﻿308 Dr. S. R. Milner on the Use of the Secohmmeter 



incomplete balance at any lead 8 is obtained by putting (J 

 zero in equation (8). 



Incomplete Balance at zero lead. — This is the commutator 

 position at which the instrument is ordinarily used. The 

 relation between the variables corresponding to the balance is 



p^k cosh&ZT Pinh A*t u u (10) 



r — k coshl^T f%zT Y J y J 



<$> is a function of zt which varies from 1 to as zr increases 

 from to oo . Its course is shown in the curves I. and I a. 

 (fig. 5), which represent <£ plotted with zt and with Ijzr for 

 the large and small values of zt respectively. The ©'s give 



a number of experimental values of j at corresponding 



values of zt, which were obtained by balancings similar to 

 those the results of which are given in Table I., p. 300. 

 (10) may be written 



p—fyr + ^l-fyk, 



and since (j> is always less than 1, we see that a balance at 

 zero lead always results in a value of p which is a weighted 

 mean between those of r and k ; but, since the weighting 

 factor is unknowm, no practical conclusion can be drawn 

 from it. The result is, however, important, as it show's that, 

 in the ordinary w r ay in which it is often used to measure 

 electrolytic resistances without attempting to balance the 

 capacities of the electrodes, the secohmmeter is very markedly 

 inferior to the telephone in the accuracy of its results. The 

 telephone gives the equality p = r independently of the value 

 of L 



Balance corresponding to r — k. — When r — k we have from 

 (12) as the condition that = 0, the relation 



This result is a simple consequence of the fact referred to 

 above that, when r = k, the curve for the unreversed galva- 

 nometer current is the same as if the bridge comprised 

 non-inductive resistances only. After reversal, the mean 

 galvanometer current is thus reduced to zero at the same 

 lead, S = Jr, as in the case of pure resistances. 



The converse proposition is of course also true. If 8 be 

 made ^, and the resistance R adjusted until the galvanometer 

 deflexion is reduced to zero, the result of the adjustment will 

 be to make -o j£ 



r = k 3 or its equivalent ^- = yj. . . (11) 



