MORSE AND SARGENT. — RESISTANCE OF LEAD ACCUMULATOR. 595 



removed, leaving the connections as shown in Figure 2. Tiie ratio of 

 the fixed arm of this auxiliary bridge was 1 : lOUO and resistances could 

 be measured on it to 0.0001 ohm. 



During the majority of our measurements a resistance 

 of a few tenths of an ohm ({0) in the figure) was kept in 

 the cell arm in series with Ci and for some measure- 

 ments of high resistances it was found necessary to 

 introduce a similar resistance in series with the slide- 

 wire and mercury resistances of E. 



Measurements were made with " cell in " and " cell 

 out " within as short a time as possible, in order to 

 eliminate any possible changes, and measurements 

 were repeated several times in each case. We were 

 thus measuring the difference between [cell -f Bi] and 

 El, where Ei is the resistance of plus the connec- 

 tions in that arm. 



Various sources of alternating current were tried, 

 but none was wholly satisfactory. We had no source 

 of pure sine-waves at our disposal and some trouble 

 from harmonics was experienced. This was removed 

 by using a transformer and various combinations of \^ 

 capacities in the circuit. 



Theory of this Type of Bridge. 



Figure 3. Vari- 

 able mercury 

 resistance. 



6. The complete theory of this type of bridge may 

 be found in Ayres's paper [20], but our method of operation was neces- 

 sarily somewhat different from his because of the small magnitudes of 

 the resistances we had to measure. 



For the ideal condition of balance we have 



(1) r/E = a/h = C,/C 



where the bridge is non-inductive, the resistances of connections are 

 negligible, a and b are the bridge-wire readings, C2 is the capacity of 

 the " known " arm, C is the resultant of the capacity of the cell with 

 Ci, r is the resistance of the cell and its leads, and E is that of the op- 

 posite arm of the bridge. 



Taking into consideration the resistances of the various connections, 

 and that of the coil inserted in the cell arm, we have, for both bridges, 

 the following equations : 



(2) 



a _o -\- r + u 

 b" E+v ' 



