596 PROCEEDINGS OF THE AMERICAN ACADEMY. 



where u and v are the resistances of the connections on the cell side 

 and the R side respectively ; 



(3) R + w= (2^ = Q(O.OOl) = q, 



where w is the resistance of connection to the auxiliary bridge. Com- 

 bining (2) and (3) gives 



(4) + r — {q — w + v)j — u. 



Upon cutting out the cell and short circuiting that arm of the bridge, 

 we have 



(5) — \^Qi ^ — w -\- vY-rj — u = {(I — w ^ V) y — u. 



Subtracting (5) from (4) gives 



. - a( ,a'h\ , a f ah \ a fab \ 



(6) r = -^[q-t^.)+-^[^^,-l)w~-^^-^,-iy. 



During the first part of the investigation a lay between the limits 

 506 mm. and 507 mm., and during the second part between 481 mm. 

 and 486 mm. In most cases the difference between a and d^ was less 

 than 0.5 mm., and it was usually about 0.3 mm. 



In view of this, the terms containing w and v can at once be neg- 

 lected. The difference between q — q\ the value actually recorded as 



resistance, and {q — q') —r,, is {—p — 1) q', which does not exceed 



0.0005 ohm, since q' did not exceed 0.25 and the value of the parenthe- 

 sis was in no case greater than 0.002. 



The following observations are deemed interesting in connection 

 with the fact that the bridge reading was not the same with the cell in 

 as when the cell was out. 



1. The bridge reading with " cell in " a is smaller than a'. 



2. Both with " cell in " and "cell out," the insertion of a condenser 

 (5.2 MF) in parallel with the leads to the cell-switch causes an increase 

 in the value of a or a' as the case may be. 



3. Decreasing the frequency by 50% causes no change in a, but a' 

 is thereby decreased. 



4. A condenser in parallel with Cx causes a and a to decrease. 

 The last observation is to be expected from the theory of the bridge. 



It is hard to see how any capacity possessed by the cell could act so as 

 to make a smaller than a ; rather the opposite effect would be ex- 



