38 Dr. J. P. Dalton on a New Continuous- Balance 



one a non-inductive resistance R', and the other, of total 

 resistance say R", a coil of inductance L in series with a 



Fig. 1. 



-R' > < 



jVVVVVv/VVVVA/vAA/nAA>VVVVAA/S^S/ 



C 3 



TTVUB aoau OVTS J 



non-inductive resistance over part of which, r, a condenser 

 of capacity C is shunted. Suppose now an alternating e.m.f. 

 is applied between the points A and B : taking its initial 

 phase to be zero, we may write for it E e^K The current 



amplitude in the upper circuit is then ^ ; it is real and 



consequently it, as well as the potential difference between 

 any two points in that branch, is always in phase with the 

 applied e.m.f. But the current amplitude in the lower 

 branch is 



E (l + Cnp) 

 (R"+Lz»(l + CWp)-r 2 CV ' * " W 



and therefore is not, in general, in the same phase as the 

 applied e.m.f. and cannot possibly be so for all values of p. 

 The same applies to the potential difference across any part 

 of the non-inductive resistance in that circuit. The phase 

 of the voltage across the coil is determined by 

 E (l + Cn>)(R c + Lfo) 

 (R" + Lt/0(l + O*»-r s Ctp' " " ' ' K ' 

 where R c is the coil resistance, and it, too, cannot possibly 

 vanish for all values of p. As long as the coil and con- 

 denser are in series in the same branch, a true balance cannot 

 be found which is independent of the frequency*. 



* Forsvthe's recent very elegant method of comparison (Phys. Rev. 

 i. ser. 2, p. 468 (1913) ; Science Abstracts, A. xvi. No. 1724 (1913)) gets 

 rid of the difficulty by placing the condenser in series with a resistance, 

 x say, across the coil, so that r now includes the coil. The current in 

 the lower branch is now 



Eo tt~ ^ ; n ;•• • (*) 



(R "-' ,) (i +L8 > + - r+ '') +(, ' +L!>) (ci +;l ')' 



id p —r 2 the phase of 

 is then continuous for any frequency 



If x=r and ~- —r 2 the phase of this vector is zero, and the balance 



