438 H. A. Rowland — Electrical Measurement. 



Method 7. 

 R 9 R 9 M 19 M 13 + ^[L 3 M 1 -M 38 M 13 ] [L 2 M 13 -M 23 M 19 ] = 



For a coil containing three twisted wires, M ia = M„ = M 2 * 

 and the self inductions of the coils are also equal to each other 

 and nearly equal to the mutual inductions. Put an extra self 

 induction L 3 in R, and a capacity C 2 in R 2 . Replace L 3 by 



L + L 8 and L 2 by L — =-— - and we can write 

 b c // 



L + L— M 



^^ =R,R, + 6'(L-M) (L 3 + L-M). 



As L — M is very small and can be readily known, the for- 

 mula will give ^ 3 . When L— M = we have 



^_or^- = R a R s 



Method 8. 



6 2 M(M + L) = rR 2£ 2 M 2 = rR + (rR)' 

 or ft'M(M-L) = (rR)' 26 2 LM = rR-(rR)' 



Placing a capacity in the circuit R, we have also 

 6 2 M(M + L)- ~ = rR 



or 6 2 M(M-L) + ^_ = rR 



In case the coil is wound with two or more twisted wires, 

 M — L is small and known. For two wires, M — L is negative. 

 For three wires, two in series against the third, M can be made 

 nearly equal to 2L. Hence M, L and C can be determined 

 absolutely, or C in terms of M or vice versa. 



To correct for the self induction, Z, of r we have the exact 

 equations 



6 2 M(M + L) = rR + 6 2 /(L + M) 

 6 2 M(M-L) = rR + W(L— M) 



£ 2 M(M + L) - ^ = rR-w(L+M- -^\ 



6 9 M(M-L) + -^-=rR-ftV^L-M- ^j 

 If the condenser is put in r, we have 



T ]VT 



or ^^1= r R + & 2 M(L-M) 



