. The London, Edinburgh and Dublin philosophical magazine and journal of science . purposes wascompared with the coefficient of self-induction of the field-magnets of an old dynamo of the Ladd pattern. The resist-ance of one of the coils (that put as a shunt to the galvano-meter) was 10*5 ohms, c>=l79 = «i, a=b= 1000, and anadditional resistance of 167 ohms was required for a balance; L/M- (100179>2 -5-65hlM- 1000x177-5 -8b&- On the Use of Shunts in finding Coefficients of MutualInduction. Let R=R1 + R/; where Rx is the resistance of the coilproper, W the added resistance, and let R2 be
. The London, Edinburgh and Dublin philosophical magazine and journal of science . purposes wascompared with the coefficient of self-induction of the field-magnets of an old dynamo of the Ladd pattern. The resist-ance of one of the coils (that put as a shunt to the galvano-meter) was 10*5 ohms, c>=l79 = «i, a=b= 1000, and anadditional resistance of 167 ohms was required for a balance; L/M- (100179>2 -5-65hlM- 1000x177-5 -8b&- On the Use of Shunts in finding Coefficients of MutualInduction. Let R=R1 + R/; where Rx is the resistance of the coilproper, W the added resistance, and let R2 be the resistanceof the second coil of the pair ; then it is easy to see that if weshunt part of the current passing through R2 into a shunt S,the coefficient of mutual induction will be diminished in theratio S:R2 + S. A precisely similar rule may be proved to hold good as theresult of shunting part of the current through R: into ashunt S. Coefficients of Self-induction and Mutual Induction. 237T=Mz0(b-y),F = i(G-. l^u + S. u~^v 4-Ri^y + ^ +The equations are of the form. ax + —u + ... =— L #o> -g.^- ■u+ + R. u—y + ... = 0.— S . u—v + Rx- v—y + ... = —Mi0,-Ri. v—y—W. u—y + ... = third of these equations gives (R1 + S)v = R,1y + Su-Mz0,which reduces the second and fourth respectively to SR, \ . „ S -G>x-u + (nf + ^-~)u-y + ...= -(R + S>^+- = M M Ri + S SRi + S ^o> *0« These are exactly what we should have got by supposingthe resistance of R^ affected in the usual way, and M dimi-nished in the ratio S : Ri + S. § 6. To express a Coefficient of Mutual Induction in Terms ofthe Capacity of a Condenser. It is evident that a condenser and resistance placed in ADinstead of an electromagnet will balance the current of mutualinduction. The conditions for this may be easily inferredfrom what precedes ; but they may be independently deducedby the general method. With the first figure of § 5, ex-cept that a condenser whose polesare
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