DIRECT CAPACITY MEASUREMENT 35 



capacity on the left of (C — C°) and (C" — C°), with equal decreases 

 on the right. Therefore 



Ci2 + Cu + {C - C°) = - (C - C°) + Cu 



Cu + (C- C°) = - (C- C°) + Cn + Ci, 



and adding gives the value of {Cu — Cn). 



(3) The condition of equal impedance ratios on the two sides, as 

 required for a balance, gives, for both the switches up and down, 



R' (Gi - Cn + C) ^ {S- R') Cn, 

 R" G, = {S- R") C, 



respectively, from which the expressions for C12 and Gi follow. 



(4) The Y of Fig. 4 has unusual properties because the total 

 conductance connecting the concealed branch-point of the Y to the 

 three bridge corners ^, ^, (? is zero. Thus the conductance between 

 any one corner and the remaining two corners joined together is infinite, 

 or in other words, the Y acts as a short circuit under all these three 

 conditions. On the other hand, if corner ^, ^, or (F is left floating 

 and ignored the conductance between the other two corners is 2/R, 

 1/2R or 2/R, respectively, and the Y is not a short circuit. These 

 statements are verified at once by applying the familiar expressions 

 for resistances in parallel and in series. 



On account of the unusual behavior of the Y, even when taken 

 alone, it is not immediately apparent how it will affect the operation 

 of the bridge of Fig. 4 with direct capacities between corners ^S^ 

 and S^C For this reason it is highly desirable to find an equivalent 

 network the behavior of which is more readily comprehended. It is 

 not feasible to employ the delta network which is equivalent to the 



Y for this has indeterminate characteristics, being made up of three 

 infinite conductances, only two of which have the same sign. We 

 may, however, make use of the Y which is equivalent to the original 



Y and direct capacities C^b and Cbc taken together. This is found as 

 follows: Any admittance delta may be replaced by a star having ad- 

 mittances equal to the sum of the products of the delta admittances 

 taken in pairs divided by the opposite delta admittance. Applied to the 

 delta of Fig. 1, we find that the star that is equivalent has the capacities 



r" — 



r" — 

 C24 — 



Cu Cn + G4 C12 



