must be substituted above in 

 place of ~R b +ibL 



R" b + ibL 



R»,+»L- b - r 



Substituting this in (12) we have 



R , . R" b + ibL 



c * <(fc->.)_ ibc'R" b + l-b*c'L 



° a K + ibl- -~ 



be 



_ R' b ( 1 -fiVL)ftc + R%6c + ^(yec'B^R^ + 5 2 cL)] 



" R a (l-&VL)6c + (l-& a cJ)&c'R* 4 — *[(1- b*c'L)(l—b*cf)-b*cc' 



[R ;/ ,R a 



As before, the condition for no deflection is that the real part 

 of this equals zero. Hence 



b 2 c[R' b (1-5VL) +R /; & ] [R« (1-6VL) c + R% (l-6V)c'] 

 = & 9 c[R' 6 R% c' + L] [(1 -b'c'h) ( 1 -#W) -6W. R" b .R a ] 



Expanding, 



R' 6 R a (l-5VL) a c-f R ff 6 (l-6W) (1-5VL)R ' 6 c' 



+ R\ R a (1 -b 2 c'L)c+R" b 2 (1 —b'ciy = 



R' & RV' (1-5VL) (l-6 a cQ +L(l-6VL) (l—b'cl) 



-b*cc'R" b R a (L+R' & R% c') 



Since c ; is small, we can drop the term in c /2 . We have, on 

 dividing by (1 — 5VL) (1 — J 2 cZ)c and rearranging terms, 



L _R' 6 R g (l-&VL) , R" 6 R« ; ™ 2 e' 



R" 2 — 

 i—O'el ' (l— 6*cf) ' 



7iVR", TC T. 



C l-tfd ^(l-b 2 cl)^ 6 e (& a -&VL) 



& R«- 



or 



(1— & a cJ) (1-6VL) 

 L _ (R' B + R\ ) R a 



R// 2 

 h 



C (l-d"eJ) n ° c (1-6VL) 



&VLR a R' 6 6VLR a R" & 



(1-&W) ' (l-b 2 cl) {l-Vc'L) 



