The London, Edinburgh and Dublin philosophical magazine and journal of science . thealgebraic condition (found as in the last statement) need vanishonly so far as the constant term and the coefficient of p. To illustrate^ let us consider the simple example (due toRimington f) in which one arm of the balance contains and the opposite arm is shunted with a The resistance operators are easily seen to be Zx = LlP + Rx, Z2 = R2, Z3 = R3, 1 T, R4 + Kp-4(R4-r4) ~\ r it4 — ?*4 — z——-y? , -+KP i + Hpn where r4 denotes the resistance of the part of R4 which| isshunted by the co
The London, Edinburgh and Dublin philosophical magazine and journal of science . thealgebraic condition (found as in the last statement) need vanishonly so far as the constant term and the coefficient of p. To illustrate^ let us consider the simple example (due toRimington f) in which one arm of the balance contains and the opposite arm is shunted with a The resistance operators are easily seen to be Zx = LlP + Rx, Z2 = R2, Z3 = R3, 1 T, R4 + Kp-4(R4-r4) ~\ r it4 — ?*4 — z——-y? , -+KP i + Hpn where r4 denotes the resistance of the part of R4 which| isshunted by the condenser K. Then the algebraic conditionfor a complete balance is or (LlP + RJ {R4 + %4(R,-r4) | = R2R3(1 + KprJ. (32) * Heaviside, Electrical Papers/ vol. ii. p. Phil. Mag. vol. xxiv, 5th ser. July 1887. Operational Methods in Mathematical Physics. 417 Equation (32) can be satisfied identically only if r4 = R4,so that the condenser is shunted against the whole resistance?R4 : and then the balance reduces to an arrangement givenby Maxwell *. Thus we find the conditions for a completebalance, r4=R4, R1R4=R2R3, Li = KR2R3 = KRiR4. (33) But, when r± is less than R4, wre can still arrange forzero time-integral by the conditions : RjR^R^, L1R4+R1K^(R4-n) = R2R3Kr4, found from the constant term and the coefficient of p in (32);these readily reduce to the forms R2R
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