DIRECT CAPACITY MEASUREMENT 37 



Yu = ^ 



1 



24 



F34 = — 7—, and by addition 



■tr ^PS Zp Z5 



{Zp + Zps) (Zs + Zps) Zps 



Substituting these values the expression for the actual ratio of the 

 bridge arms becomes 



Ki = ^. + Zps + {Zp Zs - Zls) Fi, 



^24 Zp -\- Zps + {Zp Zs — Zls) F23 



(5) When the bridge alone is balanced at readings Co and Co , 

 let CcD and Geo be the direct capacity between corners C and 2) and 

 the total direct capacity between these corners and ground. Since 

 GcD is balanced, the effective direct capacity between corners C, 2) 

 when earth is ignored, is by Fig. 1, {Ccd + G^cd/4)- Now connect the 

 three terminals 1, 2, 3, as shown with direct capacities C12, G\ — C\i, 

 Gi — C12; Gi, Gi being the grounded capacities of terminals 1 and 2. 

 The first balance with the reading C requires the equality of the 

 total capacity added on each side, i.e., 



G\ — Cn -\- {C — Co) = Gi — Cn ~ {C —Co) 

 or 



G2 - Gi = 2 (C - Co') 



For the second balance ground may again be considered an ignored 

 terminal, and since terminals 1 and 2 have been balanced to ground, 

 and their total direct capacity to ground is G12 = Gi -\- d — 2Ci2, 

 the effective direct capacity added to the bridge between corners 

 (? and 2)isCb= Cn + Gn/4:. Equating the added capacities on the 

 two sides of the bridge when balanced at the reading C", we obtain 

 G = 2 (C" - C). 



The direct capacity between (? and 2), when ground is considered 

 an accessible terminal, is assumed to be absolutely independent of 

 the setting of the condenser /. To actually meet this condition will 

 require some attention in the design of the variable condenser. 



(6) Here the bridge itself is supposed to have equal direct capaci- 

 ties from corners <?and ^to ground, while the added terminals 1 and 2 

 have different direct capacities to ground, the difference being 

 (Gi — G2), while the total direct capacity to ground is {Gn + Geo)- 

 Now two capacities in series may be replaced by their product divided 



