The London, Edinburgh and Dublin philosophical magazine and journal of science . he current inthe lower branch is now Eo tt~^ ; n ;•• • (*) (R-,)(i+L8>+-r+)+(,+L!>)(ci+;l) id p —r2 the phase ofis then continuous for any frequency If x=r and ~- —r2 the phase of this vector is zero, and the balance Method of Comparing Inductance with Capacity. 39 If the telephone is connected between two points P and Q,then balance is attained if Bap RAQ(1 + Cnp) R - (R + Lip)(l + Crip)-r2Cip> {) This determines as the frequency at which a continuousbalance is possible : 9 1 Rap .R —Raq • R fA\ P=LGr K^
The London, Edinburgh and Dublin philosophical magazine and journal of science . he current inthe lower branch is now Eo tt~^ ; n ;•• • (*) (R-,)(i+L8>+-r+)+(,+L!>)(ci+;l) id p —r2 the phase ofis then continuous for any frequency If x=r and ~- —r2 the phase of this vector is zero, and the balance Method of Comparing Inductance with Capacity. 39 If the telephone is connected between two points P and Q,then balance is attained if Bap RAQ(1 + Cnp) R - (R + Lip)(l + Crip)-r2Cip> {) This determines as the frequency at which a continuousbalance is possible : 9 1 Rap .R —Raq • R fA\ P=LGr K^ • • ; (4) and we then obtain L __ 2 r^ Raq- R — Rap . R . ... (5) C Rap Rap If, as is usually done, a steady balance is first obtained,then an inductive balance can occur only when p = 0, andthe method cannot be used with alternating current. Whenp = 0, equations (4) and (5) give the usual conditions Rap R ((»\ AQ J^ and L f . o=r (7> § o. In the Maxwell-Rimington arrangement the con-denser is removed to the upper branch circuit, and it is no Fig. longer impossible to obtain two points, one in each circuit,such that the potential differences between them and A orB are always of the same magnitude and in the same phase,whatever the frequency may be. The current in the upper circuit is now °R(l+ryO)-fSpC * * K) where R is the total resistance of that branch, and r is that 40 Dr. J. P. Dalton on a New Continuous-Balance part of it which is across the condenser terminals ; while inthe lower circuit the current is E° (9) n+Li> In Rimingtons method the indicator is placed between Qand a point X between A and P, so that the voltages whichmust be equal in order to obtain a balance are ¥L(l + ripQ)-rHp(? across AX -Eo-p//-, , JLn\ ^Ln? . . (1U) and across AQ nAQ.+~Lip nn and there is, in general, but one (real) frequency for whichthese are equal. For that we find 2 _ Raq . R; — Rax ? R /1 o\ p~ LCr(RxB-r) ^ } And then L = _^_ {^aq_( r»)}.
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
